Science, Faculty of
DSpace
UBCV
Chinchani, Abhijit Mahesh
Doctor of Philosophy - PhD
University of British Columbia
In the age of big data and large neuroscience datasets, dimensionality reduction is employed to reduce the complexity of recorded data and explain it with fewer representative variables. Unlike unsupervised methods, which rely solely on the data's inherent structure, supervised techniques leverage additional information to achieve better feature extraction and data representation. In this dissertation, I present two applications of supervised techniques: one to identify cognitive correlates of psychiatric symptoms and the other to estimate latent EEG dimensions to study the effects of transcranial alternating current stimulation (tACS). First, I applied constrained principal component analysis to identify cognitive correlates of psychiatric symptoms in two datasets. In the first dataset, I examined the overlap between cognition and hallucinatory experiences and developed a set of reliability tests to minimize the reporting of spurious results due to overfitting. Next, I improved the reliability testing algorithm and used it to find links between cognition and symptoms in schizophrenia spectrum disorder in another dataset. This approach led to a nuanced and multimodal understanding of psychiatric symptoms. Next, I applied joint decorrelation, another supervised technique, to extract latent EEG oscillations corresponding to frequency-specific oscillations and to study whether tACS affects them. I first investigated the effects of tACS on auditory steady-state responses (ASSRs). Narrowband latent oscillations for ASSRs at 40Hz were extracted, but no effects of tACS on these evoked oscillations were observed. Subsequently, I examined the effects of tACS on broadband alpha oscillations. By extracting latent dimensions corresponding to alpha frequencies, I observed that tACS affected alpha oscillations in a task-specific manner. This adds a critical variable to be considered for applications of tACS, whereby increasing the electric field by placing the anode further away from the cathode has a cost of producing a less localized effect. However, my findings show that the effects of tACS can be localized by using specific tasks that engage the desired brain areas, enhancing the precision and effectiveness of the stimulation. These applications demonstrate the utility of supervised dimensionality reduction in neuropsychiatric research, providing deeper insights into cognitive correlates of psychiatric symptoms and the neural mechanisms underlying tACS.
SUPERVISED DIMENSIONALITY REDUCTION APPLICATIONS IN IDENTIFYING COGNITIVE CORRELATES OF PSYCHIATRIC SYMPTOMS AND EXTRACTING LOW-DIMENSIONAL EEG SIGNALS TO STUDY THE EFFECTS OF TACS by ABHIJIT MAHESH CHINCHANI B.E., P.E.S. Institute of Technology, 2017 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Bioinformatics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) September 2024 © Abhijit Mahesh Chinchani, 2024 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Supervised Dimensionality Reduction Applications in Identifying Cognitive Correlates of Psychiatric Symptoms and Extracting Low-dimensional EEG Signals to study the effects of tACS submitted by Abhijit Mahesh Chinchani in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Bioinformatics Examining Committee: Todd S. Woodward, Professor, Bioinformatics, UBC Supervisor Anthony Herdman, Associate Professor, Audiology and Speech Sciences, UBC Supervisory Committee Member Rebecca Todd, Associate Professor, Psychology, UBC Supervisory Committee Member Daniela J. Palombo, Associate Professor, Psychology, UBC University Examiner William Panenka, Associate Professor, Psychiatry, UBC University Examiner Oren Griffiths, Senior Lecturer, Psychological Sciences, Newcastle University External Examiner Additional Supervisory Committee Members: Lawrence Ward, Professor, Psychology, UBC Supervisory Committee Member Roger Tam, Associate Professor, Bioinformatics, UBC Supervisory Committee Member iii Abstract In the age of big data and large neuroscience datasets, dimensionality reduction is employed to reduce the complexity of recorded data and explain it with fewer representative variables. Unlike unsupervised methods, which rely solely on the data's inherent structure, supervised techniques leverage additional information to achieve better feature extraction and data representation. In this dissertation, I present two applications of supervised techniques: one to identify cognitive correlates of psychiatric symptoms and the other to estimate latent EEG dimensions to study the effects of transcranial alternating current stimulation (tACS). First, I applied constrained principal component analysis to identify cognitive correlates of psychiatric symptoms in two datasets. In the first dataset, I examined the overlap between cognition and hallucinatory experiences and developed a set of reliability tests to minimize the reporting of spurious results due to overfitting. Next, I improved the reliability testing algorithm and used it to find links between cognition and symptoms in schizophrenia spectrum disorder in another dataset. This approach led to a nuanced and multimodal understanding of psychiatric symptoms. Next, I applied joint decorrelation, another supervised technique, to extract latent EEG oscillations corresponding to frequency-specific oscillations and to study whether tACS affects them. I first investigated the effects of tACS on auditory steady-state responses (ASSRs). Narrowband latent oscillations for ASSRs at 40Hz were extracted, but no effects of tACS on these evoked oscillations were observed. Subsequently, I examined the effects of tACS on broadband alpha oscillations. By iv extracting latent dimensions corresponding to alpha frequencies, I observed that tACS affected alpha oscillations in a task-specific manner. This adds a critical variable to be considered for applications of tACS, whereby increasing the electric field by placing the anode further away from the cathode has a cost of producing a less localized effect. However, my findings show that the effects of tACS can be localized by using specific tasks that engage the desired brain areas, enhancing the precision and effectiveness of the stimulation. These applications demonstrate the utility of supervised dimensionality reduction in neuropsychiatric research, providing deeper insights into cognitive correlates of psychiatric symptoms and the neural mechanisms underlying tACS. v Lay Summary With the advancement of technology, neuroscience and psychiatric datasets have grown larger and more complex. I employed supervised dimensionality reduction techniques to tackle this complexity and enhance interpretability. In this dissertation, I used these methods to uncover subtle connections between cognition and psychiatric symptoms. Additionally, I applied these techniques to extract latent electroencephalography signals and investigate under what conditions can they be modulated with electrical stimulation. Looking ahead, my objective is to combine insights from both areas to develop neuromodulation-based interventions targeting the improvement of cognitive deficits and psychiatric symptoms in individuals with mental illnesses. vi Preface This dissertation is the original intellectual product of the author, Abhijit Mahesh Chinchani. The analyses reported in this dissertation comprise secondary use of data from previously completed studies as well as new data collected for this work. All data collection carried out at the University of British Columbia (UBC) was approved by the UBC Clinical Research Ethics Board (ID: H20-02378). The work reported in chapter 3 is published in Cortex: Chinchani, A. M., Menon, M., Roes, M., Hwang, H., Allen, P., Bell, V., ... & Woodward, T. S. (2021). Item-specific overlap between hallucinatory experiences and cognition in the general population: A three-step multivariate analysis of international multi-site data. cortex, 145, 131-144, Copyright Elsevier. The material has been reused with permission from Elsevier. Some revisions have been made for coherence with the rest of this dissertation. These data were collected as part of a larger multi-site study (Moseley et al., 2021) from 11 data collection sites: Durham University, University of Roehampton, King’s College London, University College London, University of Cambridge (all UK), University Paul Valéry (France), University of Groningen (Netherlands), Charles University (Czech Republic), University of Bergen (Norway), University of British Columbia (Canada), and Swinburne University (Australia). All sites obtained ethical clearance from their relevant institutional review board, in accordance with the Declaration of Helsinki. The data is publicly available at https://osf.io/eqy76/. I developed and implemented the 3-step CPCA method used in this chapter under the supervision of Dr. Todd S. Woodward. I also analyzed the data and took the lead in writing the manuscript. Mahesh Menon, Meighen Roes, and Heungsun Hwang were vii involved in developing 3-step CPCA and editing the manuscript. Paul Allen, Vaughan Bell, Josef Bless, Catherine Bortolon, Matteo Cella, Charles Fernyhough, Jane Garrison, Eva Kozáková, Frank Laroi, Jamie Moffatt, Nicolas Say, Mimi Suzuki, Wei Lin Toh, Yuliya Zaytseva, and Susan L. Rossell were involved in collecting data at their respective sites and editing the manuscript. Peter Moseley conceptualized the original multi-site study and was also involved in data collection and editing the manuscript. Todd S. Woodward conceptualized the current project and was also involved in data collection and writing the manuscript. The work reported in chapter 4 is published in Schizophrenia Research with some changes to the analysis: Skiba, R. M.*, Chinchani, A. M.*, Menon, M., Lepage, M., Lavigne, K. M., Malla, A., ... & Woodward, T. S. (2024). Overlap between individual differences in cognition and symptoms of schizophrenia. Schizophrenia research, 270, 220-228, Copyright Elsevier. The material has been reused with permission from Elsevier. The analysis presented in this dissertation is publicly available as a preprint on PsyArXiV: Skiba, R. M.*, Chinchani, A. M.*, Menon, M., Lepage, M., Lavigne, K., Malla, A., ... & Woodward, T. (2023). Overlap between individual differences in cognition and all SANS and SAPS symptoms of schizophrenia (* These authors contributed equally). Some revisions have been made for coherence with the rest of this dissertation. These data were collected at the Prevention and Early Intervention Program for Psychoses (PEPP-Montreal) in Montreal, Canada. The Research Ethics Boards of the Douglas Mental Health University Institute and the McGill University Faculty of Medicine approved the research protocols. I developed the iterative CPCA method used in this chapter under the supervision of Dr. Todd Woodward. Rafal Skiba took the primary role of analyzing the data and writing the paper, and in this I was also intensively involved. Since I took the lead on the development of the viii statistical method of iterative CPCA, and Rafal Skiba took the lead in analyzing the data and writing the paper, we shared first authorship, and authorship order was determined by a coin flip. Mahesh Menon, Martin Lepage, Ashok Malla were involved in conceptualization, collecting data, and editing the manuscript. Katie M. Lavigne and Ridha Joober were involved in collecting data. Joel O. Goldberg, R. Walter Heinrichs, David J. Castle, Amy Burns, Michael W. Best, and Susan L. Rossell all contributed to collecting data and manuscript editing. Sebastian Walther was involved in investigation, drafting, and editing. Todd S. Woodward provided supervision and guidance, along with contributing to methodology, investigation, conceptualization, and both drafting and reviewing the manuscript. The data used in chapter 5 was collected at the Cognitive Neuroscience of Schizophrenia Lab at UBC, under the supervision of Dr. Todd Woodward and Dr. Christine Tipper (Ethics ID: H20-02378). The experiment was conceptualized and implemented by Ella Weik and data collected was performed by Jessica Khangura and John Krotez. I took the lead role in analyzing the data and writing up the results. The data used in chapter 6 was collected at the Cognitive Neuroscience of Schizophrenia Lab at UBC, under the supervision of Dr. Todd Woodward (Ethics ID: H20-02378). I was involved in the conceptualization and implementation of the experiment along with by Rafal Skiba. I was involved in collecting the data along with Rafal Skiba, Yvette Ni, Sage Radlmeier, Dan Vuong, Yudan Chen, Jessica Khangura, and Crystal Han. I took the lead role analyzing the data and writing up the results. ix Table of Contents Abstract ........................................................................................................................................ iii Lay Summary ................................................................................................................................. v Preface ........................................................................................................................................... vi Table of Contents .......................................................................................................................... ix List of Tables .............................................................................................................................. xiii List of Figures ............................................................................................................................. xiv List of Abbreviations ................................................................................................................... xv Acknowledgements .................................................................................................................... xvii Chapter 1: Introduction ................................................................................................................ 1 1.1 Finding cognitive correlates of psychiatric symptoms .................................................... 4 1.1.1 Prevalence of summary scores ................................................................................ 4 1.1.2 Use of supervised dimensionality reduction methods to look at individual items .. 6 1.2 Estimating latent EEG components to study the effects of tACS ................................... 7 1.2.1 Dimensionality reduction for EEG data .................................................................. 7 1.2.2 Neuromodulation ..................................................................................................... 9 1.2.2.1 tACS .................................................................................................................... 9 1.2.2.2 Mechanisms of tACS ......................................................................................... 13 1.2.2.2.1 Online tACS ................................................................................................ 13 1.2.2.2.2 Long-term effects of TACS ......................................................................... 19 Chapter 2: Supervised Dimensionality Reduction Methods .................................................... 22 2.1 Constrained principal component analysis (CPCA) ...................................................... 22 2.2 Joint decorrelation (JD) ................................................................................................. 23 Chapter 3: Item-specific overlap between hallucinatory experiences and cognition in the general population: A three-step multivariate analysis of international multi-site data. (Study 1) ........................................................................................................................................ 26 3.1 Introduction ................................................................................................................... 26 3.2 Methods ......................................................................................................................... 31 3.2.1 Participants ............................................................................................................ 31 3.2.2 Questionnaires ....................................................................................................... 32 3.2.2.1 Cardiff Anomalous Perceptions Scale (CAPS) ................................................. 32 3.2.2.2 Launay-Slade Hallucination Scale - Extended (LSHS-E). ................................ 32 3.2.3 Cognitive Measures ............................................................................................... 33 3.2.3.1 Source monitoring task (SM) ............................................................................ 33 3.2.3.2 Consonant-vowel dichotic listening (DL). ........................................................ 34 3.2.3.3 Auditory signal detection (SgD). ....................................................................... 35 3.2.3.4 Matrix reasoning (MR). ..................................................................................... 36 3.2.3.5 Backwards Digit Span (DS). ............................................................................. 37 x 3.2.4 Data Analysis ......................................................................................................... 37 3.2.4.1 Constrained Principal Component Analysis (CPCA) ........................................ 37 3.2.4.1.1 Step-1: Variance Constraints and Dimension Reduction through Constrained Principal Component Analysis (CPCA) .................................................... 38 3.2.4.1.2 Step-2: Identifying Reliable Predictor Loadings (HEs) .............................. 42 3.2.4.1.3 Step 3: Identifying Criterion Variables for Interpretation (Cognition) ....... 46 3.2.4.2 Rationale for Thresholds ................................................................................... 50 3.2.4.2.1 Component loading match correlation threshold (0.64) .............................. 50 3.2.4.2.2 Component reliability proportion threshold (0.50) ...................................... 50 3.2.4.2.3 Predictor loading match correlation threshold (0.19) .................................. 50 3.2.4.2.4 Predictor loading reliability proportion threshold (0.48) ............................. 51 3.3 Results ........................................................................................................................... 52 3.3.1 Step 1: Variance Constraints and Dimension Reduction through Constrained Principal Component Analysis (CPCA) ................................................................................ 52 3.3.2 Step 2: Identifying Reliable Predictor Loadings (HEs) ......................................... 52 3.3.3 Step 3: Identifying Criterion Variables for Interpretation (Cognition) ................. 58 3.3.4 Component Interpretation ...................................................................................... 61 3.4 Discussion ...................................................................................................................... 63 3.4.1 Limitations ............................................................................................................. 69 Chapter 4: Overlap between individual differences in cognition and symptoms of schizophrenia (Study 2) ............................................................................................................... 71 4.1 Introduction ................................................................................................................... 72 4.2 Methods ......................................................................................................................... 75 4.2.1 Participants ............................................................................................................ 75 4.2.2 Cognitive measures ................................................................................................ 76 4.2.3 Symptom rating scales ........................................................................................... 78 4.2.4 Data analysis .......................................................................................................... 79 4.2.4.1 Need for reliability testing in CPCA ................................................................. 79 4.2.4.2 Combining results from different iterations ...................................................... 80 4.2.4.3 iCPCA in detail .................................................................................................. 81 4.2.4.4 Significance test and optimization of the hyperparameter (r) ........................... 85 4.2.4.5 iCPCA interpretation ......................................................................................... 87 4.2.4.6 Identifying the dominant component loadings .................................................. 88 4.3 Results ........................................................................................................................... 89 4.3.1 iCPCA results ........................................................................................................ 89 4.3.2 Relationship of iCPCA components to other measures ......................................... 97 4.4 Discussion ...................................................................................................................... 98 Chapter 5: Computing narrow-band EEG latent dimensions to study the effects of tACS (Study 3) ...................................................................................................................................... 104 xi 5.1 Introduction ................................................................................................................. 105 5.2 Methods ....................................................................................................................... 107 5.2.1 Participants .......................................................................................................... 107 5.2.2 Experiment paradigm .......................................................................................... 108 5.2.2.1 Experimental setup .......................................................................................... 108 5.2.2.2 Study design .................................................................................................... 108 5.2.2.3 Participant groups ............................................................................................ 109 5.2.2.4 EEG recording and tACS ................................................................................ 110 5.2.3 Data analysis ........................................................................................................ 111 5.2.3.1 EEG preprocessing .......................................................................................... 111 5.2.3.2 Joint decorrelation (JD) analysis ..................................................................... 112 5.3 Results ......................................................................................................................... 113 5.3.1 JD ASSR components ......................................................................................... 114 5.3.2 Comparison between JD and PCA components .................................................. 116 5.3.3 tACS has no effect on ASSR signal .................................................................... 119 5.3.4 Conventional electrode-level analysis ................................................................. 120 5.4 Discussion .................................................................................................................... 121 Chapter 6: Computing broad-band EEG latent dimensions to study the effects of tACS (Study 4) ...................................................................................................................................... 125 6.1 Introduction ................................................................................................................. 126 6.2 Methods ....................................................................................................................... 128 6.2.1 Participants .......................................................................................................... 128 6.2.2 Experimental paradigm ........................................................................................ 129 6.2.2.1 Experimental setup .......................................................................................... 129 6.2.2.2 Study design .................................................................................................... 129 6.2.2.3 Behavioral Task ............................................................................................... 130 6.2.2.4 Participant Groups ........................................................................................... 131 6.2.2.5 EEG recording and tACS ................................................................................ 132 6.2.3 Data analysis ........................................................................................................ 134 6.2.3.1 EEG preprocessing .......................................................................................... 134 6.2.3.2 Region of interest (ROI) analysis .................................................................... 135 6.2.3.3 Joint decorrelation analysis ............................................................................. 135 6.3 Results ......................................................................................................................... 136 6.3.1 Behavioral effects of tACS .................................................................................. 136 6.3.2 Electrophysiological effects of tACS .................................................................. 138 6.3.2.1 ROI analysis .................................................................................................... 139 6.3.2.1.1 tACS does not affect alpha power in medial electrodes ............................ 139 6.3.2.1.2 tACS affects alpha power in lateral electrodes .......................................... 141 6.3.2.1.3 Control experiment .................................................................................... 142 xii 6.3.2.2 Joint decorrelation (JD) analysis ..................................................................... 145 6.3.2.2.1 JD alpha components ................................................................................. 145 6.3.2.2.2 JD alpha components have better SNR than PCA ..................................... 147 6.3.2.2.3 tACS does not affect the medial JD component ........................................ 149 6.3.2.2.4 tACS affects alpha power in lateral JD components ................................. 151 6.3.2.2.5 Control experiment .................................................................................... 153 6.4 Discussion .................................................................................................................... 155 Chapter 7: Conclusion ............................................................................................................... 158 7.1 Comparisons between CPCA and JD .......................................................................... 158 7.2 Findings from identifying cognitive correlates of psychiatric symptoms ................... 160 7.2.1 Implications ......................................................................................................... 161 7.2.2 Limitations ........................................................................................................... 162 7.2.3 Future directions .................................................................................................. 163 7.3 Findings from neuromodulation studies ...................................................................... 164 7.3.1 Implications ......................................................................................................... 166 7.3.2 Limitations ........................................................................................................... 167 7.3.3 Future directions .................................................................................................. 167 7.4 Conclusion ................................................................................................................... 168 Bibliography ............................................................................................................................... 169 Appendices ................................................................................................................................. 213 Appendix A .............................................................................................................................. 213 Appendix B .............................................................................................................................. 226 xiii List of Tables Table 1.1. Summary of mechanisms for online tACS ................................................................... 19 Table 3.1. Component loadings for the predicted (GC) solution. ................................................. 53 Table 3.2. Predictor loadings for the predicted (GC) solution. ..................................................... 54 Table 3.3. Summary of component characteristics and interpretations. ........................................ 57 Table 4.1. Measures of cognition included in the current analysis. .............................................. 77 Table 4.2. Symptom rating scales summary and total scores of SANS and SAPS for current sample (n=206). ............................................................................................................................. 79 Table 4.3. Component loadings for the predicted solution. ........................................................... 92 Table 4.4. Mean predictor loadings for SANS .............................................................................. 93 Table 4.5. Mean predictor loadings for SAPS ............................................................................... 94 Table 4.6. Descriptive of education, age, and IQ measures. Correlations between education years, age of participants, IQ measures, and CPCA components. ........................................................... 98 xiv List of Figures Figure 3.1. Schematic depicting the steps involved in Step-1: Variance Constraints and Dimension Reduction through CPCA. .......................................................................................... 41 Figure 3.2. Scree plot for CPCA. ................................................................................................... 42 Figure 3.3 Schematic depicting the steps involved in Step 2: Identifying Reliable Predictor Loadings (HEs). ............................................................................................................................. 45 Figure 3.4. Schematic depicting the steps involved in Step 3: Identify Criterion Variables for Interpretation (Cognition). ............................................................................................................. 49 Figure 3.5. Selection of criterion variables. ................................................................................... 60 Figure 3.6. Dominant component and predictor loadings. ............................................................ 63 Figure 4.1. Diagram explaining steps involved in iCPCA. ........................................................... 84 Figure 4.2. Optimization of the hyperparameter (r) ...................................................................... 87 Figure 4.3. Summary of iCPCA results ......................................................................................... 96 Figure 4.4. Selection of criterion variables .................................................................................... 97 Figure 5.1. Block diagram depicting the study design. ............................................................... 109 Figure 5.2. Electrode montage for tACS and simulated electric fields ....................................... 111 Figure 5.3. JD Scree plot ............................................................................................................. 115 Figure 5.4. JD components .......................................................................................................... 116 Figure 5.5. PCA components ....................................................................................................... 117 Figure 5.6. SNR comparison between PCA and JD .................................................................... 118 Figure 5.7. Effects of tACS on ASSR ......................................................................................... 119 Figure 5.8. Electrode level analysis ............................................................................................. 121 Figure 6.1. Block diagram depicting the study design. ............................................................... 130 Figure 6.2. Task paradigm ........................................................................................................... 131 Figure 6.3. Schematic depicting participant groups .................................................................... 132 Figure 6.4. Electrode montage for tACS and simulated electric fields ....................................... 133 Figure 6.5. Effects of tACS on medial electrodes ....................................................................... 140 Figure 6.6. Effects of tACS on lateral electrodes ........................................................................ 142 Figure 6.7. Group effects for ROI analysis ................................................................................. 144 Figure 6.8. JD Scree plot ............................................................................................................. 146 Figure 6.9. JD components .......................................................................................................... 147 Figure 6.10. PCA components ..................................................................................................... 148 Figure 6.11. SNR comparison between PCA and JD .................................................................. 149 Figure 6.12. Effects of tACS on medial JD component .............................................................. 150 Figure 6.13. Effects of tACS on lateral JD components ............................................................. 152 Figure 6.14. Group effects for JD analysis .................................................................................. 154 xv List of Abbreviations AC – Alternating Current ASSR – Auditory Steady State Response BOLD – Blood-Oxygen-Level-Dependent CA1 – Cornu Ammonis 1 CAPS – Cardiff Anomalous Perceptions Scale CCA – Canonical Correlation Analysis CL – Component Loading CPCA – Constrained Principal Component Analysis CRP – Component Reliability Proportion DES – Dissociative Experiences Scale DL – Dichotic Listening DSM – Diagnostic and Statistical Manual of Mental Disorders DS – Digit Span DSS – Denoising Source Separation EEG – Electroencephalography EGI GTEN – Electrical Geodesics Inc. Geodesic Transcranial Electrical Neuromodulation FASTER – Fully Automated Statistical Thresholding for EEG Artifact Rejection fMRI – Functional Magnetic Resonance Imaging FDR – False Discovery Rate FSS – Fatigue Severity Scale HE – Hallucinatory Experience ICA – Independent Component Analysis iCPCA – Iterative Constrained Principal Component Analysis JD – Joint Decorrelation LDA – Linear Discriminant Analysis LED – Light Emitting Diode LFP – Local Field Potential LTD – Long-Term Depression LTP – Long-Term Potentiation LSHS-E – Launay-Slade Hallucination Scale-Extended MCCB - MATRICS Consensus Cognitive Battery MR – Matrix Reasoning MRI – Magnetic Resonance Imaging NMDA – N-Methyl-D-Aspartate OCD – Obsessive Compulsive Disorder PANSS – Positive and Negative Syndrome Scale xvi PCA – Principal Component Analysis PL – Predictor Loading PLRP – Predictor Loading Reliability Proportion PNS – Persistent Negative Symptoms RB Matrix – Reliability Binary Matrix ROAST – Realistic vOlumetric Approach to Simulate Transcranial electric stimulation rTMS – Repetitive Transcranial Magnetic Stimulation SANS – Scale for the Assessment of Negative Symptoms SAPS – Scale for the Assessment of Positive Symptoms SEM – Structural Equation Modeling SgD – Signal Detection SNR – Signal to Noise Ratio SM – Source Monitoring SSD – Schizophrenia Spectrum Disorder STDP – Spike-Timing-Dependent Plasticity TAS – Tellegen Absorption Scale tACS – Transcranial Alternating Current Stimulation tDCS – Transcranial Direct Current Stimulation TMS – Transcranial Magnetic Stimulation TMT-A – Trail Making Test Part A TMT-B – Trail Making Test Part B YBOCS – Yale-Brown Obsessive-Compulsive Scale xvii Acknowledgements Firstly, I am deeply grateful to my parents, Rohini and Mahesh Chinchani, for their unwavering support and belief in me. I also extend my heartfelt thanks to my brother, Abhishek, and all other family members for their constant support and encouragement. Additionally, I express sincere appreciation to my friends for their invaluable support throughout my PhD. I would like to acknowledge that I work at UBC, located on the traditional, ancestral, and unceded territory of the Musqueam people. I extend my profound gratitude to my supervisor and mentor, Dr. Todd Woodward, for his continuous guidance, insightful advice, and the numerous opportunities he has provided me over the years. I am equally thankful to Dr. Christine Tipper for her invaluable counsel and support. I would like to thank all the past and present members of the Cognitive Neuroscience of Schizophrenia (CNOS) Lab, including but not limited to Chantal Percival, Jessica Khangura, Linda Chen, Dr. Walter Sena, Dr. Rafal Skiba, Ava Momeni, Maiya Rasheed, and John Shahki, whose contributions and friendship have been instrumental in my research journey. Special thanks go to Ella Weik, Jessica Khangura, and John Krotez for generously sharing their hearing brain data, and to Dr. Rafal Skiba for his indispensable role in the EEG-tACS experiments. I am also grateful to all the research assistants and volunteers who diligently collected data for the EEG-tACS experiment, including but not limited to Yvette Ni, Sage Radlmeier, Dan Vuong, Yudan Chen, Jessica Khangura, and Crystal Han. I extend my appreciation to my supervisory committee members, Dr. Rebecca Todd, Dr. Lawrence Ward, Dr. Anthony Herdman, and Dr. Roger Tam, for their invaluable feedback throughout my xviii doctoral studies. Special thanks to Dr. Tim Murphy and Jeffrey LeDue for welcoming me into the Brain Circuits Cluster and providing me with the opportunity to serve as a neurodata tutor. Lastly, I would like to acknowledge the generous support of funding agencies that made my research possible. I am grateful to MITACS for the opportunity to intern at UBC and collaborate with Todd, as well as for the MITACS graduate fellowship. Additional thanks to CONP, BC Children’s Hospital Research, Brain Behaviour and Development Cluster for Graduate Studentship and Trainee Boost Awards, Benjamin Feldman and Family, Bert Bauman Parkinson's Disease Research Fund, and Brain Circuits Cluster for their financial support throughout my academic journey. 1 Chapter 1: Introduction In life sciences, there have been rapid advancements in biosensor technologies, leading to the generation of enormous amounts of data across many domains. This includes biological data like microelectrode arrays for high-density neural recordings (Em et al., 2023; Jun et al., 2017), high-throughput genomics data (Churko et al., 2013; T. M. Porter & Hajibabaei, 2018), and a wide variety of imaging data like MRI, fluorescence, confocal imaging, and other techniques (Avdievich et al., 2009; Elliott, 2020; C. Li et al., 2020). Moreover, there has also been a rise in the collection of behavioral data such as psychophysics experiments (Lago, 2021; Semmelmann & Weigelt, 2017), wearable sensors that monitor physiological metrics like heart rate and activity levels (Lu et al., 2020; Ometov et al., 2021), questionnaire data collected by mobile applications for mental health assessments (Arrow et al., 2023; Martin-Key et al., 2022; Mirea et al., 2021), and other data collected over the internet like browsing history, search queries, and social media activity. An excellent example of this data explosion is the Neuralink Compression Challenge, where Elon Musk’s company issued an open challenge to achieve lossless 200x compression of neural data obtained from 1,024 electrodes at 20kHz. The availability of all this data presents researchers with opportunities to uncover connections between these various data types. One of the main trends in these data is their high-dimensional nature. High-dimensional data is one where the number of features is similar to or greater than the number of observed samples (Bühlmann & Geer, 2011; Wright & Ma, 2022). For example, MRI data from millions of voxels or electroencephalogram data from hundreds of electrodes is higher than the number of 2 participants. The high-dimensional data are often sparse or highly intercorrelated. This suggests that there exists a low-dimensional latent structure underlying the high-dimensional observed data (Cohen et al., 2017; Nagle et al., 2023; Sanchez-Bornot et al., 2021). This has necessitated developing various statistical techniques to extract the latent structure from the high-dimensional data. These dimensionality reduction techniques are used to reduce the complexity of the recorded data by representing it with fewer low-dimensional variables. They can be broadly divided into two categories. The first category aims to uncover the inherent structure of the data and is termed unsupervised dimensionality reduction techniques. Popular examples of unsupervised techniques include principal component analysis (PCA), independent component analysis (ICA), clustering, and manifold-based methods (Dash et al., 1997; J. A. Lee & Verleysen, 2010). The second category uses additional information to extract more relevant latent structures in the data, as opposed to the most dominant inherent structures. Examples include Fisher’s linear discriminant analysis (LDA), logistic regression, constrained principal component analysis (CPCA), joint decorrelation, and various machine learning methods (Chao et al., 2019; de Cheveigné & Parra, 2014; Takane & Hunter, 2001). Supervised dimensionality reduction techniques are better suited for applications where the signal in the relevant latent dimensions is smaller than the inherent structure of the data. A good example illustrating this is extracting task-based networks from functional MRI (fMRI) data. The variance in the blood-oxygen-level-dependent (BOLD) signal due to task is much smaller (< 20%) than the 3 resting state BOLD signal (Zurrin et al., 2024). Thus, using an unsupervised technique like PCA will extract networks similar to resting state networks. However, to estimate task-based networks, one must use supervised techniques that utilize task timing information to isolate task-specific variance, enabling the detection of task-based networks distinct from resting state networks (Metzak et al., 2011; Sanford et al., 2020). Similarly, in electroencephalography (EEG), supervised techniques use task timing (e.g., averaging across trials) to extract event-related potentials (Ahi et al., 2009; Nidal & Malik, 2014). The concern with supervised techniques is that they may overfit the data under some circumstances and generate false positives. Redundancy in the data may lead supervised techniques to capture spurious correlations, resulting in instability in the extracted latent dimensions, negatively impacting the generalizability of the results (Keogh & Mueen, 2017). Therefore, validating the results of supervised techniques is essential, especially when using complex non-linear machine learning methods. Moreover, more complex methods like deep learning generate results that are not readily interpretable (Barbierato & Gatti, 2024). In this dissertation, I focus on simple linear supervised dimensionality reduction techniques that generate results which facilitate interpretation. I present two applications of supervised dimensionality reduction techniques: first, to identify cognitive correlates of psychiatric symptoms, and second, to estimate latent EEG dimensions to study the effects of transcranial alternating current stimulation (tACS). Advantages and disadvantages of both techniques are discussed and compared and contrasted in Conclusion chapter. 4 1.1 Finding cognitive correlates of psychiatric symptoms Clinicians and researchers use assessment questionnaires (self-report and/or interview/observation) to qualify and quantify symptoms for diagnosing psychiatric disorders (Andreasen, 1984, 1989; Bell et al., 2006; Carleton et al., 2010; Jamieson, 2005). These assessments provide a systematic way to measure and quantify a person’s subjective experiences and behaviors (Jaspers, 1968; Krueger & Markon, 2006; Stanghellini, 2009). There have been attempts to bridge the gap between psychopathology and neurobiology, but this has proven challenging (Musalek et al., 2010; Schultze-Lutter et al., 2018). An intermediate approach involves using cognitive science to find links to both neurobiology and psychopathology (Ren, 2019; Zhou et al., 2023). The research involving studying neurobiological correlates for cognition can be found elsewhere (Nani et al., 2019; Ofen, 2012; Platt, 2002). Here, I focus on finding cognitive correlates of psychopathology as assessed by symptom questionnaires. 1.1.1 Prevalence of summary scores The Diagnostic and Statistical Manual of Mental Disorders (DSM) has been the standard for diagnosing mental illnesses for decades (Diagnostic and Statistical Manual of Mental Disorders, 2013). One of the main assumptions of the DSM is that mental disorders are categorical. However, patients within most of these categories display heterogeneous symptoms. Moreover, there are many symptom similarities between patients in different categories (Musalek et al., 2010; Schultze-Lutter et al., 2018). This has led researchers aiming to find cognitive and physiological correlates of psychopathology to focus more on symptoms. 5 When studying the links between symptom questionnaire items and cognitive/physiological measures, summary or aggregate scores of questionnaire items are typically used. For example, Mosely et al. used the sum of 32 questionnaire items from the Cardiff anomalous perceptions scale (CAPS) and 16 items from the Launay-Slade hallucination scale-extended (LSHS-E) to obtain summary scores related to hallucinatory items (Moseley et al., 2021). Okutucu, et al. used a summary of Yale-Brown obsessive-compulsive scale (YBOCS) questionnaire items to find cognitive and metabolic correlates of obsessive compulsive disorder (OCD) (Okutucu et al., 2023). Similarly, many studies reduce the diverse set of symptoms to a single summary score while finding cognitive and physiological correlates (Cadenas et al., 2020; Dijkstra et al., 2021). Such an approach misses uncovering nuanced relationships between symptoms and cognition. Thus, to find more nuanced relationships between symptoms and cognition, many studies opted to use factor scores (Bagney et al., 2015; Lepage et al., 2021; Ventura et al., 2010). Instead of using just one aggregated score of the entire set of questionnaires, researchers used multiple factor scores that were summary scores of smaller sets of items. For example, Bagney et al. used a positive and negative syndrome scale (PANSS) 5-factor model score and divided the 30-item PANSS questionnaire into 5 factors: positive, negative, disorganized/concrete, excited, and depressed, and correlated them with cognitive measures (Bagney et al., 2015). Although such an approach provides a more nuanced understanding of the relationship between cognition and symptoms, the use of pre-defined factors is suboptimal while correlating with cognition. This is because the factors are obtained using unsupervised dimensionality reduction techniques such as PCA or factor analysis, which find inherent patterns in the questionnaire data without taking into account the 6 cognitive measures. Thus, they are not the most relevant factors that link with cognitive measures. To find these “relevant” factors, one needs to use supervised dimensionality reduction approaches to find optimal factors that correlate with cognition. One reason for using aggregated scores or pre-defined factor scores is the concern regarding Type I errors associated with the assessment of multiple tests of statistical significance if carried out on each variable individually. This approach results in the neglect of the more specific information offered by individual items, leading to Type II errors. Although such neglect is acceptable for small datasets, it is not necessary when using large datasets. In this regard, we focus on using supervised dimensionality reduction methods to find links at the level of individual items. 1.1.2 Use of supervised dimensionality reduction methods to look at individual items In recent years, with the move towards large datasets and data-driven approaches, studies have increasingly employed supervised dimensionality reduction methods to find links between individual items in two or more sets of variables, not necessarily limited to psychiatric symptoms and cognitive measures. Some commonly used supervised techniques include canonical correlation analysis (CCA), partial least squares (PLS), and machine learning approaches such as random forests. For example, Zhuang et al. used CCA to find links between psychiatric symptoms and cognitive measures in clinical high-risk patients for psychosis (Zhuang et al., 2020). Lee et al. used random forest and the Boruta feature selection method to identify which individual items of the Fatigue Severity Scale (FSS) were predictive of clinically significant fatigue in Parkinson’s Disease patients (D. G. Lee et al., 2021). Recently, a review (S. Vieira et al., 2024) found that as 7 many as 39 studies used various techniques (mostly CCA and PLS) to link neuroimaging features with symptoms in psychiatric groups such as attention deficit hyperactivity disorder, autism spectrum disorders, major depressive disorder, and psychosis spectrum disorders. Here, I used a novel approach called constrained PCA to find links between symptoms and cognition at the level of individual items. 1.2 Estimating latent EEG components to study the effects of tACS 1.2.1 Dimensionality reduction for EEG data EEG records electrical activity from the scalp using many electrodes, and in high-density configurations, this can range from 100 to 300 electrodes. EEG provides excellent temporal resolution at the scale of less than a millisecond. However, it offers poor spatial resolution, which leads to significant spatial redundancy in the data (Burle et al., 2015). Specifically, the EEG activity in one electrode is highly correlated with the activity in neighboring electrodes. This redundancy necessitates the use of dimensionality reduction techniques to analyze EEG data effectively. One of the most common ways to reduce dimensionality is by selecting regions of interest (ROIs) and performing analyses by averaging the activity of all the electrodes within each region. Usually, ROIs are selected based on literature. This approach has been widely used to analyze EEG data. For instance, one study divided the electrodes into lateralized frontal, fronto-central, parieto-central, and parieto-occipital regions to study the effects of various oscillations like theta and alpha while participants performed arithmetic tasks (Brunner et al., 2021). Similar ROIs have been used 8 in many studies to focus on specific brain areas relevant to the cognitive or behavioral task being investigated (Lomelin-Ibarra et al., 2022; Mitchell et al., 2015). Another approach is to use data-driven dimensionality reduction techniques. One of the main applications of data-driven dimensionality reduction in EEG data is the use of independent component analysis (ICA). ICA is commonly used in the preprocessing step to extract latent dimensions or components of EEG. More specifically, ICA is used to extract components corresponding to EEG artifacts such as eye blinks, eye movements, and muscle artifacts (Pion-Tonachini et al., 2019). Furthermore, ICA components are also used to study the role of different brain oscillations within each component. A special method known as Fourier ICA extracts independent components that have different dominant frequencies (A. Hyvärinen et al., 2010). Many studies also employ other unsupervised approaches such as principal component analysis (PCA), clustering, and manifold-based methods to reduce the dimensionality of EEG data. These techniques help in identifying patterns and structures intrinsic in the high-dimensional data. There is also a set of studies that use supervised dimensionality reduction techniques such as partial least squares (PLS) and joint decorrelation to extract relevant EEG components. These methods leverage labeled data to focus on the most informative features such as task-timing related to specific experimental conditions or oscillations in a specific frequency bands (de Cheveigné & Parra, 2014). 9 1.2.2 Neuromodulation Neuromodulation involves using external electromagnetic stimuli in an attempt to modulate ongoing brain oscillations in a controlled fashion. In recent years, low-intensity non-invasive neuromodulation techniques have been promoted in clinical research as novel treatments for the rehabilitation of various neurological and psychiatric disorders (Berryhill & Martin, 2018; Elyamany et al., 2021; Lefaucheur & Wendling, 2019; Lisanby et al., 2002; Tremblay et al., 2019). However, using electric currents to treat mental illness is not new. Since the 1930s, electroconvulsive therapy (ECT) has been used to treat psychiatric disorders such as depression, bipolar disorder, and schizophrenia (Gazdag & Ungvari, 2019; Kellner et al., 2020; M. Li et al., 2020). During ECT, high currents of up to 50mA are used to induce seizures which have been shown to alleviate symptoms of severe depression and schizophrenia (M. Li et al., 2020; Sanghani et al., 2018). However, such a high intensity technique may have transient cognitive side effects such as difficulty in learning and memory loss (Kellner et al., 2020; R. J. Porter et al., 2020; Robertson & Pryor, 2006). There is also some evidence for permanent memory loss (MacQueen et al., 2007; Verwijk et al., 2017). This paved the way for experiments testing the potential of low-intensity stimulation to affect physiological and behavioral changes but avoiding the side effects of ECT. 1.2.2.1 tACS Transcranial alternating current stimulation (tACS) is one such low-intensity, non-invasive neuromodulation technique. It delivers low intensity alternating currents, at a frequency, through scalp electrodes, producing weak electrical fields in the brain, with the aim of augmenting ongoing 10 neural activity, and ultimately affecting behavior. Other non-invasive transcranial electrical stimulation techniques include transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS). tDCS delivers direct current to either depolarize or hyperpolarize the neurons, leading to either an increase or decrease cortical excitability, respectively (Yamada & Sumiyoshi, 2021). tRNS delivers current that is derived from a white noise source, such an oscillation will have equal power in all frequencies (Potok et al., 2022). A study compared the efficacy of tACS, tDCS, and tRNS in increasing cortical excitability in the motor cortex and found that tRNS and tACS significantly increased excitability but not tDCS (Inukai et al., 2016). Another popular non-invasive technique is transcranial magnetic stimulation (TMS). It delivers magnetic pulses to induce spiking of neurons in a spatially focused manner (Terao & Ugawa, 2002). Among all the techniques, tACS provides a unique opportunity to modulate brain oscillations in a frequency specific manner. Repetitive TMS (rTMS) can also be used to affect brain oscillations, it involves delivering brief TMS bursts in a repetitive manner with the aim of modulating brain oscillations at the stimulation frequency (Soundara Rajan et al., 2017). However, rTMS affects a wide range of frequencies apart from the stimulating frequency, whereas tACS mostly modulates oscillations at the stimulation frequency (Herrmann et al., 2013). A number of studies have suggested that tACS can modulate cognitive processes such as perception (Feurra, Paulus, et al., 2011; Strüber et al., 2014), attention (Deng et al., 2019; Hopfinger et al., 2017), working memory (Pahor & Jaušovec, 2018; Reinhart & Nguyen, 2019), and motor function (Feurra, Bianco, et al., 2011; Joundi et al., 2012). Moreover, tACS has been increasingly investigated in intervention studies to directly link brain oscillations and cognitive 11 processes. Conventional brain imaging studies involve passive neuroimaging while participants perform cognitive experiments (Carrasco, 2011; Postle & Yu, 2020). This method allows us to link brain activity (neural or blood oxygen level dependent, BOLD, signal) with cognition, but the link is almost always correlational. tACS offers the unique opportunity to interventionally perturb the brain oscillations at specific frequencies and study its effects on behavior over and above a tight control, thus establishing a causal link between brain oscillations of specific frequency ranges to cognitive processes (Herrmann et al., 2013; Hopfinger et al., 2017). Thus, tACS could provide insights into the unresolved question of whether brain oscillations are a fundamental mechanism in neural processing or are epiphenomenon (Beliaeva et al., 2021). tACS may lead to simultaneous or online changes in physiology and behavior, but it has also been suggested that some tACS effects can outlast the stimulation duration (Grover et al., 2022; Reinhart & Nguyen, 2019). Studies have suggested that spike-timing dependent plasticity (STDP) as the mechanism for these long-term effects (Dan & Poo, 2006; Vogeti et al., 2022). Such long-term effects could make tACS a very promising tool for the treatment of many neurological and psychiatric disorders. For example, there have been preliminary attempts of using tACS to treat ADHD (Rubio et al., 2016), schizophrenia (Hoy et al., 2016; Mellin et al., 2018; Sreeraj et al., 2019), autism (Vicario & Nitsche, 2013) and other mental health disorders (Elyamany et al., 2021). For example, if the neural oscillation frequency pattern underlying a specific symptom of a brain disorder were known, in theory, that symptom could be changed by neuromodulation of that oscillation frequency in the appropriate brain area(s). Although many studies claim that tACS has the potential to augment cortical activity related to behavioral impairments linked to neurological 12 and psychiatric disorders, recent studies have shown that tACS findings can be rather inconsistent, limiting its therapeutic uses (Kasten et al., 2019; Krause & Kadosh, 2014; Ridding & Ziemann, 2010). One of the major limitations of tACS is that the typically imposed low-intensity electric current (1-2mA) is not sufficient to produce electric fields (< 0.5 V/m) large enough to induce significant changes to the brain’s electrophysiology and behavior. Moreover, studies have shown that about 75% of the electrical current passes transcutaneously, along the scalp, and therefore cannot contribute to creating an electrical field on the cortical surface (Asamoah et al., 2019; Haueisen et al., 1997; P. G. Vieira et al., 2020; Vöröslakos et al., 2018). Another limiting factor of traditional tACS technology (in terms of stimulation electrode size, shape, and density) is the lack of spatial specificity of the stimulation. Precise targeting of a particular brain area or network is not possible with traditional tACS, because it not only affects the area of interest, but all the neighboring and connected areas as well (Klírová et al., 2021). In addition, the poor reliability in tACS findings could also be attributed to individual differences in brain anatomy because different size and shapes of brain structures leads to varying electric field patterns across participants, complicating application of predefined sets of stimulation parameters (Kasten et al., 2019; Stecher et al., 2021). Another major limitation of tACS studies is that it does not take into account the current state of the brain; for example, the frequency and phase of tACS may not closely match the ongoing brain oscillations (Stecher et al., 2021). Thus, it is essential to examine the mechanistic underpinnings of tACS in healthy brains before attempting to use tACS therapeutically to treat complex psychiatric disorders. My approach to address this involves aggregating knowledge derived from in-vitro experiments on neural tissue and in-vivo studies in rodents, primates, and humans. 13 1.2.2.2 Mechanisms of tACS There are currently two presumptions about how tACS exerts its effect. First, entrainment of the ongoing oscillations in the brain causes a transient change in physiology and behavior (online effect) (Herrmann et al., 2013; Liu et al., 2018; Tavakoli & Yun, 2017). Second, modulating spike-timing-dependent plasticity (STDP), causing physiological and behavioral changes outlasting the duration of stimulation by several minutes to more than an hour (long-term effect) (Herrmann et al., 2013; Polanía et al., 2018; Stagg et al., 2018). In the next sections, I discuss the mechanisms for online and long-term effects of tACS across different animal models. 1.2.2.2.1 Online tACS During tACS, alternating current (AC) is applied to the electrodes, and current flows from the anode to the cathode during one half-cycle and reverses and flows from cathode to anode in the other half-cycle. This current induces an electrical field in the brain tissue, between the anode and cathode. Electrical field is the gradient of electrical potential in the brain and is expressed in the units of Volts/meter (V/m). The magnitude and direction of the induced electric field are the main parameters that dictate the efficacy of tACS (Liu et al., 2018). Online effects of tACS are defined as the immediate effects that occur simultaneously with changes in the external electrical field's modulation of the membrane potential. Studies have shown that electrical fields parallel to the soma-dendritic axis have higher effects relative to perpendicular fields (Creutzfeldt et al., 1962; Purpura & McMurtry, 1965). The theorized mechanism underlying online effects is the entrainment of neurons by the external electrical field. For a sufficiently strong 14 field (e.g., >1V/m), the neuronal firing and the oscillations (local field potentials, LFP/EEG) synchronize with the frequency and phase of the external electrical field, this is termed as neuronal entrainment (Liu et al., 2018). More specifically, during AC stimulation, the changing electrical field makes somata of the neuron alternatively depolarized and hyperpolarized. Depolarization corresponds to making the membrane potential less negative and the generation of action potential easier, whereas hyperpolarization corresponds to making the membrane potential more negative and generation of action potential harder. During tACS, the electrical field could alternatively depolarize and hyperpolarize the neurons, thereby increasing and decreasing their firing rates respectively, leading to entrainment (Liu et al., 2018). Neurons fire mainly based on two factors: the input currents from the synapses, and the membrane potential. The membrane potential can be changed by an external electric field using tACS. Theoretical modeling of elongated neurons has shown the threshold for the electric field to interact with a neuronal network to be ~0.1V/m (Weaver et al., 1998). First, I looked at the effects of electrical stimulation on brain slices (in-vitro) because it enables the study of neurons in an extremely controlled manner. Francis and colleagues showed that electrical fields as low as 0.2V/m could affect firing of elongated pyramidal CA1 neurons in the rat hippocampus under ideal conditions (Francis et al., 2003). The external electric fields interact and compete with the ongoing changes in the intrinsic electrical fields to produce effects on neuronal firing. Generally, the intrinsic fields can be quite large, 1-2V/m in the neocortex to 5-15V/m in the hippocampus (Anastassiou et al., 2010; Fröhlich & McCormick, 2010). To study the effects of tACS on slices with intrinsic oscillations, Flavio and McCormick used active slices of ferret visual cortex that 15 spontaneously show physiological activity. They showed that high electric fields (4V/m) could induce oscillations at the external frequency, and the modulation of the neuronal firing did not depend on the frequency difference between the external field and the intrinsic network oscillations. However, at lower field strengths (2V/m), the modulation decreased with increased frequency difference between the external field and the intrinsic network oscillations. This suggests that when using a lower field strength, entraining networks may require the frequency of the external electric field to close to the frequency of the intrinsic oscillations (Fröhlich & McCormick, 2010). Studies have shown that alternating current stimulation at the same frequency as the intrinsic network oscillations can have resonance-like effects that can accumulate over multiple cycles (Fröhlich & McCormick, 2010; Herrmann et al., 2013; Liu et al., 2018). Under these special conditions, electric fields as low as 0.2-0.5V/m can cause shifts in spike timing, matching the phase of the ongoing brain oscillation with the external tACS (Deans et al., 2007; Francis et al., 2003; Reato et al., 2010) However, these effects are higher at low frequencies. Stronger electric fields are required to bias the spike timing at higher frequencies because the neuronal membrane acts like a capacitor (a component that stores electric energy, typically consists of two conducting materials separated by an insulator) and a low pass filter (Grossman et al., 2017; Vöröslakos et al., 2018). Although, in-vitro experiments provide an extremely controlled setting to answer fundamental questions regarding the effects of tACS on an ideal neural network, these studies do not reveal the conductance effects of skin, skull, dura, and cerebrospinal fluid from a living animal (Liu et al., 2018). Moreover, the effects of tACS on isolated brain slices do not reflect the effects 16 on a highly interconnected neural network in living animals. Thus, one needs to further consider at the evidence from in-vivo studies in rodents and non-human primates to better understand the effects of tACS on humans. The in-vivo tACS studies in living rodents have demonstrated that applied electric fields can alter membrane potentials, spike timing, and LFPs in a dose-dependent manner (Ozen et al., 2010; Vöröslakos et al., 2018). Moreover, some studies have also shown reliable behavioral effects such as triggering paw movement (Grossman et al., 2017). However, these studies cannot be directly compared to human studies, because they use current intensities an order of magnitude greater than allowed for human studies. Reviews have noted that the induced electrical fields in rodent studies are much higher (6.8 ± 3.8 V/m) than the human counterparts (< 1V/m), mainly due to the small size of the rodent head (Liu et al., 2018). Non-human primate studies allow invasive investigations of the effects of tACS on a brain comparable to humans. One study demonstrated that the intracranial electric field in two anesthetized monkeys is similar to that in humans, 0.21V/m and 0.39V/m (Opitz et al., 2016). The study showed that tACS affects the spike timing in a dose-dependent manner, such that the higher the electric field strength, the more neurons entrained and with higher phase-locking. Moreover, they showed that these effects can be seen with field values of <0.5V/m, which can be achieved in human studies (Johnson et al., 2020). A recent study has shown that the entrainment effects of tACS depend not only on the stimulation frequency but also on the ongoing oscillations (Krause et al., 2022). They showed that tACS decreases entrainment when there is a close mismatch 17 between the ongoing and external oscillation frequencies but increases entrainment at the precisely matching frequency and phase. Moreover, there was also increased entrainment in the frequencies where the ongoing oscillations were weak. The authors suggest that human studies should either focus on stimulating brain regions in which ongoing oscillations are relatively weak, or use a closed loop to precisely match the frequency and phase of the ongoing oscillation. Based on this evidence, researchers have conceptually distinguished five mechanisms that could affect the neural network activity during tACS (Liu et al., 2018). These mechanisms have different minimum thresholds of the external electrical field. The boundaries between these mechanisms are often unclear, and multiple mechanisms may be at play simultaneously in different brain networks. This information is summarized in Table 1.1. 1. Imposed pattern. Imposing an externally induced oscillation on a neuronal network that has strong ongoing oscillations at a different frequency. This requires extremely strong electric fields > 5V/m (Fröhlich & McCormick, 2010; Liu et al., 2018). An example would be enforcing an external beta oscillation on a network with ongoing alpha oscillations. Such high fields are not generated during tACS on humans, and thus it seems unlikely that one could impose external patterns using tACS in humans. 2. Network entrainment. An irregular neural network, one with no dominant endogenous oscillation, can be entrained to oscillate at the frequency of the external electric field if the field is strong enough (~ 1V/m). In this mechanism, the external electric fields compete with the intrinsic fields for spiking (Fröhlich & McCormick, 2010; Krause et al., 2022). Networks with weak native 18 oscillations can be entrained with weaker fields. Entraining a less regular neural network using tACS is difficult, because it requires higher magnitudes of electric fields than typically used in human experiments (< 1V/m). However, one may induce some entrainment if the appropriate brain network and behavior are targeted. 3. Temporal biasing of spikes. Moderately strong electric fields (~ 0.5V/m) can affect the membrane potential and bias the spike timing in a subset of neurons. Here, the small external field changes the intrinsic electrical fields to bias the spike timing of neurons without changing the firing rate. Studies have shown that biasing spike changes is easier when the frequencies of the external and internal oscillations are similar (Herrmann et al., 2013). Temporal biasing can be achieved in high-intensity human tACS where the phase of the ongoing oscillation can be biased towards the external electrical field. 4. Rhythm resonance. A weak electrical field (~ 0.2V/m) can change the excitability of the neurons if it is precisely timed at the depolarizing phase of the ongoing oscillations in the brain. Here, the frequency and phase of tACS should match that of the native brain oscillations. Such an approach would require a closed-loop setup where the frequency and phase of the brain oscillation is tracked in real-time and tACS is delivered precisely based on the tracked signal. Under such well-controlled, closed-loop conditions, even low intensity tACS could reliably affect physiology and behavior (Deans et al., 2007; Krause et al., 2022; Liu et al., 2018). 5. Stochastic resonance. A very weak electrical field can bias the membrane potential of some neurons randomly and thus bias their spike timing and probability. Here, even a small field can induce firing of a neuron nearing the threshold. Such weak stochastic effects are difficult to quantify as the affected neurons can be scattered (Geisler & Goldberg, 1966). 19 Table 1.1. Summary of mechanisms for online tACS Electrical Field (Humans?) Imposed pattern Network entrainment Temporal biasing of spikes Rhythm resonance Stochastic resonance > 5 V/m (No) Yes Yes Yes Yes Yes ~1 V/m (Maybe) No Yes Yes Yes Yes ~0.5 V/m (Yes) No No Yes Yes Yes ~0.2 V/m (Yes) No No No Yes Yes < 0.2 V/m (Yes) No No No No Yes Note: Table indicating whether the mechanism can occur at different magnitudes of electric fields. It also indicates whether the magnitudes of electric fields are possible in human studies, inside parentheses in the first column. Imposed pattern: Successfully imposing external oscillations on a network with strong ongoing oscillations; Network entrainment: Successfully imposing external oscillations on a network with irregular ongoing oscillations; Temporal biasing of spikes: Successfully biasing the phase of the ongoing oscillations towards the imposed external oscillations; Rhythm resonance: Successful amplitude change in brain oscillations induced by imposed external oscillations when frequency and phase are intentionally matched with tACS; Stochastic resonance: Random change in spike timing and probability when imposed external oscillation happen to match ongoing oscillations; V/m: Volts/meter. 1.2.2.2.2 Long-term effects of TACS Long-term or offline effects of tACS are defined as effects that outlast the stimulation period of tACS (Ahn et al., 2019; Grover et al., 2022; Reinhart & Nguyen, 2019). The leading hypothesis to explain these plastic changes in the brain is spike-timing dependent plasticity (STDP) (Polanía et al., 2018; Stagg et al., 2018; Vogeti et al., 2022). A pre-synaptic spike occurring prior to a post-synaptic spike leads to an increase in synaptic weight; this is termed as long-term potentiation (LTP). Conversely, a post-synaptic spike occurring prior to a pre-synaptic spike results in decrease 20 in synaptic weight; this is termed as long-term depression (LTD) (Dan & Poo, 2006; Markram et al., 2012). Studies have shown that STDP effects can be shown in human studies by using a N-methyl-d-aspartate (NMDA) receptor antagonist which is thought to inhibit LTP. A study showed that an NDMA receptor antagonist suppressed the long-term effects of repetitive TMS on motor evoked potentials as compared to a placebo (Stefan et al., 2002). A similar study showed that 20Hz tACS on the motor cortex induces NDMA receptor mediated plasticity (Wischnewski et al., 2019). STDP has been extensively studied at a cellular level, in-vitro, and in-vivo experiments in animal models (Dan & Poo, 2006). However, the exact hypothesis on how STDP induces plasticity due to tACS has only been explored recently. Zaehle et al. showed an increase in alpha power after stimulating the occipital cortex at the participants’ individual alpha frequency (Zaehle et al., 2010). The authors proposed a computational model to explain the STDP hypothesis of tACS. The model consists of a neuron which is driven by external electric current. This driving neuron is connected to other neurons in a hidden layer creating feedback loops with each of the neurons. Each of the of the feedback loops take different time durations (40-120 ms) for a spike to travel from the driving neuron to the hidden-layer neuron and back. The model suggests that if the driving neuron is stimulated at 10 Hz (i.e., period = 100 ms) then the feedback loops with durations slightly less than 100 ms will experience the post-synaptic spikes arriving after the pre-synaptic spikes resulting in LTP and strengthening of the synaptic weights. Whereas, loops with durations greater than 100 ms leads to LTD and weakening of synaptic weights (Zaehle et al., 2010). Another study improved on the above STDP model (Vossen et al., 2015). Instead of assuming equal initial weights for all frequencies, higher initial weights were assigned to the feedback loops corresponding to the 21 dominant oscillation in the network (e.g. if alpha, 8-14 Hz, is the dominant oscillation, then loops with durations 70-125 ms have higher initial weights). The model also suggests that the STDP effects are also more prominent on loops corresponding to dominant oscillations (Vossen et al., 2015). Studies have used this model to explain the after-effects of tACS on physiology (Kasten et al., 2016; Neuling et al., 2013; Vossen et al., 2015; Zaehle et al., 2010). This model suggests that if the driving neuron is stimulated at 10 Hz, networks oscillating at frequencies slightly greater than 10 Hz get stronger, whereas networks oscillating at frequencies slightly lower than 10 Hz get weaker. These predictions of the model need to be systematically verified using experiments (Vogeti et al., 2022; Vossen et al., 2015). Moreover, the model does not provide any insights regarding what the duration of tACS should be to induce long-term effects. Studies have shown that tACS effects emerge only after delivering tACS for multiple sessions (Del Felice et al., 2019; Grover et al., 2022). There is a good understanding of the relationship between the intensity of induced electric field and the type of online effect (see Table 1.1) but there is no such understanding about the relationship for STDP mediated plasticity effects. In this dissertation, I investigate the physiological effects of tACS immediately after stimulation. Reviews have suggested that entrainment as well as STDP could be involved in inducing after effects of tACS (Vogeti et al., 2022). 22 Chapter 2: Supervised Dimensionality Reduction Methods In this chapter, I provide a mathematical overview of the supervised dimensionality reduction techniques used in this dissertation – constrained principal component analysis (CPCA) and joint decorrelation (JD). A version of this explanation of CPCA can be found in the published paper (Chinchani et al., 2021): Chinchani, A. M., Menon, M., Roes, M., Hwang, H., Allen, P., Bell, V., ... & Woodward, T. S. (2021). Item-specific overlap between hallucinatory experiences and cognition in the general population: A three-step multivariate analysis of international multi-site data. cortex, 145, 131-144. The above paper constitutes chapter 3 of this dissertation. 2.1 Constrained principal component analysis (CPCA) CPCA is a supervised dimensionality reduction technique that uses multivariate multiple regression to constrain the variance and PCA for dimensionality (Hunter & Takane, 2002; Takane & Hunter, 2001; Takane & Shibayama, 1991). CPCA extracts of orthogonal latent dimensions in the criterion variables (Z) that are optimized to be predictable from a set of predictor variables (G). Details of the theory and proofs for this technique can be found elsewhere (Takane & Hunter, 2001; Takane & Shibayama, 1991). CPCA consists of two main steps, external and internal analyses. In the external analysis, multivariate multiple regression is applied to separate the total variance in the criterion variables (Z) into variance that is predictable from the predictor variables (G) and the noise (i.e., variance that is not predictable). This step splits the criterion matrix (Z) into two matrices with orthogonal variance sources: one composed of regression-based predicted scores 23 (GC), and the other residual variance or error scores (E). The external analysis can be denoted by the regression equation: Z = GC + E where, Z = matrix of criterion variables, G = matrix of predictor variables, C = (G’G)-1G’Z is a matrix of regression coefficients, GC = regression-based predicted score matrix, and E = residual scores (variance in Z not explained by predictor variables in G). The external analysis is followed up by the internal analysis, which involves performing a PCA (or singular value decomposition) on the predicted scores (GC) and can be denoted as follows: GC = UDV’ where U is the matrix of left singular vectors, and V is the matrix of right singular vectors. When V is combined with the diagonal matrix D, this gives the component loadings (𝑉𝐷/√𝑁). When U is scaled by square root of N, this provides the component scores (√𝑁U). Component loadings indicate the contribution of each criterion variable to the component. Component scores (√𝑁U) are further correlated with the columns of G to create predictor loadings (P). These predictor loadings indicate the degree to which each predictor is related to each component score extracted in the PCA of GC. U and V and P can be simultaneously rotated in accordance with convention, or, U and V can be rotated, and P computed as correlations between G and rotated U, with the latter method being used in the current dissertation (Chinchani et al., 2021). 2.2 Joint decorrelation (JD) Joint Decorrelation (JD) or Denoising Source Separation (DSS) is a technique that identifies linear latent dimensions within high-dimensional, noisy electrode data, optimizing for power in specific 24 frequency bands (de Cheveigné & Parra, 2014). The algorithm whitens the electrode signals and then rotates the data to maximize variance in the desired feature (here, 40Hz auditory steady state response in chapter 5 and alpha power, 8-14Hz, in chapter 6). Each JD latent dimension (X) is a linear combination of the preprocessed EEG signals (Z; X=ZW), where W is the weight or projection matrix that maps electrodes to latent dimensions. JD estimates the projection matrix (W) by maximizing the difference between two covariance matrices—one containing only the desired feature (C1) and the other containing the raw data (C0). The equations explaining JD are from the paper by de Cheveigné and Parra (2014). The algorithm involves the following steps: First, the C0 covariance matrix is computed. This is the covariance of the full spectrum of EEG data. More specifically, it contains the desired feature (signal) and the noise. C0 = ZT Z Next, C1 covariance matrix, which is the covariance of only the desired feature (i.e. only signal), is computed. In order to compute the C1 matrix, first, Z is whitened using Eigen decomposition. C0 P = P D Where, P contains the orthonormal eigenvectors and D contain the eigenvalues. The whitened data, Zw is computed as follows: Zw = Z P N Where, N=1/√𝐷 . Next, the whitened data, Zw is bias filtered along the dimension of the desired dimension. This is obtained by performing a linear transformation on Zw by multiplying with the bias filter, Lf. 25 Zwf = Zw Lf In case of bias filtering the data to a desired range of frequencies, Lf is the Fourier transform operator in the desired frequency range. Then, the biased covariance matrix is computed as follows: C1 = ZwfT Zwf Then eigen decomposition is performed on the biased covariance and the transformation matrix W is computed. C1 Q = Q Dwf W = P N Q X = Z W This transformation converts the raw data, Z, into the desired latent dimensions, X, which maximally express power in the desired frequency range. More details regarding the algorithm can be found here (de Cheveigné & Parra, 2014). 26 Chapter 3: Item-specific overlap between hallucinatory experiences and cognition in the general population: A three-step multivariate analysis of international multi-site data. (Study 1) In this chapter, I apply constrained principal component analysis (CPCA), a supervised dimensionality reduction technique, to identify cognitive correlates of hallucinatory experiences in the general population. Utilizing data from an international multisite study on non-clinical participants (n=419), I examined the overlap between two multivariate sets of variables—one measuring cognition and the other measuring hallucinatory experiences—at the level of individual items. Additionally, to reduce the risk of overfitting, I employed a three-step supervised dimensionality reduction method with reliability tests. This approach allows for the study of item-level overlap while minimizing the reporting of spurious results. A version of this chapter has been published in Cortex (Chinchani et al., 2021): Chinchani, A. M., Menon, M., Roes, M., Hwang, H., Allen, P., Bell, V., ... & Woodward, T. S. (2021). Item-specific overlap between hallucinatory experiences and cognition in the general population: A three-step multivariate analysis of international multi-site data. cortex, 145, 131-144, Copyright Elsevier. 3.1 Introduction Hallucinations are a prominent symptom of schizophrenia spectrum disorder, with 60-80% of diagnosed patients experiencing auditory hallucinations, and a smaller percentage experiencing visual and other types of hallucinations (Bauer et al., 2011; Lim et al., 2016; Waters et al., 2014). 27 Research has shown that approximately 10-15% of the general population also report experiences similar to hallucinations (Sommer et al., 2010), leading to the proposal of a continuum model of hallucinatory experiences (HEs) from health to disease (Aleman & Larøi, 2008; Powers et al., 2017; Siddi et al., 2019). Similarities have been reported in terms of featural and clinical characteristics, such as vivid and frequent voices, third-person hallucinations, personification, a recurrent course of hallucinations, and an increased risk for adverse negative events (Waters & Fernyhough, 2017). This proposed continuum presents an accessible opportunity to investigate the cognitive mechanisms underlying HEs in a healthy sample, without the potential confounds of antipsychotic medications, stigma, and institutionalization. Candidate cognitive mechanisms include dysfunctional source monitoring, heightened signal detection, or impaired attentional processes. Through this approach, researchers can develop mechanistic models to better understand distressing or disabling experiences and assist in developing interventions based on the recognition that pathological hallucinations can be understood as extreme versions of healthy cognitive biases. Previous attempts to study the cognitive mechanisms underlying HEs, either in clinical samples or in healthy populations under the assumption of a continuum, have shown inconsistent and sometimes contradictory findings. For example, studies have shown that a bias in source monitoring (SM; i.e., externalization of internal cognition) is related to HEs in schizophrenia patients reporting hallucinations (Bentall et al., 1991; Brookwell et al., 2013; Morrison & Haddock, 1997; Woodward et al., 2007; Woodward & Menon, 2011). Although a study has found a similar relationship in the general population (Larøi et al., 2004), others have reported no link 28 between misattribution of internal cognition to an external source with non-clinical hallucinations (Alderson-Day et al., 2019; Garrison et al., 2017). A number of studies have used auditory signal detection (SgD) tasks to understand the cognitive and sensory mechanisms underlying hallucinations, suggesting a link between false alarm rates (of detecting a signal in white noise) and the severity of HEs in patients (Varese et al., 2012) and the general population (Barkus et al., 2011; Rankin & O’Carroll, 1995; Waters et al., 2012). There has also been evidence suggesting that reduced language lateralization in the brain is related to HEs. To assess this, studies have mainly used a consonant-vowel dichotic listening (DL) task, where the aim is to differentiate between auditory stimuli presented simultaneously to both ears. Typically, a left-hemisphere lateralization (i.e. right-ear advantage) is observed in the general population (Bless et al., 2015), with reduced lateralization reported for hallucinating psychosis patients (Ocklenburg et al., 2013). Whereas, studies in the general population show no such reduction for hallucination prone participants (Aase et al., 2018; Conn & Posey, 2000). These inconsistencies could be partly due to small sample size and lack of standard protocols across various studies. To address this issue, Moseley et al., (2021) carried out a pre-registered international multisite study (N = 1394) to investigate the link between relevant cognition measures and HEs. Using an online protocol, non-clinical participants performed SM, DL, backwards digit span (DS), matrix reasoning (MR) and auditory SgD tasks, along with assessments of HEs using the 32 items of the Cardiff Anomalous Perceptions Scale (CAPS; Bell et al., 2006) and the 16 items of the Launay-Slade Hallucination Scale - Extended (LSHS-E; Larøi et al., 2004) across 11 data collection centers. Most cognitive tasks were selected based on theoretical models 29 on HE (e.g., Waters et al., 2012), with the exception of the MR task, which was included to provide a general index of non-verbal intelligence. The CAPS and LSHS-E inquire about anomalous perceptions in multiple sensory modalities (viz., vision, sound, taste, temperature and pressure); therefore, a summary score would not capture modality-specific information. It was found that the false alarm rate in auditory SgD was associated with HEs, as measured by the aggregate score for the CAPS and LSHS-E items, with no associations between the HE scales and other cognition measures. When studying overlap between two sets of variables, results are often reported in terms of summed aggregate variables or summary scores, due to concerns regarding Type I errors associated with assessment of multiple tests of statistical significance if carried out on each variable individually. Although this approach is valid, it results in neglect of the more specific information offered by individual items. However, this neglect is not necessary, because methods are available that allow the study of overlap between two sets of variables (e.g., HE and cognition) at the level of individual items, without an increased concern over reporting spurious results. One of these methods is used in this study. It involves using a three-step process described in detail below. The published version of the data analyzed in this work (Moseley et al., 2021) measured HEs by the summing scores for all items on the CAPS, and four hypotheses were pre-registered about how each domain of cognition would relate to this summary scale. The purpose of pre-registering hypotheses and using only one summed-score independent variable for HEs, was to avoid 30 publishing Type I errors (false positives) by limiting the number of statistical tests performed. In contrast, in the current study, instead of controlling Type I errors by computing one summary independent variable, which focusses only on what is common between all items and not on the variance specifically measured by each individual item, the same general hypothesis, and its one statistical hypothesis test, was formulated at the multivariate level. That is to say, Type I errors were limited to the 5% level for overlap between two sets of variables (viz., overlap between all HE variables on one hand, and all cognition variables on the other hand). Statistical significance at this step (step 1) set into motion two additional steps designed to determine which specific individual variables are responsible for this overlap, with step 2 applied to the set of dependent variables, and step 3 to the set of independent variables (cognition and HEs, respectively, in this case), and involve variance constraints, dimension reduction, and split-half reliability checks to determine which specific combinations of dependent and independent variables reliably describe the significant overlap between the two sets of variables. This three-step process simultaneously controls Type I errors, and detects signal at the level of individual variables which might be considered off-limits when summary scores are analyzed, potentially providing finer delineation of the nature of the overlap between two sets of variables, and better informing future hypotheses. Thus, the approach is not exclusively exploratory (the multivariate hypothesis is posed of overlap between all HE variables on one hand, and all cognition variables on the other hand), but is exploratory in the sense that any one item is not given a higher theoretical importance than any other item, and interpretation is focused on those individual items which provide the most reliable signal with respect to overlap between HE and cognition. 31 3.2 Methods 3.2.1 Participants Data were collected as part of a larger multi-site study (Moseley et al., 2021). Data from 647 participants were collected in person at one of 11 data collection sites: Durham University, University of Roehampton, King’s College London, University College London, University of Cambridge (all UK), University Paul Valéry (France), University of Groningen (Netherlands), Charles University (Czech Republic), University of Bergen (Norway), University of British Columbia (Canada), and Swinburne University (Australia). Data were also collected for a subset of tasks from 866 participants online, although this was not included in the present analysis, as not all task measures of interest (viz., auditory SgD) were collected online. Participants were required to be aged 18-75 years, fluently speak the native language of the respective country, and have no diagnosed hearing impairments. Participants were given a nominal honorarium for participation at the discretion of each participating site, or were rewarded with course credits, where applicable. All sites obtained ethical clearance from their relevant institutional review board, in accordance with the Declaration of Helsinki. In the present work, first we applied the exclusion criteria as described in Moseley et al., (2021), which reduced the sample size to 594, largely based on quality control (more details in individual task/questionnaire descriptions below). Second, due to the multivariate nature of the analysis, we included only participants who had valid data for all questionnaire items (CAPS and LSHS-E) and all cognition measures (consonant-vowel DL, MR, SM, auditory SgD, and DS tasks), resulting in a final sample of 419. 32 3.2.2 Questionnaires 3.2.2.1 Cardiff Anomalous Perceptions Scale (CAPS) The CAPS (Bell et al., 2006) consisted of 32 items inquiring about anomalous perceptions in the sensory modalities of vision, sound, taste, temperature, pressure, and smell (e.g., Do you ever notice that sounds are much louder than they normally would be?), and provides yes/no as response options. Conventionally, the total number of items for which the participant responded ‘yes’ (scored as 1, so that scores varied from 0 to 32) was used as a metric for indicating the degree of HEs, with higher values indicating higher levels of HEs. For each item that the participants responded to as ‘yes’, they were also prompted to rate how much distress it caused them, how disruptive or intrusive, and how frequent the experiences were on a Likert scale of 1-5. In this study, only yes/no responses to the main 32 items were included in the analysis and were considered separately with no summary score computations. Histograms for all CAPS items are shown in Figure A.2. 3.2.2.2 Launay-Slade Hallucination Scale - Extended (LSHS-E). The LSHS-E (Larøi et al., 2004) consisted of 16 items inquiring about anomalous perceptions in the sensory modalities of vision, sound, pressure, and smell (e.g., I often hear a voice speaking my thoughts aloud), and participants were asked to respond on a 5-point Likert scale as to how much each item applies to them (0 = Certainly does not apply to me, 4 = Certainly applies to me). Conventionally, the overall score is calculated as the sum of the score for each item (0-64). In this study, the responses recorded for each of the 16 items were analyzed, and no summary score was computed. Histograms for all LSHS-E items are shown in Figure A.3. 33 3.2.3 Cognitive Measures In the current study, we included 18 cognitive measures from various tasks such as – source monitoring, consonant-vowel dichotic listening, matrix reasoning, digit span, and auditory signal detection. Each of the tasks is explained in detail below. The z-score normalized histograms for all the cognitive measures is shown in Figure A.1. 3.2.3.1 Source monitoring task (SM) SM required participants to recall whether words had been presented as spoken stimuli through headphones (HEAR trials), or whether they had simply been instructed to imagine hearing the words (IMAGINE trials). Three lists of 24 words were assembled and matched for the number of letters, syllables, frequency of use, concreteness, and imageability. For each participant, one list was randomly assigned to the HEAR trials, and another to the IMAGINE trials. The third list was assigned to the NEW condition in the second stage of the task. In the first stage of the task, participants were presented with a series of words in the center of the screen (duration = 3s), each preceded by the word HEAR or IMAGINE (duration = 1s). For trials on which they heard the stimuli, a word from the HEAR condition was presented in the center of the screen, and an audio clip of that word being spoken by a male, in a neutral tone, was presented concurrently. For trials on which participants were instructed to imagine the word, a word from the Imagine condition was presented on the screen, but no speech clip was played. The HEAR and IMAGINE trials were randomly interleaved. The second stage of the task began immediately after the first was completed. Participants were presented with all 48 words from Stage 1, presented in 34 random order, as well as 24 new words. For each word, they were instructed to decide whether they had heard the word, imagined the word, or whether the word was new. Nine SM variables were included in the analysis - three correct response counts (viz, Hear-Hear, Imagine-Imagine and New-New), and six incorrect response counts (viz. Hear-Imagine [internalization], Imagine-Hear [externalization], Hear-New [miss], Imagine-New [miss], New-Hear [false positive external], and New-Imagine [false positive internal]). Data from four participants (out of 594) for this task were excluded if they met one of the following exclusion criteria: scoring at or below 33.3% accuracy (n = 4), with one of these four participants also meeting the exclusion criteria of scoring at or below 50% on old-new accuracy (n = 1). 3.2.3.2 Consonant-vowel dichotic listening (DL). The DL task is designed to assess language lateralization in an unforced condition, with two additional ‘forced attention’ conditions which are sensitive to attentional control. The task involved the simultaneous presentation of two audio clips of spoken consonant-vowel syllables, with a different syllable presented to each ear. The presented syllables are ‘ba’, ‘da’, ‘ka’, ‘ta’, ‘pa’, and ‘ga’, with each clip lasting approximately 350ms. In the ‘non-forced attention’ condition, the participant was required to select the syllable they could hear most clearly. In the ‘forced right’ and ‘forced left’ conditions, the participant was instructed to select the syllable they believe had been presented to the right or left ear, respectively. Participants provided a response via mouse click on a visual display of all 6 syllables spelled out in capital letters. Participants first performed 35 the non-forced task, followed by the forced ones. The order of the forced left and right was counterbalanced across subjects. There were 36 trials in each condition, presented in a random order, including 6 homonym trials (with the same syllable presented to each ear). The homonym trials were excluded from data analysis and were used only as a data quality check (see below). The remaining 30 trials consisted of all possible combinations of the 6 syllables presented to each ear. Total number of syllable responses corresponding to the right ear (Right ear score, RES) and the left ear (Left ear score, LES) were calculated for all conditions. The laterality index for all three conditions was calculated as follows: Laterality Index = [(RES – LES) / (RES + LES)] *100. The laterality indices were computed for the ‘non-forced attention’, ‘forced right’ and ‘forced left’ conditions separately, and these were submitted to the analysis. Dichotic Listening: 36 participants (out of 594 total) were excluded from the dichotic listening task performance due to scoring < 50% accuracy on homonymous trials in any of the three task conditions (n = 24) and/or scoring a laterality index of 100% to one ear (n = 12), similar to Bless et al. (2015). 3.2.3.3 Auditory signal detection (SgD). The auditory SgD task required the participant to respond whether they believed a speech clip had been embedded in noise. The signal-to-noise ratio (SNR; that is, the ratio of the volume of the voice clip to the noise) was determined individually at each site using a short calibration task, in 36 which participants, who did not participate in the main study (N = 10 per site), were presented with speech clips embedded in noise at a variety of SNRs. In the main task, the participants were presented with 72 bursts of ‘pink noise’ of 3.5s duration, with a 1.5s speech clip in the middle, presented at one of four SNRs in 36 trials (speech-present), and with no speech clip presented at all in 36 trials (speech-absent). The speech clips were the same as those used in previous studies using this task (Barkus et al., 2011), consisting of a male voice reading a text (taken from an instruction manual) in an emotionally neutral tone. After each burst of noise, participants were presented with the text “Did you hear speech?” and they responded by clicking a mouse button for Yes or No. For each trial, they were also then prompted to enter a confidence rating. Confidence ratings were not analyzed as part of this study. SgD measures sensitivity (dˈ), and response bias (β) were estimated (Stanislaw & Todorov, 1999). The hit rate, false alarm, sensitivity, and response bias were included in the analysis. Data from 11 participants (out of the 647 in-lab participants) were excluded from the auditory SgD task data, scoring a dˈ of ≤ 0 (indicating at or below chance performance) (n = 10), or a hit rate of ≤ 10% (n = 1). Two participants met both criteria. 3.2.3.4 Matrix reasoning (MR). This task was included to provide a brief assessment of non-verbal reasoning ability. 10 items were taken from the International Cognitive Ability Resource (previously tested in a general population sample of > 97,000 participants; Condon & Revelle, 2014). The task is based on Raven’s 37 Progressive Matrices, with participants completing a 3 × 3 grid of shapes, choosing from six options, within 60s. Raw number of correct responses (maximum 10) was used as an assessment of non-verbal reasoning ability, and this MR score was included in the analysis. 3.2.3.5 Backwards Digit Span (DS). The DS task assessed verbal working memory performance in participants. In each trial, a series of numeric digits were shown, and then the participants were asked to recall these digits in reverse order. Digits (1-9) were randomly sampled without replacement (until after trial length of 10) and were presented on the center of the screen for 1s each. In each trial, the length started at 2 digits, and was varied according to the rules set out in Woods et al., 2011); that is, when the participant correctly recalls the digit string, trial length is increased by 1, whereas the trial length was decreased by 1 if there are two consecutive incorrect responses. Participants completed 14 trials and responded using a mouse to click the digits they wished to input on an on-screen keypad. Performance was assessed using the mean span metric, that is, the length of trial at which the participant performs with 50% accuracy. 3.2.4 Data Analysis 3.2.4.1 Constrained Principal Component Analysis (CPCA) In order to determine the links between cognitive measures and HE items, CPCA was used, which combines the variance constraints of multivariate multiple regression and the dimension reduction of PCA into a unified framework (Hunter & Takane, 2002; Takane & Hunter, 2001; Takane & Shibayama, 1991). The current application of CPCA involves extraction of orthogonal dimensions 38 in the criterion variables (cognition) that are optimized to be predictable from a set of predictor variables (HEs). The component loadings indicate the importance of each criterion variable (cognition) for each component, and predictor loadings indicate the importance of each predictor variable (HEs) for each component. Component loadings and predictor loadings must be interpreted in conjunction because they are different pieces of information about the same components. Namely, component loadings and predictor loadings are computed as correlations with rotated component scores, but these correlations are computed with the variance-constrained cognition variables and the HE variables, respectively. The three-step CPCA methodology is explained in detail below. 3.2.4.1.1 Step-1: Variance Constraints and Dimension Reduction through Constrained Principal Component Analysis (CPCA) The use of dimension reduction when relating scales capturing the severity of the signs and symptoms of psychotic illness to cognition is certainly not new, with the standard methodology involving using separate techniques to find dimensions in one set of variables, and then correlating dimension scores with items from the other set of variables post hoc (e.g., O’Leary et al., 2000; Woodward et al., 2003). For example, one could find orthogonal dimensions in the cognitive measures by using principal component analysis (PCA), and then perform a multiple regression using the cognition-based PCA scores as criterion (dependent) variables, and HE scale items as predictor (independent) variables. Although this PCA method uses dimensions of cognition that explain the maximum variance in the cognition variables, these dimensions are not optimized to be predictable from the HE items and will always be contaminated to some extent by variance 39 from other sources. Therefore, to find dimensions of cognition optimized to be predictable from HE scales, variance constraints must be used. Namely, multivariate multiple regression can be carried out prior to dimension reduction, allowing isolation of the variance in the cognitive measures that is predictable from the individual HE items, and then, PCA is applied to the predicted scores from the multivariate multiple regression. In this way, variance constraints are achieved by saving the set of predicted scores from a multivariate least-squares multiple regression prior to PCA. Applied to the current data, the advantage of CPCA is that it provides specific dimensions of cognition that are optimally linked to HE items, instead of providing dimensions that simply explain the most variance in cognition (which may or may not be related to hallucinations per se; Lavigne et al., 2013; Luk et al., 2018; Sanford & Woodward, 2017). This is a special case of a more general constrained principal component analysis framework (Takane & Hunter, 2001; Takane & Shibayama, 1991), a technique which combines multivariate multiple regression and PCA into a unified framework, applied here to find dimensions in cognitive measures that are optimized to be predictable from individual HE scale items. In this basic application of CPCA, the multivariate multiple regression and PCA steps are the standard applications, combined in sequence. Orthogonal dimensions in the criterion variables are extracted that are optimized to be predictable from a set of predictor variables. A schematic diagram depicting Step 1 (CPCA) is presented in Figure 3.1. The equations and further details of the method can be found in chapter 2. 40 In the current study, cognitive variables from five tasks were included: auditory signal detection, consonant-vowel dichotic listening, source monitoring, backwards digit span, and matrix reasoning. This involved three variables from the dichotic listening task (laterality indices for non-forced, forced left, and forced right conditions), nine from the source monitoring task (three correct and six incorrect counts), one from the matrix reasoning task (total score), four from the signal detection task (hit rate, false alarm rate, sensitivity and response bias), and the mean span metric from the backwards digit span task. All 18 task-based variables were available for 419 participants, so this led to the construction of the 419 × 18 criterion variable matrix (Z). The G matrix (i.e., the predictor variables) consisted of the HE questionnaire items. There are 32 items on the CAPS and 16 items on the LSHS-E. This led to the construction of the 419 × 48 predictor variable matrix (G). A scree plot (Figure 3.2) was used to determine the number of components to extract . Varimax rotation was performed on the extracted dimensions. All computations were performed using MATLAB R2019b software with in-house scripts. 41 Figure 3.1. Schematic depicting the steps involved in Step-1: Variance Constraints and Dimension Reduction through CPCA. Note: The Z matrix (and the resulting GC components) and G matrix differ between the preliminary application of Step 1 (using all of the cognitive measures and participants) and a subsequent application of Step 1 in (a) using half the number of participants, in the Z and G matrices, in the split-half reliability tests in Step 2, and (b) using all but one criterion variables in Z to estimate interpretable criterion variables, in Step 3. §In the final step of Step 3, Step 1 is performed, but component scores are recomputed using only a selected set of criterion variables. These recomputed scores are used to compute predictor loadings. 42 Figure 3.2. Scree plot for CPCA. Note: The scree plot is obtained by performing a PCA (or singular value decomposition) on the predicted scores matrix (GC). Based on this scree plot, 6 components were selected for further analyses (Cattell & Vogelmann, 1977). 3.2.4.1.2 Step-2: Identifying Reliable Predictor Loadings (HEs) To test the reliability of predictor loadings at the individual item level, we performed 1,000 iterations of a split-half reliability test. A schematic depicting the split-half reliability tests in Step-2 is presented in Figure 3.3. First, we aim to match the components across both the split halves and the full sample. In each iteration, the data (Z and G) were divided randomly into two non-0 5 10 15 20No. of components051015202530% variance explained 43 overlapping halves, GC was computed, and PCA was carried out on GC for each of the halves independently using the same CPCA analysis protocol as was carried out on the full sample (see section on Step-1; Figure 3.1), with the exception of the rotation. In place of varimax, orthogonal Procrustes rotation was performed separately on the resulting component loadings from each split half, in order to align them optimally with components of the full-sample CPCA (the latter providing the target for the former in the Procrustes rotation). The two sets of component loadings (one from each split-half) were then correlated, and component pairs with Pearson correlation coefficients >= 0.64 were deemed reliable. The threshold value of 0.64 was determined using a permutation test with p <= 0.005 as a criterion for significance (Benjamin et al., 2018). For more details, see section on Rationale for Thresholds, Component loading match correlation threshold (0.64). Following this, we attempted to match each reliable component pair to one from the full sample CPCA, since components can be split up or reordered. This was achieved by correlating the component loadings for a reliable split-half pair (averaged over the two split halves) with the set of component loadings from the full-sample CPCA. Correlations >= 0.64 were used to indicate a match. A component reliability proportion (CRP in Figure 3.3) was computed for each full-sample CPCA component as the proportion of the 1,000 iterations for which component pairs were not only deemed reliable, but also passed the criteria for being declared a match to one component from the full sample. Components with component reliability proportions (CRP) < 0.5 were rejected due to unreliable component loading structure (for more details on the choice of the threshold 0.5, see section on Rationale for thresholds, Component reliability proportion threshold (0.50)). 44 Next, we compute a reliability metric for each predictor loading, but only for components with component reliability proportions >= 0.5. To compute predictor loadings, component scores (√𝑁U) are first rotated based on the rotation transformation matrix computed in the previous section (through Procrustes rotation), and then correlated with the columns of G. These predictor loadings indicate the degree to which each predictor variable in G is related to each rotated component score U extracted in the PCA of GC. A predictor loading reliability proportion (PLRP in Figure 3.3) was computed as the proportion of the matched component pairs from the 1,000 iteration procedure that showed predictor loadings >= 0.19 in both split-half solutions, and this can be computed separately for positive (>= 0.19) and negative loadings (<= -0.19). This threshold of 0.19 is estimated using a permutation test with p <= 0.005 (Benjamin et al., 2018); for more details, see section on Rationale for thresholds: Predictor loading match correlation threshold (0.19). Predictor variables (SPV in Figure 3.3) with loading reliability proportions >= 0.48 were considered for interpretation (for rationale, see section on Rationale for thresholds: Predictor loading reliability proportion threshold (0.48)). For components with component reliability proportions < 0.5, the predictor loading reliability proportions are assigned as zero or n/a (as populated in Table A.3 and Table A.4). 45 Figure 3.3 Schematic depicting the steps involved in Step 2: Identifying Reliable Predictor Loadings (HEs). Step 1 = methodology described in Figure 3.1; CL = Component loading; PL = Predictor loading. Note: The Z matrix (and the resulting PLRP values) differ between the preliminary application of Step 2 (using all of the cognitive measures) and a subsequent application using the subset of criterion variables in Z are found to be reliable in Step 3. *Details regarding the choice of the thresholds can be found in the section on Rationale for Thresholds. ‘c’ and ‘p’ are index values for components and predictor variables respectively. 46 3.2.4.1.3 Step 3: Identifying Criterion Variables for Interpretation (Cognition) A schematic diagram depicting Step 3 is presented in Figure 3.4. CPCA provides component loadings that indicate the importance of each criterion variable (cognitive measures) for each component. Instead of interpreting all the loadings, we use a data-driven leave-one-out procedure to determine the sets of component loadings for interpretation with respect to the predictor variables. To determine this, we regress out each criterion variable (i), that is, one column in Z (Z{1:N}, i), from the remaining set of criterion variables (Z{1:N}, {1:Zdim} - i) and perform CPCA again, including recomputation of the predictor loading reliability proportions (PLRPi in Figure 3.4) similar to Step 2. For this analysis, we only consider the predictor loading reliability proportions for the predictor variables determined to be reliable at Step 2 (SPV in Figure 3.3), for each component. It is important to note that rules of Step 2 still apply in the recomputation of PLRPi values, i.e., PLRPi values for a component will be automatically assigned to zero if the component reliability proportion < 0.5, when a variable of interest (i) is regressed out of Z. We compute the mean predictor loading reliability proportion (PLRPi) across only the set reliable predictor variables deemed reliable in Step-2 (SPV), with the influence of each criterion variable (i) removed for each component, as plotted in Figure 3.5. The average predictor loading reliability proportion reductions induced when criterion variables are regressed out are used to help determine which criterion variables can be interpreted to convey the overlap between the two sets of variables. This is similar to selecting components based on a scree plot (Cattell & Vogelmann, 1977). 47 As a final step, we re-run the three-step CPCA analysis (Steps 1 and 2), but the component scores are recomputed (CSCV) corresponding to the component loadings for only the set of selected criterion variables (CV). The component scores are recomputed using the following equations: CSCV = GC * WCV WCV = √𝑁V/D ⊙ MCV where, GC = regression-based predicted score matrix; WCV is the unmixing weight matrix where only the selected criterion variable entries are non-zero; N = sample size (419); V is the matrix of right singular vectors from PCA on GC; D is the diagonal matrix from PCA on GC; ⊙ is dot multiplication operator that performs element-wise multiplication between two matrices; MCV is the selection matrix populated with 1s and 0s, the entries corresponding to the selected criterion variables for each component are marked as 1, and the rest as 0. The recomputed component scores are used to estimate the predictor loadings (same as Step 1). The procedure for estimating predictor loading reliability proportions for the selected set of criterion variables (PLRPCV in Figure 3.4) remains the same as described in Step 2, but instead of using regular component scores, the recomputed scores are used, as described above. Based on this, we can interpret the set of predictor and component loadings that were reliable in both of the CPCA analyses; one with the full set and the other with only the selected set of criterion variables. The 3-Step CPCA method put forward here allows exploration at the level of individual items, achieved through variance constraints, dimension reduction, split-half reliability, and permutation tests. Compared to factor-based structural equation modeling (SEM), CPCA allows the components to be formed based on the extracted signal, as opposed to hypothesizing latent factors 48 although often the final latent factor model is often formed by following data-driven modification indices that could be described as exploratory (Joreskog, 1970; MacCallum & Austin, 2000). Other concerns with latent-variable SEM that are not shared by component-based methods include: (1) latent variable scores are not unique such that different scores can lead to the same model fit, known as factor score indeterminacy, (2) frequent problems of non-convergence, or convergence to improper solutions (e.g., negative variance estimates), and (3) relatively stringent distributional assumptions, such as the multivariate normality of observed variables (Hwang et al., 2010). 49 Figure 3.4. Schematic depicting the steps involved in Step 3: Identify Criterion Variables for Interpretation (Cognition). Note: Step 1 = methodology described in Figure 3.1; Step 2 = methodology described in Figure 3.3; PV = Predictor variable; PL = Predictor loading; PLRP = Predictor loading reliability proportion. ‘c’ and ‘p’ are index values for components and predictor variables respectively. SPV{c} = set of reliable predictor variables for component c, estimated in Step 2. *Details regarding the choice of the thresholds can be found in the section on Rationale for Thresholds. Step 1§ is the condition where recomputed component scores for the selected set of criterion variables, are used to compute predictor loadings; as depicted in Figure 3.1. Step 2§ is same as Step 2 depicted in Figure 3.3, but during the reapplication of Step 1, recomputed component scores, for selected criterion variables, are used to compute predictor loadings as depicted in Step 1§. 50 3.2.4.2 Rationale for Thresholds 3.2.4.2.1 Component loading match correlation threshold (0.64) In Step 2 of the reliability tests, two sets of component loadings (one from each split-half) were correlated to find reliable component pairs. Pairs with Pearson correlation coefficients >= 0.64 were deemed reliable. This threshold value of 0.64 was determined using a permutation test, where two pseudorandom data vectors of the same size as the number of cognitive measures (18) were correlated. 10,000 pairs of pseudorandom data vectors were drawn from a standard normal distribution, and Pearson correlation coefficients were calculated for each pair. This set of correlation coefficients formed the null distribution. The threshold was defined such that only 0.5% of the permutations will have higher correlation coefficients than the threshold (p <= 0.005) (Benjamin et al., 2018). 3.2.4.2.2 Component reliability proportion threshold (0.50) In Step 2, components with component reliability proportions < 0.50 were rejected. This threshold is arbitrary and was chosen to ensure that at least 50% of the 1000 split-half component pairs were available to estimate predictor loading reliability proportions, which is a proportion of only the matched component pairs. This ensures that, at minimum, 500 (50%) iterations of the split-half tests will be used to compute predictor loading reliability proportions. 3.2.4.2.3 Predictor loading match correlation threshold (0.19) In Step 3 of the reliability tests, the predictor loading reliability proportions were computed as the proportion of the matched component pairs from the 1,000-iteration procedure that showed 51 predictor loadings >= 0.19. This threshold value of 0.19 was estimated using a permutation test, where two pseudorandom data vectors of the same size as participants in the split-half test (209) as the component scores (or the G matrix) were correlated. 10,000 pairs of pseudorandom data vectors were drawn from a standard normal distribution, and Pearson correlation coefficients were calculated for each pair. This set of correlation coefficients forms the null distribution. The threshold is defined such that only 0.5% of the permutations will have higher correlation coefficients than the threshold (p <= 0.005) (Benjamin et al., 2018). 3.2.4.2.4 Predictor loading reliability proportion threshold (0.48) In Step 3 of the reliability tests, predictor loading reliability proportions were estimated for each predictor item. We interpret items with predictor loading reliability proportions >= 0.48. This threshold of 0.48 was calculated using a permutation test, where the rows of the predictor matrix of HE items (G matrix) were randomly permuted, and all the three steps of CPCA analysis is performed on Z and the permuted G matrix, and the predictor loading reliability proportions were computed for each of the permuted G matrices. We tested 1,000 permutations of the G matrix. The threshold is set such that only 0.5% of the predictor loading reliability proportions are greater than the threshold (p <= 0.005) (Benjamin et al., 2018). 52 3.3 Results 3.3.1 Step 1: Variance Constraints and Dimension Reduction through Constrained Principal Component Analysis (CPCA) CPCA was performed with 18 cognitive measures as the criterion variables and 48 HE questionnaire items as the predictor variables. The multivariate overlap between cognition and HEs revealed that HE items accounted for 13% of the total variance of the cognition variables, and six components (determined by the scree plot, Figure 3.2, Cattell & Vogelmann, 1977) were extracted from PCA on the predicted score matrix of cognition variables. These six components captured 77.02% of the variance in the set of predicted scores and were varimax rotated. 3.3.2 Step 2: Identifying Reliable Predictor Loadings (HEs) The component loadings for all six extracted components are presented in Table 3.1. A split-half reliability followed by matching of component loadings determined that component 6 should be excluded from further interpretation due to a low component reliability proportion score. An example correlation matrix from one of the 1,000-iteration reliability iterations is shown in Table A.1 and the component reliability proportions that resulted from completion of the reliability and match process are presented in Table A.2. Table 3.2 lists all predictor loadings for the full sample (relating HE variables to components). Split-half permutation tests for predictor loadings served to identify those predictor loadings that reliably loaded onto the CPCA components, and these predictor loading reliability proportions are presented in Table A.3 (positive loadings) and Table A.4 (negative loadings). Reliable predictor loadings are listed in Table 3.3 and are indicated by bold font and cell borders in Table 3.2, based on positive predictor loading reliability proportions 53 tabulated in Table A.3. All negative predictor loading reliability proportions were extremely low, and therefore no negative predictor loadings were interpreted. Table 3.1. Component loadings for the predicted (GC) solution. Components 1 2* 3* 4 5 6 Dichotic Listening (DL) Laterality Indices Non-forced -0.03 0.09 -0.23 -0.05 -0.01 0.15 Forced left 0.03 0.07 0.24 -0.12 0.05 0.16 Forced right 0.06 -0.05 -0.31 -0.01 0.02 -0.03 Source Memory Task (SM) Measures (Source - Response) Hear - Hear 0.12 -0.01 -0.04 -0.01 0.29 -0.01 Hear - Imagine -0.25 -0.08 0.04 0.11 -0.17 0.03 Hear - New 0.13 0.11 0.01 -0.11 -0.19 -0.03 Imagine - Imagine 0.02 -0.01 0.03 0.03 0.21 0.17 Imagine - Hear -0.02 0.03 -0.01 -0.05 0.01 -0.27 Imagine - New -0.01 -0.01 -0.03 -0.00 -0.26 0.03 New - New 0.34 0.08 0.02 0.15 0.03 0.08 New - Hear -0.11 0.01 -0.01 -0.33 0.01 -0.08 New - Imagine -0.33 -0.10 -0.02 0.00 -0.04 -0.05 Matrix Reasoning (MR) MR Score 0.21 0.02 -0.14 0.11 -0.04 -0.08 Digit Span (DS) Mean Span -0.03 0.13 -0.03 0.15 0.06 -0.01 Signal Detection Task (SgD) Hit Rate 0.13 0.32 -0.02 0.07 0.07 -0.05 False Alarm Rate 0.12 0.35 -0.01 -0.04 -0.03 0.04 Sensitivity (dˈ) -0.01 -0.20 -0.03 0.07 0.1 -0.05 Response bias (β) -0.03 -0.29 -0.03 -0.06 -0.01 0.04 54 Note. *Components that were deemed reliable according to the component reliability proportions presented in Table A.2 and predictor loading reliability proportions in Tables A.3 and A.4. Component reliability proportions for components 1-6 are as follows – 1.00, 1.00, 0.83, 0.64, 1.00, and 0.35. Dominant component loadings, determined in Step 3, are highlighted as bold. CPCA requires Table 3.2 (component loadings) and Table 3.3 (predictor loadings) to be interpreted in conjunction. Table 3.2. Predictor loadings for the predicted (GC) solution. Components 1 2* 3* 4 5 6 CAPS Questionnaire Items CAPS Item 1: Do you ever notice that sounds are much louder than they normally would be? 0.14 0.19 0.19 -0.08 -0.08 0.12 CAPS Item 2: Do you ever sense the presence of another being, despite being unable to see any evidence? 0.01 0.32 0.13 -0.19 -0.08 -0.22 CAPS Item 3: Do you ever hear your own thoughts repeated or echoed? 0.04 0.11 0.26 0.08 -0.03 0.03 CAPS Item 4: Do you ever see shapes, lights or colours even though there is nothing really there? -0.09 0.12 0.11 0.12 -0.08 0.06 CAPS Item 5: Do you ever experience unusual burning sensations or other strange feelings in or on your body? 0.06 0.11 -0.19 0.02 -0.27 -0.07 CAPS Item 6: Do you ever hear noises or sounds when there is nothing about to explain them? 0.14 0.02 0.24 -0.05 -0.2 0.16 CAPS Item 7: Do you ever hear your own thoughts spoken aloud in your head, so that someone near might be able to hear them? 0.15 0.03 0.29 0.00 -0.09 0.10 CAPS Item 8: Do you ever detect smells which don't seem to come from your surroundings? 0.23 0.17 0.25 -0.05 -0.21 -0.04 CAPS Item 9: Do you ever have the sensation that your body, or a part of it, is changing or has changed shape? -0.03 -0.07 0.05 0.20 -0.07 -0.02 CAPS Item 10: Do you ever have the sensation that your limbs might not be your own or might not be properly connected to your body? 0.16 0.25 -0.12 0.22 -0.01 0.14 55 CAPS Item 11: Do you ever hear voices commenting on what you are thinking or doing? 0.22 -0.12 0.12 -0.14 -0.1 0.08 CAPS Item 12: Do you ever feel that someone is touching you, but when you look nobody is there? -0.06 0.11 0.03 0.09 -0.1 0.08 CAPS Item 13: Do you ever hear voices saying words or sentences when there is no-one around that might account for it? 0.13 0.48 -0.13 -0.05 -0.05 0.25 CAPS Item 14: Do you ever experience unexplained tastes in your mouth? -0.02 0.22 0.20 0.10 0.06 -0.02 CAPS Item 15: Do you ever find that sensations happen all at once and flood you with information? 0.19 0.14 0.39 0.12 -0.08 0.08 CAPS Item 16: Do you ever find that sounds are distorted in strange or unusual ways? -0.02 0.24 0.18 0.01 -0.09 0.08 CAPS Item 17: Do you ever have difficulty distinguishing one sensation from another? 0.24 0.28 0.26 0.12 0.03 -0.05 CAPS Item 18: Do you ever smell everyday odours and think that they are unusually strong? 0.04 0.21 0.04 0.06 -0.36 -0.01 CAPS Item 19: Do you ever find the appearance of things or people seems to change in a puzzling way, e.g. distorted shapes or sizes or colour? -0.11 0.30 0.12 -0.17 0.00 0.04 CAPS Item 20: Do you ever find that your skin is more sensitive to touch, heat or cold than usual? 0.04 -0.07 0.02 0.03 0.17 0.21 CAPS Item 21: Do you ever think that food or drink tastes much stronger than it normally would? 0.13 -0.01 0.13 0.20 0.13 -0.35 CAPS Item 22: Do you ever look in the mirror and think that your face seems different from usual? -0.10 0.16 0.09 0.11 0.15 0.06 CAPS Item 23: Do you ever have days where lights or colours seem brighter or more intense than usual? -0.01 0.07 0.04 0.03 -0.04 -0.04 CAPS Item 24: Do you ever have the feeling that of being uplifted, as if driving or rolling over a road while sitting quietly? 0.20 0.33 -0.10 0.04 -0.02 -0.03 CAPS Item 25: Do you ever find that common smells sometimes seem unusually different? -0.02 0.23 0.15 0.21 -0.24 0.09 CAPS Item 26: Do you ever think that everyday things look abnormal to you? 0.19 0.41 0.19 -0.22 0.09 0.20 CAPS Item 27: Do you ever find that your experience of time changes dramatically? 0.15 0.10 0.03 0.10 0.19 -0.01 CAPS Item 28: Have you ever heard two or more 0.15 0.15 0.03 -0.04 0.15 0.16 56 unexplained voices talking with each other? CAPS Item 29: Do you ever notice smells or odours that people next to you seem unaware of? 0.06 0.20 0.01 0.07 -0.12 -0.20 CAPS Item 30: Do you ever notice that food or drink seems to have an unusual taste? -0.12 0.14 0.17 0.09 -0.11 -0.16 CAPS Item 31: Do you ever see things that other people cannot? 0.30 0.03 0.17 0.23 -0.18 0.21 CAPS Item 32: Do you ever hear sounds or music that people near you don't hear? 0.28 0.29 0.01 0.14 -0.05 0.02 LSHS-E Questionnaire Scores LSHS-E Item 1: Sometimes a passing thought will seem so real that it frightens me 0.03 0.21 0.26 -0.14 -0.07 -0.03 LSHS-E Item 2: Sometimes my thoughts seem as real as actual events in my life -0.02 0.21 0.24 0.03 -0.15 0.03 LSHS-E Item 3: No matter how hard I try to concentrate on my work unrelated thoughts always creep into my mind -0.10 0.01 0.11 0.08 -0.12 0.13 LSHS-E Item 4: In the past, I have had the experience of hearing a person’s voice and then found that no one was there 0.03 0.30 0.10 0.13 0.09 0.12 LSHS-E Item 5: The sounds I hear in my daydreams are generally clear and distinct 0.15 0.10 0.23 -0.07 0.25 0.04 LSHS-E Item 6: The people in my daydreams seem so true to life that I sometimes think that they are 0.04 0.20 0.35 0.17 0.08 0.11 LSHS-E Item 7: In my daydreams I can hear the sound of a tune almost as clearly as if I were actually listening to it 0.02 0.02 0.19 0.04 0.09 0.05 LSHS-E Item 8: I often hear a voice speaking my thoughts aloud 0.09 0.00 0.06 -0.09 -0.17 -0.05 LSHS-E Item 9: I have been troubled by hearing voices in my head 0.25 0.36 0.24 -0.19 -0.12 -0.05 LSHS-E Item 10: On certain occasions, I have seen the face of a person in front of me, but there was no one 0.04 0.17 0.33 0.01 0.04 0.33 LSHS-E Item 11: Sometimes, immediately prior to falling asleep or upon awakening, I have had the experience of having seen or felt or heard something or someone that wasn’t there or the feeling of being touched even though no one was there 0.05 0.04 -0.07 -0.36 0.00 0.19 LSHS-E Item 12: Sometimes, immediately prior to 0.04 0.09 -0.19 0.07 0.10 -0.09 57 falling asleep or upon awakening, I have had a sensation of floating or falling or that I left my body temporarily LSHS-E Item 13: On certain occasions I have had the feeling of the presence of someone close who has deceased -0.15 -0.01 0.25 -0.19 0.03 -0.09 LSHS-E Item 14: In the past, I have smelt a particular odour when there was nothing there -0.05 0.21 0.34 -0.12 -0.05 -0.12 LSHS-E Item 15: I have had the feeling of touching something or being touched and then found that nothing or no one was there 0.15 0.11 0.11 -0.09 -0.07 0.00 LSHS-E Item 16: Sometimes I have seen things or animals when nothing was in fact there -0.23 0.19 0.06 -0.01 -0.04 0.15 Note: *Components that were deemed reliable according to the component reliability proportions presented in Table A.2 and predictor loading reliability proportions in Tables A.3 and A.4. Reliable predictor loadings are highlighted in bold font and cell borders, and this is based not on the magnitude seen in this table, but on the reliability proportions for positive and negative predictor loadings presented in Table A.3 and A.4 respectively. Component 2 corresponds to lower sensitivity and more liberal responses in the auditory signal detection task and Component 3 is associated with reduced laterality measured by the dichotic listening task. Component 6 is not interpreted due to low component reliability proportions (see Table A.2). Components 1, 4, and 5 are not interpreted due to low predictor loading reliability proportions (see Table A.3 and A.4). CPCA requires Table 3.2 (component loadings) and Table 3.3 (predictor loadings) to be interpreted in conjunction. CAPS = Cardiff Anomalous Perceptions Scale; LSHS-E = Launay-Slade Hallucination Scale - Extended. Table 3.3. Summary of component characteristics and interpretations. Dominant component loadings (Cognitive Variables) Reliable predictor loadings (HE Variables) Interpretation Component 2 SgD Hits (.32) SgD False alarms (FA) (.35) SgD Sensitivity (dˈ) (-.20) SgD Response bias (β) (-.29) CAPS 13: Hear voices (.48) CAPS 26: Things look abnormal (.41) LSHS-E 9: Troubled by voices (.36) Liberal SgD/ perceptual distortions 58 Component 3 DL Non-forced laterality index (-.23) DL Forced left laterality index (.24) DL Forced right laterality index (-.31) CAPS 15: Sensations flood (.39) Reduced laterality/ sensory overload Note. The component and predictor loading values (in parenthesis) are a measure of effect size. HE = hallucinatory experiences; SgD = signal detection; DL= dichotic listening; CAPS = Cardiff Anomalous Perceptions Scale; LSHS-E = Launay-Slade Hallucination Scale - Extended. 3.3.3 Step 3: Identifying Criterion Variables for Interpretation (Cognition) To determine sets of criterion variables for interpretation, using a leave-one-out procedure, we regressed out each criterion variable from the remaining set of criterion variables (cognitive measures) and recomputed the predictor loading reliability proportions, as described in Steps 1 and 2. The average predictor loading reliability proportions for all the reliable predictor loading items (determined on full Z matrix), after regressing out each criterion variable from the remaining set of criterion variables, is plotted in Figure 3.5, left panel, for Component 2 and right panel for Component 3 (the only two components with reliable predictor loadings computed on the full Z matrix). Components 1, 4, and 5 were not analyzed further due to having no reliable predictor loadings at Step 2, and Component 6 was rejected due to low component reliability proportions at Step 2. The criterion variables in Figure 3.5 are sorted left-to-right based on ascending values of mean predictor loading reliability proportions, averaged over all predictor loadings reliable at Step 2 (full Z matrix), once the criterion variable in question has been regressed out of the remaining criterion variables. Thus, the criterion variables that substantially reduce the mean predictor 59 loading reliability proportions when regressed out are selected for interpretation. For example, regressing signal detection false alarm rate out of all other criterion variables resulted in a reduction in the average reliability of the four full-Z-reliable predictor loadings (i.e., those that were reliable in the main analysis in Steps 1 and 2) to essentially zero (Figure 3.5), suggesting that false alarm rate must be retained. Using criteria similar to scree plots for component selection (Cattell & Vogelmann, 1977), we interpret the first 4 variables in Figure 3.5 as component loadings for Component 2 – signal detection false alarm rates, hits, response bias (β), and sensitivity (d’). Similarly, for Component 3, regressing dichotic listening forced right laterality index resulted in a reduction in the reliability of sensory overload (reliable in the main analysis) to essentially zero, suggesting that dichotic listening forced right laterality index must be retained, along with dichotic listening forced left laterality index, and dichotic listening laterality index. 60 Figure 3.5. Selection of criterion variables. Note: (left) Average predictor loading reliability proportions obtained by regressing each criterion variable out of the remaining criterion variables (see section on Step 3: Identifying Criterion Variables for Interpretation), for Component 2. For example, regressing SgD FA out of all other criterion variables resulted in a reduction in average reliability of all four-predictor loading (those that were reliable in the main analysis) to essentially zero, suggesting that SgD FA is essential to the dimensional structure of the results. Using a criterion similar to component selection in a scree plot (Cattell & Vogelmann, 1977b), we retain first 4 variables as dominant component loadings for Component 2 – SgD FA, hits, β, and d’. SgD = signal detection task; FA = False alarms; β = response bias; d’ = sensitivity. (right) Average predictor loading reliability proportions obtained when regressing each criterion variable out of the remaining criterion variables, for Component 3. For example, regressing DL forced-right laterality index out of all other criterion variables resulted in a reduction in reliability of sensory overload (reliable in the main analysis) to essentially zero, suggesting that DL forced right laterality index is essential to the dimensional structure of the results. We retain 3 variables – DL forced right laterality index, DL forced left laterality index, and DL non-forced laterality index. DL = dichotic listening task. 5 10 15 20Dominant criterion variable rankDominant criterion variable rankSdD FASdD HitsSdD βDL forced rightDL forced leftDLnon-forcedSdD d'00.20.40.60.8Avg. predictor reliability proportionFigure 1A: Component 25 10 15 2000.20.40.60.8Figure 1B: Component 3 61 3.3.4 Component Interpretation The interpretation of components is based on the information summarized in Table 3.3 and/or Figure 3.6. Interpretation is limited to Components 2 and 3 because these were the only ones with reliable predictor loadings (as described in Step 3). Component 2 was dominated in the cognition domain by loadings for auditory signal detection features: positive loadings for hits (r = 0.32) and false alarms (r = 0.35), and negative loadings for sensitivity (dˈ, r = -0.20) and response bias (β, r = -0.29). This indicates that high component scores corresponded to participants using a liberal criterion when detecting speech against background noise. This component was dominated in the HE domain by three predictor items, with two being related to auditory HEs: 'Do you ever hear voices saying words or sentences when there is no-one around that might account for it?’ (CAPS 13, r = 0.48) and ‘I have been troubled by hearing voices in my head’ (LSHS 9, r = 0.36), and the other one related to perceptual distortions: 'Do you ever think that everyday things look abnormal to you?' (CAPS 26, r = 0.41). The predictor item, ‘Do you ever sense the presence of another being, despite being unable to see any evidence?’ (CAPS 2, r = 0.32) was deemed reliable in Step 2, but did not pass the reliability test at Step 3 when only 4 criterion variables were selected, thus is not interpreted. Component 3 consisted of the dichotic listening measures. It had dominant positive component loadings for forced left laterality index (r = 0.24), and strong negative loadings for forced right laterality index (r = -0.31), and non-forced laterality index (r = -0.23). This indicates that higher scores on this component correspond to higher left-ear advantage, interpreted as reduced left-brain lateralization for phoneme detection. This component had high predictor loading reliability 62 proportions (see Table 3.3) for only one item: 'Do you ever find that sensations happen all at once and flood you with information?' (CAPS 15, r = 0.39). This indicates a link between reduced left-brain lateralization and feeling overwhelmed by an overload of sensory information. Components 1, 4, and 5 were dominated by component loadings for source-monitoring-based cognition measures. Although the component loading structures were reliable, no individual predictor loadings passed the reliability criteria for Components 1, 4, or 5 (see Table C.3 and C.4). As mentioned above, Component 6 was excluded from interpretation due to low component reliability proportions. 63 Figure 3.6. Dominant component and predictor loadings. Note: Dominant component loadings (circles and bold font) and predictor loadings (triangles and italic font) with Component 2 plotted against Component 3, for values displayed in Tables 3.1 and 3.2. C2 = Component 2; C3 = Component 3; SgD β = signal detection response bias; SgD dˈ = signal detection sensitivity; DL = dichotic listening; SgD Hits = signal detection hit rate; SgD FA = signal detection false alarm rate. Component loadings and predictor loadings must be interpreted in conjunction because they display different pieces of information about the same components. 3.4 Discussion In this international multisite study, the overlap between two sets of variables was investigated, one measuring cognition, and the other HEs. This overlap was studied at the level of individual items, and avoided reporting spurious results by using variance constraints, dimension reduction, 64 split-half reliability tests, and permutation tests. The results showed that HEs overlapped with cognition on two reliable dimensions: (1) HEs involving sensory distortions (hearing voices, troubled by voices, everyday things look abnormal) were associated with a lowered criterion for signal detection of auditory stimuli, and (2) HEs involving experiences of sensory overload were associated with reduced laterality in the dichotic listening task. Based on these results, the overlap between HEs and cognition variables can be conceptualized as bi-dimensional: one involving distortions/liberal signal detection, and the other involving overload/reduced laterality. The cognition aspect of Component 2 was composed of auditory signal detection measures, such that lower sensitivity (dˈ) and a lower response bias (β), and the ensuing lowered criterion for signal detection in cognition (higher hits and false alarms), were associated with modality-general HEs involving sensory distortions (hearing voices, troubled by voices, and everyday things look abnormal). In the pre-registered study (Moseley et al., 2021), one of the hypotheses was that false alarms would be positively associated with HEs, which was supported in that work by a correlation between false alarms and the CAPS summary score; in addition, significant correlations between the CAPS summary score and hit rate and response bias in signal detection were also reported, as was an association with sensitivity (the latter was non-significant, but also was reported to be not statistically equivalent to 0). Thus, the cognition side of the results (strong contributions for false alarms, hit rate and response bias, and weaker but still meaningful contributions for sensitivity) were similar to the previously reported results based on data collected in the same study (Moseley et al., 2021). However, using the current individual-item-level analysis allowed specification of the three HE items (collectively interpreted as perceptual distortions) that were underlying the 65 association between signal detection parameters and the CAPS summary score. This more refined result is novel relative to the literature, because all previous signal detection studies either (1) compared between schizophrenia and controls (Chhabra et al., 2016), (2) grouped participants based on scale summary scores (Barkus et al., 2007, 2011; Bentall & Slade, 1985; Rankin & O’Carroll, 1995), (3) grouped based on one general symptom rating scale item (Vercammen et al., 2008), or (4) correlated with/grouped based on scale summary scores (Moseley et al., 2016; Varese et al., 2012), meaning that the dimensional contribution of individual HE items has not previously been reported. The link between distorted perception and the signal detection parameters can be described as increased perceptualization (Beck & Rector, 2003), which can be explained by an increased overlap between signal and noise distributions, and compensated for by a more liberal decision criteria, and which may become exacerbated by the stress often associated with hallucinatory experiences (Beck & Rector, 2003). Accordingly, it has been demonstrated that fewer available cognitive resources, and a negative emotional state, lead to increased false alarms in signal detection tasks, and that the degree of certitude is correlated with a higher degree of hallucination proneness (Laloyaux et al., 2019). The cognition aspect of Component 3 involved dichotic listening measures, showing strong positive loadings for forced left laterality index, and strong negative loadings for forced right laterality index and non-forced laterality index, indicates that higher scores on this component correspond to reduced left-brain lateralization for phoneme detection. The HE aspect of this component involved feeling overwhelmed by sensory overload. In the pre-registered study (Moseley et al., 2021), effects for dichotic listening did not emerge, and the reliable effects 66 involving dichotic listening measures in the present set of results suggests that the CAPS and LSHS-E summed scores were less sensitive than the individual items, possibly leading to a Type II error with respect to a relationship between dichotic listening and HE in the pre-registered study. This result is novel relative to the literature because contribution of individual HE items in relation to cognition has not previously been reported. All previous dichotic listening studies focusing on hallucinations either (1) grouped participants based on scale summary scores (Conn & Posey, 2000), (2) grouped participants based on general symptom rating scale item/s, or (3) correlated with a general symptom rating scale item (Hugdahl et al., 2012, 2013; Hugdahl, Løberg, Jørgensen, et al., 2008; Hugdahl, Løberg, Specht, et al., 2008; Levitan et al., 1999; Løberg et al., 2004; Rominger et al., 2016). The current set of results suggests that reduced laterality measured from the dichotic listening task may index a property of the hallucinating brain that is associated with sensory overload. In addition to the “Sensations flood” CAPS item 15, two marginally sub-threshold (< .52) predictor loading reliabilities on Component 3 (see Table A.3) may assist with interpretation: “On certain occasions, I have seen the face of a person in front of me, but there was no one” (.46), and “The people in my daydreams seem so true to life that I sometimes think that they are” (.43). This provided a richer interpretation of the sensory overload interpretation, because these items overlap substantially with the absorption – dissociation spectrum of anomalous experiences (Carleton et al., 2010). Daydream-themed intensity is included in in the Tellegen Absorption Scale (TAS) (Jamieson, 2005) and the Dissociative Experiences Scale (DES) (Carlson & Putnam, 1993); specifically, ‘I find that I become so involved in a fantasy or daydream that it feels as though it 67 were really happening to me’ (DES 18), and ‘If I wish, I can imagine (or daydream) some things so vividly that they hold my attention as a good movie or story does (TAS 7)’. Previous work in non-clinical populations has suggested that psychosis-spectrum and dissociation-spectrum anomalous experiences may be co-present, but represent distinct constructs (Humpston et al., 2016). This interpretation of the results presented here suggests that dissociation-spectrum anomalous experiences related to sensory overload/vividness of daydreams might be associated with reduced laterality, whereas psychosis-spectrum experiences of voices are associated with liberal criterion when detecting speech against background noise. Several studies have suggested that the relationship between trauma and psychosis is mediated by dissociative processes (e.g., Perona-Garcelán et al., 2012; Sun et al., 2018), raising the possibility that reduced laterality of attentional processing is a candidate for a mediating mechanism, but that this would be related specifically to sensory overload/vividness aspect of the HE scales, not the three HE items (collectively interpreted as perceptual distortions (hearing voices, troubled by voices, and everyday things look abnormal). Previous studies have linked reduced laterality with hallucinatory experiences (Bless et al., 2015; Hugdahl et al., 2012; Ocklenburg et al., 2013). However, the use of summary scores may have obscured a more nuanced finding that it is specifically the experiences on the dissociation spectrum aspect of schizotypy, and not the psychosis aspect of schizotypy, that are associated with reduced laterality. Previous studies have shown links between hallucinations and liberal criterion during auditory signal detection task (Barkus et al., 2007; Rankin & O’Carroll, 1995); as well as reduced laterality of attentional processing during dichotic listening task (Hugdahl et al., 2012). The use of a single 68 aggregate score in these studies prevented the dimensional perspective of splitting HEs into psychosis-spectrum distortion experiences of voices on one hand and dissociation-spectrum sensory overload on the other. This demonstrates how using HEs aggregate scores may obscure more nuanced dimensional associations. Using novel methodology, we were able to specify that the overlap between the HEs and cognition variables can be conceptualized as bi-dimensional: HEs involving psychosis-spectrum distortions (including voices) underpinned by liberal criterion for signal detection in cognition, and dissociation-spectrum sensation overload underpinned by reduced laterality in cognition. We hypothesize that these two distinct mechanisms could explain multiple pathways to the development of HEs in different individuals: hallucinations involving psychosis-spectrum experiences underpinned by liberal criterion for signal detection, and dissociation-spectrum anomalous experiences like vivid daydreams and sensory overload, underpinned by reduced laterality of attention. In the future, these item-level hypotheses could be tested using the pre-registered approach. Moreover, researchers should also focus on longitudinal studies involving neuroimaging like electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), to better understand the neural correlates of multiple pathways of HE development and develop efficacious neuromodulation treatments. It should be noted that different sets of HE questionnaire items will be optimal for predicting distinct dimensions of criterion variables analyzed. Therefore, future research may benefit from an approach holding that (1) subscales of items (e.g., pre-set scales measuring HEs) need not be mandatory, and (2) sets of scale items of theoretical interest and empirical importance (e.g., items on HE scales) will change depending on the set of criterion variables analyzed. For example, 69 different sets of HE scale items would optimally predict personality, cognition, daily functioning, demographics, brain activity, and other general measures of mental/physical health, opening up the possibility for more expansive and comprehensive exploration of how the items captured on HE scales relate to the more complete experiences of individuals. 3.4.1 Limitations The main limitations of the three-step CPCA method include several critical issues. One major limitation is matching components across iterations. Performing dimensionality reduction multiple times poses a challenge, as components cannot be directly compared across different CPCA runs. For instance, the predictor loadings from any two iterations cannot be directly compared because the components in one iteration will not exactly match those in another (i.e., the component loadings differ). To address this, we used Procrustes rotation to align the component loadings in each iteration with the global component loadings. Only those iterations where the rotated component loadings significantly matched (with Pearson's correlation above a threshold) the global ones were considered, leading to another problem: too many arbitrary thresholds. At each analysis step, we had to determine the reliability of parameters, setting thresholds for component loading match correlation (0.64), component reliability proportion (0.5), predictor loading match correlation (0.19), and predictor loading reliability proportion (0.48). Although we provided rationales for these thresholds, a better solution could be found. Additionally, the issue of multiple comparisons arises when performing significance tests at various stages of the analysis. 70 While we use a conservative p-value of ≤0.005, a multiple comparison corrected p-value could be more appropriate. Overall, the three-step CPCA is our ad hoc approach to mitigate overfitting and false positives from using supervised methods. However, a more streamlined approach could be developed to address these limitations. 71 Chapter 4: Overlap between individual differences in cognition and symptoms of schizophrenia (Study 2) In this chapter, I address the limitations of the three-step CPCA method used in the previous chapter and develop an improved analysis pipeline. The major problem with the previous approach was matching components across iterations, which led to the use of many arbitrary thresholds throughout the analyses. To mitigate this issue, I vertically concatenated all the constrained matrices (GC) obtained in each iteration to form a large concatenated matrix. Instead of performing PCA on the individual matrix of each iteration, I now performed a single PCA on the concatenated matrix. This approach ensures that the component loadings for all iterations are matched, thereby preventing the need for arbitrary thresholds to determine whether components across iterations are matched. Additionally, I used the Benjamini-Hochberg correction for multiple comparisons to further minimize false positives. I applied this improved pipeline, referred to as iterative CPCA, to a sample of Schizophrenia spectrum disorder patients in the early stages of psychiatric treatment (n = 206) to determine the cognitive correlates of psychiatric symptoms measured by the Scale for the Assessment of Negative Symptoms (SANS) and the Scale for the Assessment of Positive Symptoms (SAPS). A preprint version of this chapter is available on PsyArXiV (Skiba et al., 2023): Skiba, R. M.*, Chinchani, A. M.*, Menon, M., Lepage, M., Lavigne, K., Malla, A., ... & Woodward, T. (2023). Overlap between individual differences in cognition and all SANS and SAPS symptoms of schizophrenia. Also, a modified version has been published (Skiba et al., 2024): Skiba, R. M.*, 72 Chinchani, A. M.*, Menon, M., Lepage, M., Lavigne, K. M., Malla, A., ... & Woodward, T. S. (2024). Overlap between individual differences in cognition and symptoms of schizophrenia. Schizophrenia research, 270, 220-228, Copyright Elsevier. *These authors contributed equally. 4.1 Introduction Schizophrenia spectrum disorders (SSDs) are a group of brain disorders characterized by hallucinations and delusions, disorganized speech and actions, and negative symptoms (Diagnostic and Statistical Manual of Mental Disorders, 2013). Cognitive deficits are considered a core aspect of SSD, particularly in attention, processing speed, verbal learning, and working memory (Heinrichs, 2001; Heinrichs & Zakzanis, 1998; Kahn & Keefe, 2013). The overlap between psychotic symptoms and cognition in SSDs is of interest to the field in that elucidating the biological underpinnings that may be responsible for this overlap can potentially provide new symptom-specific treatment targets for medication and/or neuromodulation (Tseng et al., 2022). Reviews of studies investigating the overlap between individual differences in cognitive impairment and psychotic symptoms indicate that hallucinations and delusions are not correlated with performance on standard neurocognitive tests (Dominguez et al., 2009; Harvey et al., 2006; Pillny et al., 2022; Toh et al., 2020; Ventura et al., 2009, 2010). In contrast, negative symptoms and disorganization have been reported to be associated with neurocognitive measures such as attention, processing speed, reasoning and problem-solving, verbal/visual memory, and working memory (Aleman et al., 1999; Bagney et al., 2015; Dominguez et al., 2009; Lepage et al., 2021; O’Leary et al., 2000; Pillny et al., 2022; Ventura et al., 2009, 2010). However, the overlap has also 73 been reported as restricted to social cognition (Yolland et al., 2021), and results are often mixed with respect to the specificity of negative symptoms versus disorganization (Harvey et al., 2006; Ventura et al., 2009; Yolland et al., 2021). The main purpose of the current study is to explore the dimensions of cognition and how they relate to psychotic symptoms. In a study examining the dimensions of a set of variables, such as cognition, it is important to optimize these dimensions to be the overlapping set of variables, such as psychotic symptoms and their severity. For instance, in the analysis of cognitive test batteries, the first step is typically principal component analysis (PCA), used to determine the dominant dimensions of the cognitive test battery; alternatively, summary scores are computed based on the assumed dimensions (August et al., 2012; Bagney et al., 2015; Good et al., 2004; Kern et al., 2008; McDowd et al., 2011; Yolland et al., 2021). Although these components (or summary scores) would be optimized to index the primary dimensions in the cognitive test scores without consideration of any other set of overlapping variables, they would not be optimized to index the primary dimensions in the portion of the variance of the cognitive test scores that overlaps with ratings of symptom severity, or of any other set of variables measured on the same sample. The latter always differs from the former, sometimes substantially (Hunter & Takane, 2002; Takane & Hunter, 2001). Two steps must be employed to index the primary dimensions in the cognitive test scores that are optimized to be overlapping with symptom severity ratings; namely, multivariate multiple regression in step one, to constrain the variance in cognitive test scores to that overlapping with symptom severity ratings, and PCA in step two, carried out on the variance-constrained cognitive test scores. 74 Bagney and colleagues (Bagney et al., 2015) reported on the overlap between cognition and symptom severity using the summary score methodology. Based on the recommendations of MATRICS Consensus Cognitive Battery (MCCB) (Kern et al., 2008; Nuechterlein et al., 2008), they computed summary scores for seven neurocognitive domains: Speed of Processing, Attention/Vigilance, Working Memory, Verbal Learning, Visual learning, Reasoning and Problem-solving, and Social Cognition. Bagney et al. (2015) also used the Positive and Negative Symptom Scale (PANSS) (Kay et al., 1987) to measure symptoms by computing summary scores based on the five-factor NIMH consensus model for symptom domains (i.e., Positive, Negative, Cognitive, Excited and Depressed factors) (Wallwork et al., 2012). The authors concluded that there is a small to moderate significant association between the PANSS Cognitive factor and MCCB neurocognitive domains of Processing Speed, Working Memory, and Verbal Learning (Bagney et al., 2015). Although using summary scores is common and valid, it restricts analyses to the variance common to all aggregated variables, neglecting the specific variance independently measured by each scale item (Chinchani et al., 2021). Close inspection of the set of results from Bagney and colleagues’ (Bagney et al., 2015) reveals how reliance on summary scores leaves some questions unanswered. For example, some of the other PANSS factors were very close to the correlation cut-off for significance (r = .24), such as Verbal Learning with the PANSS Negative factor (r = 0.23) and the Social Cognition with the PANSS Depressed factor (r = 0.23). Thus, there could have been individual cognitive tests or individual symptom items underlying these statistically borderline 75 correlations which, if optimized to overlapping variance, may have shown a stronger relationship with cognition. This tradition of using summed aggregate scores when studying associations between symptoms and cognition is likely due to concerns regarding Type I errors, which would affect multiple tests of statistical significance if each variable was individually analyzed (Chinchani et al., 2021). The methodology introduced here allows the study of the overlap between cognition and symptoms at the level of individual items without an increased concern over Type I errors. We analyzed a subset of already published data (Lepage et al., 2021), and instead of using summary scores, components of cognition were optimized to overlap with all items from the SANS and SAPS symptom rating scales (Andreasen, 1984, 1989) To achieve this, we applied an iterative application of Constrained Principal Component Analysis (CPCA) (Chinchani et al., 2021; Hunter & Takane, 2002; Takane & Hunter, 2001) which combines multivariate multiple regression and principal component analysis (PCA) into a unified framework, and uses iterative methodology to determine reliability of the conclusion regarding overlap between sets of variables. 4.2 Methods 4.2.1 Participants This analysis involved 206 participants (Mean age = 23.03, SD = 4.00, 140 males and 66 females) who were a subset of an already published data set (n = 435) described in detail elsewhere (Lepage et al., 2021). Due to the multivariate nature of the analysis, we could only include participants who completed a full set of cognitive measures (18 cognitive measures listed in Table 4.1) and symptom 76 rating scales (58 items from SANS and SAPS, see Table 4.4 and Table 4.5). Age, years of education, and IQ scores are presented in Table 4.6. Nearly 40% of participants from the original data set (n = 435) were missing some cognitive tasks only, 6.2% were missing some of the symptom items only, and 4.7% were missing some of both, resulting in a final sample size of 206. In this sample, 60% (n = 125) of participants were diagnosed with Schizophrenia/Schizophreniform Disorder, 28% (n = 57) with Affective Disorders with Psychosis, and 12% (n = 24) with Delusional Disorder/Psychosis. The participants were diagnosed at the Prevention and Early Intervention Program for Psychoses (PEPP-Montreal) in Montreal, Canada. The Research Ethics Boards approved the research protocols of the Douglas Mental Health University Institute and the McGill University Faculty of Medicine. 4.2.2 Cognitive measures In the current study, we included many of the same neurocognitive tests reported by Lepage and colleagues (Lepage et al., 2021). We used only raw scores without any standardization or correction for demographic variables. We used the number of correct trials for most of the cognitive measures. However, we used the completion time for Trail Making Test Part A (TMT-A) and Trail Making Test Part B (TMT-B). Therefore, a lower score on these two measures reflects better performance. The complete list of cognitive domains, tests, and descriptions is presented in Table 4.1. Z-score normalized histograms for each cognitive measure are shown in Figure B.1. 77 Table 4.1. Measures of cognition included in the current analysis. Cognitive domains Name of test Description of the main task Processing speed Neutral Stroop Color Naminga Naming the color of ink patches for 45 sec Processing speed Congruent Stroop Word Readinga Reading words written in the congruent ink color from a list for 45 sec Processing speed Trial Making Test Part Ab Connecting numbered dots in ascending order as quickly as possible Sustained attention Incongruent Stroop Color Naminga Naming the ink color of color words written in the incongruent ink color for 45 sec Executive functions Processing speed Trail Making Test Part Bb Connecting numbered and lettered dots in an alternating sequence as quickly as possible Sustained attention Processing speed Digit Symbolc Drawing the symbol that is matched to nine numbers as quickly as possible for a series of numbers Sustained attention D2 Sustained Attention Testd Identifying a target letter (letter d with two marks of any kind, such as lines or dots) surrounded by distractors and crossing it out Executive functions Motor operations Block designc Copying a pattern formed by colored blocks (full white, full red, half red and half white) Verbal working memory Digit Spanc Recalling the digits' names in both forward and backward orders in which they were presented aloud. A difference score was used, a difference between the forward and backward trials. Visual working memory Spatial Spanc backward and forward Recalling the color and position of squares in both forward and backward orders. Both forward and backward trials were included in the analysis. 78 Verbal working memory Logical Memoryc immediate, delayed and recognition trials Repeating words from a story immediately (Immediate), and with a 20-30 min delay (Delayed), and recognizing them (Recognition) Visual working memory Visual Reproductionc immediate and delayed trials Reproducing (drawing) figures from a test page immediately (Immediate), and with a 20-30 min delay (Delayed). a (Stroop, 1935); b (Reitan, 1986); c(Wechsler, 2001); d (Brickenkamp & Zillmer, 1998) 4.2.3 Symptom rating scales The Scale for the Assessment of Negative Symptoms (SANS, Andreasen, 1989) consists of 25 items grouped into five global categories: flat affect, alogia, apathy, anhedonia, and attention. The Scale for the Assessment of Positive Symptoms (SAPS, Andreasen, 1984) consists of 34 items grouped into four global categories: hallucinations, delusions, bizarre behavior, and formal thought disorder, expressed as observable behavior rated on a six-point scale from absent (0) to severe (5). Table 4.2 shows both total scores and global symptom values for the patients included in the current analyses. However, for our analysis, we use the data at the level of individual items. SAPS item 32 was not used for analysis because it had zero variance. Histograms for each SANS and SAPS item are shown in Figure B.2 and Figure B.3 respectively. 79 Table 4.2. Symptom rating scales summary and total scores of SANS and SAPS for current sample (n=206). Factor Mean SD SANS Total 33.08 17.09 Flat affect 8.68 7.37 Alogia 3.11 3.59 Apathy 8.47 4.38 Anhedonia 9.98 5.06 Attention 2.85 3.05 SAPS Total 8.87 11.15 Hallucinations 3.33 5.61 Delusions 3.62 5.09 Bizarre Behavior 1.76 2.64 Formal Thought Disorder 1.18 2.28 4.2.4 Data analysis 4.2.4.1 Need for reliability testing in CPCA CPCA is a technique that is used to infer links between two sets of variables (for details, see chapter 2). More specifically, it is a supervised dimensionality reduction technique that extracts low-dimensional component loadings (𝑉𝐷/√𝑛) and component scores (√𝑛 𝑈) from variance in the criterion variables (Z), such that the component scores are predictable from the predictor variables 80 (G). The links between criterion and predictor variables can be inferred by correlating the component scores (√𝑛 𝑈) with the predictor variables (G) to generate the predictor loadings (P). However, such an approach is circular, because the predictor variables (G) are used to estimate the component scores (√𝑛 𝑈), which then are correlated back with predictor variables (G) to compute predictor loadings. To minimize the number of false positives in such a supervised approach, in past published work we put forward a three-step procedure that used a split half reliability test to determine reliable predictor loadings (Chinchani et al., 2021). In this method, the data (Z and G) is split into two halves, and the analysis is run separately on each half. The results (predictor loadings, P) were compared to ensure that they are consistent and reliable. However, this procedure was affected by the uncertainty surrounding how to match the components between the split halves. In the current procedure, we overcome this uncertainty while still using the split-halves procedure to compare predictor loadings across halves to ensure that they are consistent and reliable. This process is repeated for 1000 iterations. With more reliability tests, this novel iterative version of CPCA is termed iterative CPCA (iCPCA). 4.2.4.2 Combining results from different iterations As described above, the CPCA analysis is performed 2000 times (2 halves x 1000 iterations). One of the challenges of performing dimensionality reduction multiple times is that one cannot directly compare components across different CPCA runs. For example, the results (predictor loadings) in any two iterations cannot be directly compared because the components in one iteration will not 81 exactly match the components in the other (i.e., the component loadings are different). Thus, to overcome this issue (Chinchani et al., 2021), we first vertically concatenate the GC matrices across all iterations to generate a concatenated GC matrix. The concatenated GC matrix has 1000*n (no. of iterations * no. of subjects) rows. Instead of performing PCA analysis on the individual GC matrix of each half/iteration as we did in past work (Chinchani et al., 2021), here we perform only one PCA analysis on the concatenated GC matrix. Such an approach ensures that the component loadings for all folds/iterations are matched. Then, the computed concatenated component scores matrix is split into component scores for each fold/iteration, and the predictor loadings are computed for each fold/iteration separately. The mean predictor loadings across all the folds/iterations, and the component loadings from the concatenated GC matrix are used to interpret the results. 4.2.4.3 iCPCA in detail This section describes the iCPCA methodology in detail (also see Figure 4.1). The entire data of criterion variables (Z! # $%&') and predictor variables (G! # (%&') are divided into two halves: ((Z1)!/* # $%&', (G1)!/* # (%&') and ((Z2)!/* # $%&', (G2)!/* # (%&'), where, n is the number of participants (206 in this case), zDim is the number of criterion variables (18 cognitive measures in this case), and gDim is the number of predictor variables (46 SANS+SAPS questionnaire items in this case). CPCA is run separately on each of the split halves to get the GC matrix for each of the halves. First half: (Z1)!/* # $%&'= (G1)!/* # (%&' (C1)(%&' # $%&' + (E1)!/* # $%&' 82 Where, (C1)(%&' # $%&' = (G1′G1)+,G1′Z1 Second half: (Z2)!/* # $%&'= (G2)!/* # (%&' (C2)(%&' # $%&' + (E2)!/* # $%&' Where, (C2)(%&' # $%&' = (G2′G2)+,G2′Z2 The above split half procedure is repeated for 1000 iterations, and the GC matrices are obtained for each half and each iteration (as shown in Figure 4.1A). The GC matrices for all halves and iterations are concatenated along the rows to form a concatenated GC matrix (see section on Combining results from different iterations and Figure 4.1B). (GC),---! # $%&'= ⎣⎢⎢⎢⎢⎢⎢⎢⎡ (𝐺,𝐶,)!/* # $%&'&./01.&2! ,(𝐺*𝐶*)!/* # $%&'&./01.&2! ,(𝐺,𝐶,)!/* # $%&'&./01.&2! *(𝐺*𝐶*)!/* # $%&'&./01.&2! *⋮(𝐺,𝐶,)!/* # $%&'&./01.&2! ,---(𝐺*𝐶*)!/* # $%&'&./01.&2! ,---⎦⎥⎥⎥⎥⎥⎥⎥⎤ PCA is performed on the concatenated GC matrix to generate component scores for each half/ iteration, and one common set of component loadings. (GC),---! # $%&' = (U),---! # 3 (D)3 # 3(V')3 # $%&' Where, k is the number if components selected. In the current study, 3 components were selected based on the scree plot (Cattell, 1966; Cattell & Vogelmann, 1977). The common component loadings (L) and the concatenated scores (S) are computed as follows: 83 (L)$%&' # ' = 1√1000𝑛 (V)$%&' # 3 (D)3 # 3 (S),---! # 3 = √1000𝑛 (U),---! # 3 The concatenated scores are split into component scores for each of the halves and iterations and are correlated with the G matrices to obtain predictor loadings (P) for each iteration and each half. ⎣⎢⎢⎢⎢⎢⎢⎢⎡ (𝑆,)!/* # 3&./01.&2! ,(𝑆*)!/* # 3&./01.&2! ,(𝑆,)!/* # 3&./01.&2! *(𝑆*)!/* # 3&./01.&2! *⋮(𝑆,)!/* # 3&./01.&2! ,---(𝑆*)!/* # 3&./01.&2! ,---⎦⎥⎥⎥⎥⎥⎥⎥⎤= (S),---! # 3 (𝑃,)(%&' # 3&./01.&2! , = (𝐺,)!/* # (%&'&./01.&2! , ⋆ (𝑆,)!/* # 3&./01.&2! ,(𝑃*)(%&' # 3&./01.&2! , = (𝐺*)!/* # (%&'&./01.&2! , ⋆ (𝑆*)!/* # 3&./01.&2! ,(𝑃,)(%&' # 3&./01.&2! * = (𝐺,)!/* # (%&'&./01.&2! * ⋆ (𝑆,)!/* # 3&./01.&2! *(𝑃*)(%&' # 3&./01.&2! * = (𝐺*)!/* # (%&'&./01.&2! * ⋆ (𝑆*)!/* # 3&./01.&2! *⋮ = ⋮(𝑃,)(%&' # 3&./01.&2! ,--- = (𝐺,)!/* # (%&'&./01.&2! ,--- ⋆ (𝑆,)!/* # 3&./01.&2! ,---(𝑃*)(%&' # 3&./01.&2! ,--- = (𝐺*)!/* # (%&'&./01.&2! ,--- ⋆ (𝑆*)!/* # 3&./01.&2! ,--- Where, the ‘⋆’ operator indicates Pearson’s correlation. The means of the predictor loadings (mean P, Figure 4.1B) averaged over all the split halves and iterations indicate the effect sizes. To determine reliable predictor loadings in each iteration, we check if predictor loadings in both split halves have a correlation coefficient greater than an optimized value which, in this case, was |r| ≥ 0.18 (see section on Significance test and optimization of the hyperparameter (r)). We represent the reliability of predictor loadings as reliability binary (RB) matrices, where reliable and unreliable predictor loadings are assigned a 84 value of ‘1’ and ‘0’, respectively. To determine the reliability of the predictor loadings across all the iterations, we computed a metric - predictor loading reliability proportions (PLRP, Figure 4.1B) - which is an average of the RB matrices across all iterations. In other words, for the current study, PLRP was the proportion of iterations that showed Pearson correlation r ≥ 0.18 in both split-half solutions. Figure 4.1. Diagram explaining steps involved in iCPCA. Note: A) In each split-half iteration, the cognitive measures (criterion variables, Z) and symptom items (predictor variables, G) were randomly split into two halves: (Z1, G1) and (Z2, G2). CPCA was performed on both halves independently to obtain GC matrices. This was repeated for 1000 iterations. B) GC matrices for both the halves and all 1000 iterations were vertically concatenated. PCA was performed on the concatenated GC matrix to obtain common component loadings (L) 85 and concatenated component scores (S) that were split and correlated with the corresponding G matrices to obtain predictor loadings (P) for each fold/iteration. Predictor loadings were averaged across folds/iterations to obtain mean predictor loadings (mean P). Predictor loading reliability proportions (PLRPs) were computed, for each element (r) in the P matrix, as the proportion of iterations for which the predictor loadings (P) in both the split halves was greater than or equal to 0.18 (optimized r value for this study, see section on Significance test and optimization of the hyperparameter (r) and Figure 4.2). 4.2.4.4 Significance test and optimization of the hyperparameter (r) To test the significance of the PLRP values, we perform a permutation test for 1000 random permutations. The rows of the G matrix are randomly permuted for each permutation, and the entire iCPCA analysis (as described above) is performed on the original Z and the permuted G matrix to generate a PLRP matrix. This procedure is repeated 1000 times. It is important to note that this is not the same as 1000 iterations of split-halves. In the permutation test, the 1000 iterations are performed to obtain a PLRP matrix for each permutation of the G matrix to form the null distribution. PLRP values (of the non-permuted iCPCA analysis) that passed the p ≤ 0.05, after correcting for multiple comparisons using the Benjamini-Hochberg correction with an FDR = 0.05, were deemed significant (Benjamini & Hochberg, 1995). Thus, we interpreted predictor loadings whose PLRP values were deemed significant in the permutation test. The PLRP null distribution generated above varies as a function of the hyperparameter, r. The PLRP null distributions for three different r-values are shown in Figure 4.2B-D. For example, if the r is very low (r = 0.04, see Figure 4.2B), then the null distribution will be shifted to the right. More specifically, there is a higher chance that the predictor loading values, generated from Z and the permuted G matrix, will be higher than r = 0.04 in both iterations of the split-half (just by 86 chance), and the null distribution will be skewed towards the ceiling value of 1. In this situation, the PLRP values corresponding to barely significant (p = 0.05; blue vertical line) and very significant (p = 0.001; red vertical line) will both correspond to very high PLRP values, leading to a collapse of the difference between the cut-offs for barely significant (p= 0.05) and very significant (p= 0.001) PLRP values, and this is not optimal for significance testing. Conversely, if the r-value is too high (r = 0.30, Figure 4.2D), then the null distribution is skewed to the left, and again leading to a collapse of the difference between the cut-offs for barely significant (p = 0.05) and very significant (p = 0.001) PLRP values, which is also not suitable for significance testing. Heuristically, we define the optimal r-value to have a maximum separation between the cutoffs for barely significant (p = 0.05) and very significant (p = 0.001) PLRP values (i.e. PLRP (p = 0.001) – PLRP (p = 0.05)). To find the optimal PLRP value cut-offs, we computed PLRP (p = 0.001) – PLRP (p = 0.05) for a range of r-values (from 0.04 to 0.30), and determine the optimal r-value by plotting this difference on the Y axis and the range of r-values along the X axis. As shown in Figure 4.2A, the optimal PLRP value cut-off in the current study was 0.18 (also see Figure 4.2C). Although we present the results for r = 0.18, a range of r-values around the optimal produced the same set of reliable predictor loadings (r in the range of from 0.16 to 0.20). 87 Figure 4.2. Optimization of the hyperparameter (r) Note: Optimization of the hyperparameter (r) based on predictor loading reliability proportions (PLRP), computed as the proportion of iterations that showed significant predictor loadings in both split-half solutions. A) Plot of PLRP (p=0.001) – PLRP (p=0.05) vs r-values. We defined optimal r-value to have a maximum separation between barely significant (p = 0.05) and significant (p= 0.001) PLRP values. For the current dataset, we obtained an optimal r=0.18 (Black vertical line). B-D) Null distributions were obtained using very liberal (B), optimal (C), and very conservative (D) r-values. Blue and red vertical lines represent the barely significant (p = 0.05) and very significant (p=0.001) PLRP values, respectively. 4.2.4.5 iCPCA interpretation Since the component and predictor loadings are correlation coefficients (Pearson's r), they also provide effect sizes because the loading value squared (r2) is the variance explained between variables, equivalent to the effect size used in the analysis of variance (Levine & Hullett, 2002). The mean of all predictor loadings across all the folds/iterations, and the component loadings from the concatenated GC matrix, are used as effect sizes to interpret the results. The component 88 loadings indicate the importance of each criterion variable for each component, and predictor loadings indicate the importance of each predictor variable for each component. Component loadings and predictor loadings must be interpreted in conjunction because they are different pieces of information about the same components. More specifically, component loadings and predictor loadings are computed as correlations with rotated component scores, but these correlations are computed with the variance-constrained cognition variables and the symptom rating variables, respectively. Since the component and predictor loadings are correlation coefficients (Pearson's r), they also provide effect sizes because the loading value squared (r2) is the variance explained between variables, equivalent to the effect size used in the analysis of variance (Levine & Hullett, 2002). The mean of all predictor loadings across all the folds/iterations, and the component loadings from the concatenated GC matrix, are used as effect sizes to interpret the results. The component loadings indicate the importance of each criterion variable for each component, and predictor loadings indicate the importance of each predictor variable for each component. Component loadings and predictor loadings must be interpreted in conjunction because they are different pieces of information about the same components. More specifically, component loadings and predictor loadings are computed as correlations with rotated component scores, but these correlations are computed with the variance-constrained cognition variables and the symptom rating variables, respectively. 4.2.4.6 Identifying the dominant component loadings CPCA provides component loadings that indicate the importance of each criterion variable (cognitive measures) for each component. The dominant loadings are conventionally interpreted 89 in PCA, often using an arbitrary threshold. With iCPCA, we employ a leave-one-out procedure to determine the importance of each criterion variable in a given component for determining the value of the significant predictor variables (estimated above). This step is performed on the concatenated GC matrix. The columns of the concatenated GC matrix correspond to the criterion variables. For determination of the dominant component loadings, each criterion variable was regressed out of the remaining criterion variables in the concatenated GC matrix (leave-one-out procedure for cognitive measures), and the component scores were recomputed. Then, the PLRP values were computed using the same procedure described above (see Figure 4.1). PLRP values were then re-computed with each criterion variable regressed out of the remaining criterion variables. When regressed out, the criterion variables which substantially reduced the mean PLRP of the significant predictor variables were considered dominant and were interpreted. To help determine this, we can rank all component loadings in dominance (from the greatest to the lowest reduction on the PLRP values for each iCPCA component), and check for breaks in dominance, analogous to the usage of scree plots. However, the final selection of component loading is, as is the case with PCA, to some degree arbitrary (note that this is not the case with the predictor loadings). 4.3 Results 4.3.1 iCPCA results The multivariate overlap between cognitive measures and symptom rating scale items was 60.45%, averaged across all 1000 iterations. We extracted three components from PCA determined by the scree plot (Cattell & Vogelmann, 1977). The components were varimax rotated. These three 90 components accounted for 62.09% of the symptom-constrained cognitive score variance averaged over all iterations (C1 = 23.14%, C2 = 14.72%, C3 = 24.23% for varimax-rotated components). Our process of component interpretation has been summarized in Figure 4.3, which shows selected criterion variables and reliable predictor variables associated with each component. Additionally, all 18 component loadings are listed in Table 4.3, and all 58 predictor loadings and scores are presented in Table 4.4 and Table 4.5. We relied on the permutation reliability percentage and multiple comparison correction tests to interpret reliable predictors. Component 1 (C1) was dominated by three variables: Logical Memory recognition (r = 0.72), immediate (r = 0.67), and delayed (r = 0.64). All three Verbal Logical Memory test trials assess verbal memory and short-term/working memory and long term/episodic memory. Participants are asked to recall a story read to them in three trials (immediate: immediately recall any words from the story; delayed: recall words after a delay; recognition: recognition of immediate and delayed recall, and recognition of story elements). We labelled it as C1 Verbal Memory. This component overlapped with nine SANS items and three SAPS items. To simplify interpretation, we grouped these overlapping symptoms into three categories. The first was Disorganized Communication, Language & Thought (including Positive Formal Thought Disorder) with three SAPS items: Illogicality (r = -0.35, PLRP = 97%, p ≤ 0.01), Derailment (r = -0.27, PLRP = 55%, p ≤ 0.05) and Tangentiality (r = -0.26, PLRP = 67%, p ≤ 0.05), and one SANS item: Inappropriate Affect (r = -0.26, PLRP = 68%, p ≤ 0.05). The second category was Impoverished Communication, Language & Thought (including Negative Formal Thought Disorder) with six SANS items: Global Rating of 91 Alogia (r = -0.34, PLRP = 97%, p ≤ 0.01), Increased Latency of Responses (r = -0.32, PLRP = 92%, p ≤ 0.01), Unchanging Facial Expression (r = -0.30, PLRP = 88%, p ≤ 0.01), Blocking (r = -0.28, PLRP = 76%, p ≤ 0.05), Poor Eye Contact (r = -0.27, PLRP = 74%, p ≤ 0.05), and Poverty of Speech (r = 0.26, PLRP = 69%, p ≤ 0.05). The third group, Inattentive, consisted of two SANS items: Global Rating of Attention (r = -0.32, PLRP = 91%, p ≤ 0.01; measuring both clinical and cognitive aspects of attention during the clinical interview) and Social Inattentiveness (r = -0.29, PLRP = 84%, p ≤ 0.01). Component 2 (C2) consisted of working memory measures: Digit Span Forward (r = 0.73) and Digit Span Backward (r = 0.72), Spatial Span Forward (r = 0.39) and Backward (r = 0.33). Digit Span is a verbal analog of the Spatial Span task measuring working memory performance by recalling digits or geometrical shapes (forward-span) or reversing order (backward-span). We labelled it as C2 Working Memory. C2 overlapped with two predictors shared with C1: Global Rating of Attention (r = -0.33, PLRP = 94%, p ≤ 0.01) and Social Inattentiveness (r = -0.25, PLRP = 71%, p ≤ 0.05). It distinctly overlapped with two items related to the Impoverished Motor System: Paucity of Expressive Gestures (r = -0.28, 87%, p ≤ 0.01), and Affective Nonresponsivity (r = -0.26, PLRP = 74%, p ≤ 0.05). Finally, it overlapped with one predictor shared with Component 3 (C3): Inattentive During Mental Status Testing (r = -0.31, PLRP = 85%, p ≤ 0.01). C3 was dominated by five positive component loadings: Stroop Incongruent (r = 0.66), D2 Sustained Attention (r = 0.42), Block Design (r = 0.44), Stroop Congruent (r = 0.40), Spatial Span Forward (r = 0.30), and two negative component loadings: TMT-B (r = -0.49), TMT-A (r = -0.48). We labelled this component Attention and Processing Speed. This component was reliably 92 associated with only one SANS item: Inattentive During Mental Status Testing (r = 0.31, PLRP = 81%, p ≤ 0.05, shared with C2), which is a rating of patients’ performance when subtracting 100 – 7 serially, and spelling ‘world’ backwards. Table 4.3. Component loadings for the predicted solution. Component C1 Verbal Memory C2 Working Memory C3 Attention & Processing Speed Digit Symbol 0.34 -0.01 0.48 Trail Making Test Part A -0.16 -0.16 -0.48 Trail Making Test Part B -0.30 -0.19 -0.49 D2 Sustained Attention 0.38 0.10 0.45 Digit Span Forward 0.11 0.73 0.17 Digit Span Backward 0.02 0.72 0.08 Spatial Span Forward 0.22 0.39 0.30 Spatial Span Backward 0.37 0.33 0.18 Visual Reproduction (immediate) 0.22 0.10 0.32 Visual Reproduction (delayed) 0.26 0.21 0.40 Logical Memory (immediate) 0.67 0.13 0.18 Logical Memory (delayed) 0.64 0.10 0.14 Logical Memory (recognition) 0.72 0.04 0.12 Block Design 0.32 0.26 0.44 Stroop Neutral 0.39 0.08 0.34 Stroop Congruent 0.38 0.19 0.40 Stroop Incongruent 0.19 0.14 0.66 93 Stroop Inference -0.01 0.08 0.58 Note. Dominant component loadings are set in bold font. Table 4.4. Mean predictor loadings for SANS Predictor loadings Component SANS Items 1 2 3 1 Unchanging Facial Expression -0.30** -0.07 0.04 2 Decreased Spontaneous Movements -0.16 -0.21 -0.06 3 Paucity of Expressive Gestures -0.17 -0.28* 0.01 4 Poor Eye Contact -0.27* -0.18 -0.03 5 Affective Nonresponsivity -0.21 -0.26* 0.09 6 Lack of Vocal Inflections -0.09 -0.13 -0.10 7 Global Rating of Affective Flattening -0.23 -0.05 0.05 8 Inappropriate Affect -0.26* -0.14 -0.02 9 Poverty of Speech -0.26* -0.22 0.12 10 Poverty of Content of Speech -0.23 -0.07 -0.04 11 Blocking -0.28* -0.07 -0.15 12 Increased Latency of Response -0.32** -0.06 -0.07 13 Global Rating of Alogia -0.34** -0.17 0.02 14 Grooming and Hygiene -0.17 -0.06 0.10 15 Impersistence at Work or School -0.19 0.16 0.11 16 Physical Anergia -0.09 -0.06 0.09 17 Global Rating of Avolition/Apathy -0.16 0.06 0.05 18 Recreational Interests and Activities 0.01 -0.04 0.05 19 Sexual Activity 0.10 -0.06 -0.06 20 Ability to Feel Intimacy and Closeness 0.10 -0.08 0.10 21 Relationships with Friends and Peers 0.03 -0.09 0.04 22 Global Rating of Anhedonia/Asociality 0.08 -0.09 0.06 94 23 Social Inattentiveness -0.29** -0.25* 0.01 24 Inattentiveness During Mental Status Test -0.19 -0.29** -0.31** 25 Global Rating of Attention -0.32** -0.33** -0.14 Note. The values are Person r coefficients. Significant predictor loadings are set in bold font. ** p ≤ .01, * p ≤ .05 from the Benjamini-Hochberg multiple comparison correction test. Table 4.5. Mean predictor loadings for SAPS Predictor loadings Component SAPS Items 1 2 3 1 Auditory Hallucinations -0.20 -0.09 -0.16 2 Voices Commenting -0.14 -0.02 -0.15 3 Voices Conversing -0.08 -0.04 -0.16 4 Somatic or Tactile Hallucinations 0.01 -0.15 -0.06 5 Olfactory Hallucinations 0.00 -0.01 0.07 6 Visual Hallucinations -0.21 0.04 -0.04 7 Global Rating of Hallucinations -0.21 -0.08 -0.14 8 Persecutory Delusions -0.11 -0.06 0.07 9 Delusions of Jealousy -0.01 -0.03 0.05 10 Delusions of Guilt or Sin -0.16 -0.15 0.08 11 Grandiose Delusions -0.15 -0.03 -0.19 12 Religious Delusions -0.05 -0.17 -0.13 13 Somatic Delusions -0.01 -0.08 0.05 14 Delusions of Reference -0.02 -0.03 -0.16 15 Delusions of Being Controlled 0.00 -0.11 -0.06 16 Delusions of Mind Reading -0.03 -0.13 -0.08 17 Thought Broadcasting -0.08 -0.04 0.01 18 Thought Insertion 0.04 -0.04 -0.02 19 Thought Withdrawal -0.05 -0.08 -0.08 20 Global Rating of Delusions -0.10 -0.03 -0.05 95 21 Clothing and Appearance 0.05 -0.19 0.01 22 Social and Sexual Behavior -0.14 -0.15 -0.03 23 Aggressive and Agitated Behavior 0.00 -0.04 0.04 24 Repetitive or Stereotyped Behavior 0.02 -0.10 -0.14 25 Global Rating of Bizare Behavior -0.08 -0.17 -0.10 26 Derailment -0.27* 0.05 -0.03 27 Tangentiality -0.26* -0.07 -0.12 28 Incoherence -0.20 -0.04 -0.05 29 Illogicality -0.35** -0.09 0.06 30 Circumstantiality 0.01 0.07 -0.08 31 Pressure of Speech 0.16 -0.07 0.01 33 Distractible Speech -0.12 -0.15 -0.02 34 Global Rating of Positive Formal Thought Disorder -0.24 -0.04 -0.07 Note. The values are Person r coefficients. Significant loadings are set in bold font. ** p ≤ .01, * p ≤ .05 from the Benjamini-Hochberg multiple comparison correction test. No SAPS predictor loading were significant for C2 or C3. 96 Figure 4.3. Summary of iCPCA results Note: On the left side are reliable predictor loadings grouped into symptom types. All symptom names include scale names (SANS in green or SAPS in orange); additionally, we added explanations of symptoms in parentheses to aid interpretation. On the right side are components (C) and their dominant component loadings grouped by three colors: yellow is C1, dark pink is C2, and dark blue is C3. The yellow, dark pink and dark blue lines connect symptoms with C1, C2 and C3, respectively. The component and predictor loading values (in parenthesis) measure effect size; a minus sign precedes negative values. If predictors were shared between two components, the colored underlines corresponded to the proper components. ** p ≤ .01, * p ≤ .05 from the Benjamini-Hochberg multiple comparison correction test. 97 Figure 4.4. Selection of criterion variables 4.3.2 Relationship of iCPCA components to other measures A comparison of the component scores (averaged over 1000 iterations) revealed that females (M = 0.18, SD = 0.84) had significantly higher scores than males (M = -0.17, SD = 0.91) on C1 (Verbal Memory), t(204) = 2.58, p ≤ 0.01, d = 0.39. There was no significant effect of sex on C2 (Working Memory), t(204) = -0.83, p = 0.41, nor C3 (Processing Speed and Attention), t(204) = 0.25, p = 0.80. The years of education variable was also significantly correlated with C1 (r = 0.30, p ≤ 0.001) but not with C2 (p = 0.08) nor C3 (p = 0.73). Finally, all three CPCA components were significantly 98 correlated with three measures of WAIS IQ: Full, Verbal, and Performance. Table 4.6 provides the complete set of results. Table 4.6. Descriptive of education, age, and IQ measures. Correlations between education years, age of participants, IQ measures, and CPCA components. Measure M SD 1. Edu. 2. Age 3. FSIQ 4. VIQ 5. PIQ 6. C1 7. C2 1. Education years# 11.70 2.60 2. Age years 23.03 4.00 0.46** 3. WAIS Full IQ 94.83 15.85 0.34** 0.10 4. WAIS Verbal IQ 96.42 15.32 0.41** 0.06 0.91** 5. WAIS Performance IQ 92.87 17.07 0.20** 0.14* 0.88** 0.60** 6. C1 Verbal Memory ## - - 0.28** 0.12 0.47** 0.47** 0.36** 7. C2 Working Memory## - - 0.13 0.09 0.36** 0.42** 0.26** -0.02 8. C3 Attention & Processing Speed ## - - 0.02 -0.01 0.43** 0.28** 0.51** 0.01 0.05 Note: ** p ≤ 0.01 (2-tailed); * p ≤ 0.05; # n = 206 for all measures but Education years n = 203; ## for CPCA component measures (6, 7 and 8) all scores were standardized and their Means = approx. 0, and SDs = approx. 1. 4.4 Discussion This study aimed to investigate the components of cognition that optimally overlap with symptoms of SSD in the early stages of psychosis treatment. Our analysis allowed focus on individual items while avoiding spurious results using variance constraints, dimension reduction, iterative bootstrapping, permutation, and multiple comparisons test correction. We observed three 99 components of cognitive functions that were optimally predictable from symptoms. The first was labelled Verbal Memory, the second Working Memory, and the third Attention and Processing Speed. Symptoms related to disorganized and impoverished communication, language and thought overlapped with the Verbal Memory component. Symptoms related to motor impoverishment overlapped with Working Memory component. Finally, only the SANS “serial 7s” item overlapped with the Attention and Processing Speed component. A correlation between formal thought disorder and verbal memory has been noted in past work (Oeztuerk et al., 2022). However, here we observed that C1 (Verbal Memory) overlapped not only with formal thought disorder (e.g., derailment and tangentiality) but also with other disorganized aspects of communication such as inappropriate affect, as well as with items such as impoverished thinking, wooden expression, poor eye contact, and poverty of speech. Additionally, the Social Inattentiveness item overlapped with C1 (Verbal Memory). The fact that such a wide range of disturbances of communication, language and thought (negative and positive, linguistic and social) overlapped with decreases in verbal memory suggests that the impaired brain networks underlying verbal memory may extend past the language system proper, interacting with other networks related to social communication, social engagement and thought (Palaniyappan, 2022; Palaniyappan et al., 2023). Notably, this overlapping set of symptoms covers both negative and positive formal thought disorder (Jerónimo et al., 2018; Kircher et al., 2018). 100 In contrast to the overlap with communication, language and thought noted in C1 (Verbal Memory), C2 (Working Memory) overlapped with the impoverished motor system, suggesting a distinct brain network. This suggests that prefrontal mechanisms crucial for performance in working memory tasks, such as the dorsolateral prefrontal cortex and the anterior cingulate cortex, are often impaired in the SSD population (Glahn et al., 2005; Smucny et al., 2022). Other working-memory-related brain regions that may be implicated in this overlap are cortical premotor and motor areas, cerebellum, thalamus, and insufficient interaction of thalamocortical loops (Walther, 2015; Walther & Strik, 2012). Moreover, the supplementary motor area, a critical region in the motor system (Nachev et al., 2008), is also crucial for the energizing network active during the encoding processes in working memory, for which network-level hypoactivity is associated with poorer working memory performance (Sanford & Woodward, 2021). The same SANS symptom (Inattentiveness During Mental Status Testing or ‘Serial 7s’) measuring working memory impairment overlapped with C3 (Attention and Processing Speed) and C2 (Working Memory), suggesting that this item taps into general attentional processes. The SANS symptoms related to motor system impoverishment overlapped with C2 rather than C3, which may seem surprising, considering that movement control problems should affect tasks that depend on reaction time as a primary dependent measure. Therefore, different aspects of motor and memory processes may be involved in these tasks (Kantak & Winstein, 2012), as the tasks crucial for C3 - such as TMT, Stroop and D2 tests - depend on complex cognitive processes such as scanning and selective and sustained attention processes contributing to response time. 101 We observed that females performed better on mean C1 (Verbal Memory) scores than males, consistent with previous research on women's verbal memory and learning advantages in the SSD population (Buck et al., 2020; Sota & Heinrichs, 2003). This advantage of females in processing verbal information is also apparent in the general population (Kramer et al., 1988, 2003; Van der Elst et al., 2005; Wong et al., 2020). Additionally, C1 component scores were positively and moderately correlated with years of education in our sample. This supports the proposition that better verbal learning and memory support better academic performance; again, this is widely observed in the general population (Davis et al., 2017). Both Lepage and colleagues (Lepage et al., 2021) and our investigation shed light on the association between neurocognitive impairments in early psychosis SSD patients, albeit with different methodological approaches. Lepage et al. (2021) categorized patients into three groups based on persistent negative symptoms (PNS), secondary PNS (sPNS), and non-PNS using total scores of the SANS and SAPS and the Calgary Depression Scale for Schizophrenia (Addington et al., 1990). They examined the neurocognitive functions of these groups and found that patients grouped on negative symptom summary scores showed impairment in verbal and working memory. Our current findings elucidate which symptoms are differentially associated with these two memory systems. Our study has several limitations. First, our sample had more participants with prominent negative and fewer positive symptoms (please see Table 4.2). Notably, the number of patients with 102 prominent hallucinations and delusions is much smaller than other symptom groups measured by both rating scales. Therefore, the associations between cognition and positive symptoms might be limited due to the restricted range in the sample. Verifying our findings in other groups of SSD patients would be essential. Second, due to the requirement that all subjects completed all tests and symptom ratings, the sample size was relatively small, considering the high number of predictors used in the analysis. However, iCPCA computed reliability predictor loadings scores, which reduces the chances of Type 1 errors even in smaller samples. Third, our cognitive assessment battery did not include any social cognition tasks, which have been deemed important for symptom overlap in the past work (Hagiya et al., 2015; Lepage et al., 2021). Therefore, future research could apply our method to study the relationship between symptoms and cognition in larger samples, including social cognition measures in SSD. Finally, we observed that all our component scores are correlated with general intelligence scores. Therefore, we cannot rule out that the variance of the general cognitive impairment impacts components and their relationships with overlapping psychotic symptoms. In conclusion, the iCPCA allowed us to explore the associations between individual items, optimized to understand the overlap between symptoms and cognition. This analysis revealed two distinct symptom clusters: disorganized and impoverished communication, language and thought associated with verbal memory, and motor impoverishment overlapping with working memory. These novel findings can inform future therapeutic interventions to increase verbal and nonverbal communication skills in patients diagnosed with SSD through psychotherapeutic approaches (Vianin et al., 2014) and neuromodulation (Tseng et al., 2022) targeting specific brain networks 103 related to particular cognitive functions. Future studies can benefit from an approach holding that (1) the use of instrument-prescribed subscales (e.g., the global score for negative symptoms) need not be mandatory for data analysis, and (2) sets of scale items of theoretical interest and practical importance (e.g., items on SANS/SAPS scales) will change depending on the set of predictor variables of interest and can be analyzed taking this into account. 104 Chapter 5: Computing narrow-band EEG latent dimensions to study the effects of tACS (Study 3) In the previous chapters, I used a supervised dimensionality reduction technique called constrained principal component analysis (CPCA) to find cognitive correlates of psychiatric symptoms. The following chapters explore the use of supervised dimensionality reduction techniques to extract latent dimensions from EEG signals and investigates whether transcranial alternating current stimulation (tACS) can influence these signals. Studies have shown that tACS is more likely to affect EEG oscillations when their frequencies and/or phases are matched (Klink et al., 2020; Liu et al., 2018; Orendáčová & Kvašňák, 2021; Vogeti et al., 2022). However, natural brain oscillations are non-stationary, meaning their frequency and phase vary over time. To address this, I focused on evoked brain oscillations, whose frequency and phase can be experimentally controlled. These oscillations also have a high signal-to-noise ratio and can be easily measured (Norcia et al., 2015; Picton et al., 2003). In this chapter, I used auditory evoked potentials, also known as auditory steady-state responses (ASSRs), at 40 Hz to determine if tACS at 40 Hz can modulate ASSR signals. I employed joint decorrelation (JD), a supervised dimensionality reduction technique, to extract latent sources of evoked oscillations at their specific frequencies: 40 Hz for ASSRs. 105 5.1 Introduction Transcranial alternating current stimulation (tACS) is a non-invasive technique that delivers low-intensity alternating currents to influence brain activity and behavior (Liu et al., 2018). While recent research has highlighted the inconsistent and often non-replicable effects of tACS (Kasten et al., 2019; Krause & Kadosh, 2014), in-vitro studies suggest that electric fields as low as 0.2 V/m (see Table 1.1) can affect spike timing under ideal conditions (Francis et al., 2003). Our primary objective is to identify the conditions under which tACS can effectively influence brain activity, as measured by EEG signals, and behavior. However, the main challenge in measuring EEG signals during tACS is that the magnitude of ongoing electrophysiological oscillations is miniscule compared to the stimulation artifact, often by a factor of approximately 1000. Additionally, the non-linear properties of the skull, scalp, and brain distort the stimulus signal, leading to stimulation artifacts in the harmonics of the main frequency (Liu et al., 2018). Consequently, most studies focus on observing electrophysiological signals immediately after tACS rather than during stimulation to avoid these artifacts (Brignani et al., 2013; Clancy et al., 2022; Lafleur et al., 2021; Lafon et al., 2017; Vossen et al., 2015). A number of possible mechanisms of action of tACS have been proposed to explain its immediate effects, broadly categorized as the aftereffects of entrainment (online effects) and/or spike-timing-dependent plasticity (STDP) mediated plasticity effects (Liu et al., 2018; Vogeti et al., 2022). A leading hypothesis in the field regarding the optimal conditions for tACS to affect physiology and behavior is that the frequency of tACS should match the frequency of the dominant oscillations in 106 the target brain region. Under such conditions, it should be possible to entrain and modulate ongoing brain oscillations. This claim is supported by numerous tACS studies in humans (Feurra, Paulus, et al., 2011; Grover et al., 2022; Hopfinger et al., 2017; Joundi et al., 2012; Lafon et al., 2017; Pahor & Jaušovec, 2018), albeit the results may be unreliable (Kasten et al., 2019; Krause & Kadosh, 2014). Since many tACS and experimental parameters vary between studies, it is difficult to pinpoint the reasons behind the discrepancies. One reason could be that the frequency and power of endogenous brain oscillations vary over time. To overcome this non-stationarity, we use evoked oscillations— these stationary signals are responses to externally controlled stimuli. The auditory steady-state response (ASSR) is one such type of evoked oscillation. ASSRs are neural responses to tonal auditory stimuli in adults with normal hearing (Galambos et al., 1981). ASSR signals are distinct from natural gamma oscillations (Ross et al., 2005). ASSRs also have a high signal-to-noise ratio at the frequency of the auditory stimulus. They are thought to originate in auditory cortical and subcortical regions (Herdman et al., 2002). Recently, there has been an increase in tACS studies focusing on ASSRs in the gamma frequency band, most commonly at 40 Hz (Ahn et al., 2019; Baltus et al., 2018; de la Salle et al., 2024; Wang et al., 2021). A few tACS studies have observed that alpha stimulation suppressed ASSR signal in the gamma frequency band (P. Hyvärinen et al., 2018; Wang et al., 2021). These studies were performed in healthy volunteers, with tACS applied bilaterally to the temporal lobe. In contrast, a study conducted on schizophrenia patients reported an increase in phase-locking values of ASSR (Ahn et al., 2019). Studies have shown mixed results on ASSR signals using theta tACS (de la Salle et 107 al., 2024; P. Hyvärinen et al., 2018). The only study where 40 Hz tACS was used to investigate the effects on 40 Hz ASSR showed no difference between the effects of 40 Hz tACS and sham stimulation (de la Salle et al., 2024). In this experiment, we studied the effects of 40Hz tACS on 40Hz ASSR signals. The tACS was delivered at 40 Hz bihemispherically near the auditory cortex. The objective of this study was to demonstrate that tACS can temporarily increase the signal-to-noise ratio (SNR) of 40Hz ASSR oscillations in the auditory cortex of healthy participants. We compared the 40Hz SNR before and immediately after 40 Hz tACS, 11 Hz tACS (active control), and sham modulation (control condition). We hypothesized that the 40 Hz tACS group would show increased 40 Hz SNR in response to the 40 Hz tone, the 11 Hz tACS group would show a decrease in 40 Hz SNR, and the control group would show no difference between pre- and post-stimulation ASSR. 5.2 Methods 5.2.1 Participants We recruited 45 participants with corrected-to-normal vision for the experiment. All participants provided written, informed consent, and the Human Ethics Committee at the University of British Columbia (UBC), Vancouver, approved all experimental procedures. Participants were screened for eligibility to participate in the tACS procedure based on several exclusion criteria. Participants with a diagnosis potentially related to psychosis, history of neurological problems, history of migraines, metallic implants in the head, severe head injury, frequent or prolonged loss of consciousness, recent concussion, pregnancy, severe sleep disturbances, taking medication known 108 to increase the risk of stroke and/or seizure, or severe current substance dependence were ineligible to participate in the study. Among the 45 participants, 15 were stimulated at 40 Hz, another 15 were stimulated at 11 Hz to control for frequency-specific effects, and the remaining 15 underwent a sham stimulation. 5.2.2 Experiment paradigm 5.2.2.1 Experimental setup Participants performed the task in a dark room, with their heads positioned 60 cm away from the monitor on a chin rest. The task instructions were presented on a 24.5-inch LED monitor with a resolution of 1920x1080 at a 60 Hz screen refresh rate. The auditory stimuli were presented using earphones, one in each ear at 44.1KHz. The experiment protocol was coded and presented using PsychToolbox 3 in MATLAB 2019A (Brainard, 1997; Pelli, 1997). 5.2.2.2 Study design In this study, each participant performed three blocks of the experiment. The first (pre-stimulation, PRE) and the last (post-stimulation, POST) blocks involved listening to a 40Hz audio stimulus in both ears. Each 40Hz stimulus lasted for 1 second, and each block consisted of 140 such stimuli with an inter-stimulus interval ranging from 1.8 to 2.2 seconds. Participants were instructed to pay attention to the 40Hz audio tone. EEG data were recorded throughout the first and third blocks. In the second block, participants underwent 40Hz, 11Hz, or sham transcranial alternating current stimulation (tACS) for 15 minutes without performing any task. A schematic of the study design is shown in Figure 5.1. 109 Figure 5.1. Block diagram depicting the study design. Note: Schematic showing the three blocks of the experiment. PRE – pre stimulation block; POST – post stimulation block; EEG – electroencephalography; tACS – transcranial alternating current stimulation; min = minutes; Hz = Hertz, unit for frequency. 5.2.2.3 Participant groups Forty-five participants performed the experiment. In this study, we divided participants into three groups: those who underwent 40Hz gamma stimulation, those who underwent 11Hz alpha stimulation, and those who underwent sham (0Hz) stimulation. Each group consisted of 15 participants. 110 5.2.2.4 EEG recording and tACS During the pre- and post-stimulation blocks, EEG signals were recorded from participants' scalps to monitor their brain activity. EEG recordings were made using the Electrical Geodesics Inc. Geodesic Transcranial Electrical Neuromodulation (EGI GTEN) system with 256 electrodes. This setup provided high-density data, capturing detailed information about electrical activity across the scalp. The sampling frequency was set at 1000 Hz, allowing for high temporal resolution and accurate tracking of rapid changes in brain activity. In the stimulation block, the GTEN system was used to deliver transcranial alternating current stimulation (tACS). A high-definition setup was employed to deliver tACS bihemispherically near the auditory cortex, as shown in the electrode montage in Figure 5.2A. Sinusoidal alternating current stimulation was delivered at a peak amplitude of 1.8 mA. The simulated electric fields for the tACS montage, generated using the Realistic vOlumetric Approach to Simulate Transcranial electric stimulation (ROAST) MATLAB toolbox (Huang et al., 2018), are shown in Figure 5.2B. 111 Figure 5.2. Electrode montage for tACS and simulated electric fields Note: A. The electrode montage used for tACS. Red and blue electrodes correspond to anodes and cathodes. The anodes and cathodes reverse every half cycle because the stimulation is alternating in nature. B. Simulated electric field for the tACS electrode montage at 1.8mA. 5.2.3 Data analysis 5.2.3.1 EEG preprocessing The EEG data recorded using the GTEN system was analyzed using in-house MATLAB scripts, with preprocessing conducted through FASTER (Fully Automated Statistical Thresholding for EEG Artifact Rejection) (Nolan et al., 2010). This method removes EEG artifacts based on statistical parameters. Fifty face electrodes out of the total 256 electrodes were rejected, leaving 206 electrodes for analysis. The EEG data from only the PRE and POST blocks were analyzed, as the data from the stimulation block was heavily contaminated by the tACS artifact. The EEG data were downsampled from 1000Hz to 250Hz after passing it through an anti-aliasing filter. Then, the data were filtered using an IIR bandpass filter with stop band frequencies at 1Hz and 55Hz. 112 Noisy electrodes were identified and rejected based on three metrics: mean correlation with other electrodes, variance, and the Hurst exponent. Electrodes that deviated more than 2.5 standard deviations in any of these metrics were deemed noisy, rejected, and their activity interpolated based on neighboring electrodes. The EEG data were then average-referenced and epoched to include 1s of data after the start of 40Hz auditory stimulus. Noisy epochs were rejected based on deviations greater than 2.5 standard deviations in any of the following metrics: epoch's mean deviation from electrode means, epoch variance, and maximum amplitude range. Subsequently, Independent Component Analysis (ICA) was performed. Outlier components were identified and rejected based on the median gradient for high frequency, kurtosis of the spatial map, and the Hurst exponent. Components classified as either eye or muscle artifacts by ICLabel (Pion-Tonachini et al., 2019) with a confidence greater than 70% were also rejected. Further cleaning was done by interpolating noisy channels within each epoch using parameters like median of consecutive difference, variance, range, and mean deviation from electrode mean. The cleaned data were then used for further analysis. 5.2.3.2 Joint decorrelation (JD) analysis Preprocessed EEG data with epochs of one second recorded during the presentation of 40 Hz audio tones were considered for the JD analysis (de Cheveigné & Parra, 2014). A detailed explanation of JD can be found in Chapter 2. Briefly, JD estimates latent dimensions that maximize the difference between two covariance matrices—one containing only the signal (C1) and the other 113 containing both the signal and noise (C0). In this case, the covariance matrix of the full spectrum EEG is C0, and the covariance matrix of the EEG data filtered at 40 Hz is C1. Thus, JD estimates latent dimensions that maximize the covariance in C1 while suppressing the overall covariance in C0. The data used for this analysis contained EEG activity from 206 electrodes for one second, for approximately 140 trials in each block (pre- and post-stimulation) for each participant. We computed 206x206 covariance matrices for the full spectrum EEG (C0) and the 40 Hz filtered EEG (C1) for each one-second epoch. We averaged the covariance matrices across all epochs and participants and performed a single joint decorrelation analysis for all participants. The joint decorrelation analysis provided component loadings or weights for latent dimensions that best explain the ASSR signal at 40Hz. The full spectrum EEG data were then projected onto the JD weights to obtain the JD components. 5.3 Results In this experiment, we examine the effects of transcranial alternating current stimulation (tACS) on evoked EEG oscillations, specifically focusing on auditory steady state response (ASSR) signals at 40Hz. We analyze the EEG data during the 1-second periods when the 40Hz audio tone is being played. An advantage of evoked oscillations is that their frequency and phase can be externally controlled, ensuring that the phase of the ASSR signal is consistent for each 1-second trial of the 40Hz audio tone presentation. Consequently, the ASSR signal-to-noise ratio can be 114 enhanced by averaging the EEG signals across all trials. This averaging process retains only the ASSR signal, whose frequency and phase match across trials, while other signals are canceled out. Since we record EEG from 206 scalp electrodes (out of a total of 256 electrodes, with an additional 50 electrodes on the face), analyzing this high-dimensional data can be cumbersome. To address this, we employ a data-driven dimensionality reduction technique to estimate the source of the ASSR signal. Specifically, we use a supervised dimensionality reduction technique called joint decorrelation, or denoising source separation, to extract components at the ASSR frequency (40Hz). Briefly, joint decorrelation identifies latent dimensions in the high-dimensional EEG data that maximize the signal-to-noise ratio of power at a given frequency (here, 40Hz) while suppressing power at other frequencies. More details regarding the joint decorrelation analysis can be found in the methods section on JD analysis and in chapter 2. Here, we investigate whether tACS affects the trial-averaged ASSR component extracted using JD by comparing post-stimulation results to pre-stimulation results. 5.3.1 JD ASSR components We performed joint decorrelation analysis on all 45 participants to extract latent dimensions that maximize power at the ASSR frequency (40 Hz). The scree plot obtained is shown in Figure 5.3. Based on the scree plot, we selected the top two components and performed a varimax rotation to obtain more interpretable components. The topographical plots for JD component loadings and the signal-to-noise ratio (SNR) of the power spectrum (calculated as the ratio of power at a frequency 115 to mean power in the nearby frequencies, +/- 5 Hz) of the trial average EEG time series for the two extracted components are shown in Figure 5.4. We observed that the first component has high loadings in the left temporal electrodes. However, this component does not have the highest SNR at the ASSR frequency (40 Hz). The second component has loadings near the central medial electrodes. This component also had a high signal-to-noise ratio. Thus, we use this component as the JD component for ASSR at 40 Hz in subsequent analyses. Figure 5.3. JD Scree plot Note: The scree plot obtained from the joint decorrelation (JD) analysis. Based on this plot, the top two components, which explain the maximum variance, were selected for further analyses. 116 Figure 5.4. JD components Note: A. The power spectrum signal-to-noise-ratio (SNR) for the EEG timeseries for joint decorrelation (JD) component 1. The purple line and shaded area correspond to the mean and standard error of SNR of power spectrum across all participants (n=45). (inset) topographical map depicting component loadings for JD component 1. B. Same as A, but for component 2. 5.3.2 Comparison between JD and PCA components Next, we verified whether the JD component better represents the ASSR signal compared to unsupervised methods like principal component analysis (PCA). To do this, we performed PCA on the same EEG data used for the JD analysis. We selected the top two components and performed a varimax rotation, similar to the JD analysis. The topographical plots for PCA component loadings and the SNR for the power spectrum of trial-averaged EEG time series for the two extracted components are shown in Figure 5.5. We selected the first PCA component for comparison with the JD component because it had the higher SNR. 117 We then computed the 40Hz signal-to-noise ratio (SNR) for both PCA and JD component for all participants. SNR is defined as the log ratio (in dB) of power at the ASSR frequency (40 Hz) to power in the neighboring frequencies (35-45 Hz). The SNR values for PCA and JD analyses for all participants are plotted in Figure 5.6. We observed that the JD analysis provides a 2.21 dB (1.7x) higher SNR than PCA (mean SNR difference = 2.21 dB [95% CI 0.795, 3.57], p=0.004). Thus, JD analysis estimates components with significantly higher ASSR SNR than PCA. Figure 5.5. PCA components Note: A. The power spectrum signal-to-noise-ratio (SNR) for the EEG timeseries for principal component (PC) 1. The purple line and shaded area correspond to the mean and standard error of SNR of power spectrum across all participants (n=45). (inset) topographical map depicting component loadings for PCA component 1. 118 B. Same as A, but for component 2. Figure 5.6. SNR comparison between PCA and JD Note: (left) ASSR signal-to-noise ratio (SNR) for PCA and JD analyses. The red, blue, and green circles correspond to sham, 11Hz, and 40Hz tACS stimulation groups respectively. Black dot and error bar: mean and standard error. (right) Effect size plot. Black dot and error bar: Mean effect size as measured by paired mean difference and 95% confidence interval, respectively, for the difference of SNR between JD and PCA conditions. Gray histogram: bootstrap sampling distribution for paired mean difference. Dashed horizontal line: Datum indicating zero effect size. 119 5.3.3 tACS has no effect on ASSR signal We examined whether the signal-to-noise ratio (SNR) at the ASSR frequency (40 Hz) changed with tACS. To do this, we computed the change in ASSR SNR from pre-stimulation to post-stimulation (Δ = POST - PRE). We then checked whether the change in ASSR SNR differed among the different stimulation groups (sham vs. 11 Hz vs. 40 Hz). The changes in ASSR SNR for the sham, 11 Hz, and 40 Hz stimulation groups are shown in Figure 6.12. We performed a one-way ANOVA and did not find any significant group effect for stimulation (one-way ANOVA, F(2, 42)=0.9, p=0.416). This indicates that the effect of tACS on ASSR at the matched frequency (40 Hz) is not different from that of sham and alpha (11 Hz) stimulation. The Bayes factor for the one-way ANOVA is 0.307, indicating substantial evidence in favor of the null hypothesis, suggesting no group effect of stimulation on ASSR SNR. Figure 5.7. Effects of tACS on ASSR 120 Note: The beeswarm plot depicts the change in ASSR SNR for sham (red), 11 Hz (blue), and 40 Hz (green) stimulation groups. The dots correspond to the SNR change values for individual participants. The vertical lines with slits represent the means and standard deviations for each group. 5.3.4 Conventional electrode-level analysis We also conducted an electrode-level analysis, as shown in Figure 5.8A, which presents the topographical plot of the average signal-to-noise ratio (SNR) of the ASSR signal at 40 Hz across all subjects. The plot reveals no consistent region with a high SNR, with the maximum average SNR being approximately 1.5, which is lower than that observed in the joint decorrelation (JD) analysis (Figure 5.4B). This underscores the advantage of using JD analysis over conventional electrode-level analysis. Next, we investigate whether the SNR at the ASSR frequency (40 Hz) varied with tACS for each electrode. In this regard, we performed one-way ANOVAs for each electrode with ASSR SNR as the dependent variable and group (sham vs. 11 Hz vs. 40 Hz) as the categorical factor. The f-statistic and the -log10 of the p-value, corrected for multiple comparisons using the Bonferroni-Hochberg correction (FDR = 0.05), are plotted in Figures 5.8B and 5.8C, respectively. The results indicate that no electrode showed a significant group effect for stimulation after correcting for multiple comparisons. 121 Figure 5.8. Electrode level analysis Note: A. Topographical plot for average signal-to-noise ratio at 40Hz. B. Topographical plot for f-statistic obtained using one-way ANOVA for each electrode. C. Topographical plot for -log10 of p-value obtained using one-way ANOVA for each electrode after Bonferroni-Hochberg FDR correction. 5.4 Discussion In this study, we investigated the effects of 40 Hz transcranial alternating current stimulation (tACS) on 40 Hz auditory steady-state response (ASSR) signals. We used joint decorrelation (JD) to estimate latent components that best capture the ASSR signal. We analyzed the difference in ASSR signal-to-noise ratios (SNRs) in the JD component between post-stimulation and pre-stimulation conditions across three different stimulation groups: sham, 11 Hz tACS, and 40 Hz tACS. Our hypothesis was that sham stimulation would not alter the ASSR signal, 11 Hz tACS would suppress it, and 40 Hz tACS would enhance the ASSR signal due to frequency matching. Contrary to our hypothesis, our results did not reveal any significant differences between the different stimulation conditions. Specifically, we observed that the ASSR signal did not change for the sham condition. Although the effects were not significant, the overall trend for 11 Hz and 40 Hz stimulation was that the ASSR signal was suppressed post-stimulation. This trend of ASSR 122 signal suppression due to alpha tACS is supported by a few studies (P. Hyvärinen et al., 2018; Wang et al., 2021). The lack of effect of tACS on ASSR signals could be due to various factors. One important reason could be that the electrical montage used for stimulation (see Figure 5.2) generates electric fields of only 0.02V/m (ROAST, Huang et al., 2018). This is an order of magnitude lower than the electric fields (~0.2V/m, Table 1.1) required to induce rhythm resonance, where there is a change in the amplitude of the brain oscillation when its frequency and phase are matched to that of tACS (see Table 1.1 in Chapter 1, section on mechanisms for tACS). Additionally, in this study, we matched only the frequency of tACS with the brain oscillations, but not the phase. Temporal biasing of spikes, which is associated with this mechanism, requires even higher electric fields (~0.5V/m, see Table 1.1) (Liu et al., 2018). In our study, the lower electric field is due to the close placement of the anode and cathode. Since more than 70% of the electric current applied passes through the scalp without reaching the cortex (Vöröslakos et al., 2018) , placing the anode and cathode closer together reduces the electric fields induced in the brain, as shown in the simulation for this montage (see Figure 5.2). This raises a conundrum: to induce large electric fields, we need to place the anode and cathode far apart. However, placing them far apart will lead to the induced electric fields being non-localized and spreading out in most parts of the brain. However, it is important to note that it is still debated whether changes in brain oscillations right after stimulation are due to the after-effects of entrainment (i.e., online effects of tACS) or long-term plastic changes (Vogeti et al., 2022). The above-mentioned mechanisms—rhythm resonance 123 and temporal biasing of spikes—are ways by which tACS affects brain oscillations during stimulation, i.e., the online effects of stimulation. If changes in the ASSR signal due to tACS depended on the aftereffects of entrainment (online effects of tACS), then the required electric fields are certainly an order of magnitude lower (Liu et al., 2018). However, a systematic study of the effects of electric fields on long-term plastic changes has not been conducted. Most studies that show changes in brain oscillations due to tACS in humans use a conventional montage where the anode and cathode are placed further apart, resulting in much higher induced electric fields than in the current experiment (Hopfinger et al., 2017; P. Hyvärinen et al., 2018; Lafleur et al., 2021; Lafon et al., 2017; Orendáčová & Kvašňák, 2021; Vossen et al., 2015). Another important factor to consider is that we use evoked brain oscillations rather than natural brain oscillations. Our rationale for using evoked brain oscillations is that their frequency and phase can be experimentally controlled, allowing for better matching with the frequency and phase of tACS. Additionally, they have a high signal-to-noise ratio when averaged across trials. However, at the level of a single trial, evoked brain oscillations are orders of magnitude smaller than natural brain oscillations. This is relevant because simulated models for long-term effects suggests that the STDP effects are also more prominent on loops corresponding to dominant oscillations (Vossen et al., 2015). Thus, evoked oscillations may not be the best targets for tACS. Moreover, the mechanisms underlying tACS were mostly inferred by studying natural oscillations (Liu et al., 2018; Vogeti et al., 2022). The distinction between these two types of oscillations is crucial: natural oscillations are thought to arise from interactions between the thalamus and cortex. In this context, both thalamic and cortical activity influence each other in a closed-loop manner. 124 Conversely, in the case of evoked oscillations, the influence is unidirectional—an external source affects cortical activity without reciprocal influence. Therefore, the mechanisms inferred from natural oscillations may not directly translate to evoked oscillations. Another reason for the lack of effects of tACS could be heterogeneous brain states during stimulation (Krause & Kadosh, 2014). The current experiment did not involve any specific task either while the audio was being played or during stimulation, leading to different participants likely having different brain states at different time points. There is also no systematic evidence indicating whether a specific task is necessary during and post-stimulation. Some studies have shown the effects of tACS on EEG activity during resting state or performing an unrelated task (de la Salle et al., 2024; P. Hyvärinen et al., 2018; Vossen et al., 2015), while others used tasks that have been linked with the EEG oscillations targeted by tACS (Grover et al., 2022; Joundi et al., 2012; Pahor & Jaušovec, 2018). Additionally, variability in brain anatomy could also account for the lack of consistent effects. It would be beneficial to estimate participant-specific electrode montages for stimulation. Poor reliability in tACS findings may be attributed to individual differences in brain anatomy, as different sizes and shapes of brain structures lead to varying electric field patterns across participants (Kasten et al., 2019; Stecher et al., 2021). In the next study, we aim to address some of the above reasons and better understand under what conditions tACS affects EEG activity. 125 Chapter 6: Computing broad-band EEG latent dimensions to study the effects of tACS (Study 4) In this chapter, I addressed the limitations of the previous study on the effects of 40 Hz tACS on auditory steady-state response (ASSR) signals, where the results did not reveal any significant differences between the different stimulation conditions. The major problem with the previous approach was that the electric fields induced in the brain were an order of magnitude lower than required to induce changes. This was due to the fact that a stimulation montage where the anode and cathode were placed close together was used; to achieve a more spatially focal effect of tACS. A study showed that more than 70% of the electric current applied passes through the scalp without reaching the cortex (Vöröslakos et al., 2018). This problem is amplified when the anode and cathodes are placed close together. To rectify this, I separated the anode and cathode far apart so that the induced electric fields in the brain were sufficient to induce changes. In this regard, I prioritized achieving a greater electric field over a more localized effect. Additionally, I targeted natural oscillations, such as alpha oscillations, rather than evoked oscillations, as their magnitude is significantly higher. Lastly, I introduced a simple behavioral paradigm before, during, and after stimulation to standardize brain states across participants. In this study, I examined the effects of tACS on alpha oscillations (8-14 Hz). Alpha oscillations are ongoing natural oscillations in the brain whose peak frequency varies for each individual and can vary with time within an individual, usually between 8 to 14 Hz. Here, I employed joint decorrelation (JD), a supervised dimensionality reduction technique, to extract latent components 126 of natural oscillations in their specific frequency bands. Specifically, I used JD to extract latent components of alpha activity and study whether tACS affects this activity. Moreover, I compared the differences in the alpha signal captured by JD with conventional region-of-interest analysis. 6.1 Introduction Human studies have shown that different thalamo-cortical circuits have distinct dominant frequencies, such as alpha oscillations in the occipital cortex, beta oscillations in the parietal cortex, and gamma oscillations in the frontal cortex (Okazaki et al., 2021; Rosanova et al., 2009). Alpha oscillations, which typically range between 8 and 14 Hz, are observed during wakefulness and are generally linked to resting state activity (Bazanova & Vernon, 2014; Schürmann & Başar, 2001). For example, when the eyes are closed, there is an enhancement in alpha amplitude in the posterior electrodes, whereas there is a suppression while performing mental activity. Alpha oscillations are known to be involved in various cognitive processes like attention and working memory (Başar & Güntekin, 2012; Clements et al., 2021; Klimesch, 2012; Ward, 2003). Researchers have hypothesized that alpha oscillations reflect top-down, inhibitory control processes (Klimesch et al., 2007). TACS experiments that stimulate these natural frequencies, such as alpha in humans, show mixed results. Many of these studies have investigated the electrophysiological and behavioral effects of tACS immediately after stimulation (Brignani et al., 2013; Clancy et al., 2022; Lafleur et al., 2021; Lafon et al., 2017; Vossen et al., 2015). For instance, one study showed a decrease in visual detection by stimulating the visual cortex at a fixed alpha frequency (10 Hz) compared to gamma 127 (25 Hz) and sham stimulation. However, the effect was not frequency-specific, as theta (6 Hz) stimulation also showed a decrease in visual detection performance (Brignani et al., 2013). Another study found no behavioral effect of 10 Hz stimulation on an audiovisual switching task (Clayton et al., 2018). One study reported an increase in alpha oscillation amplitude after 10 Hz stimulation over the visual cortex (Clancy et al., 2022), whereas another study found no change in alpha or beta power after 10 Hz and 20 Hz stimulation (Lafleur et al., 2021). Some studies have found an increase in motor evoked potentials after beta tACS stimulation (Feurra, Bianco, et al., 2011), whereas others showed no such effects (Rjosk et al., 2016). A few studies have tried delivering tACS at participant-specific individual frequencies. One study stimulated the occipital cortex at participants’ individual alpha frequency (IAF) for 10 minutes and showed an enhancement of alpha power after stimulation (Zaehle et al., 2010). Another study by the same research group replicated this result in a new cohort and also showed that the increase in alpha power persisted for at least 30 minutes after stimulation (Neuling et al., 2013). Moreover, a study found a correlation between the mismatch between tACS frequency and individual alpha frequency and the magnitude of increase in alpha power post-stimulation. Specifically, a smaller mismatch corresponded to a stronger increase in alpha power, and a greater mismatch to a weaker increase in alpha power (Kasten et al., 2019). However, other studies have found no such correlation (Ahn et al., 2019), and some even found the opposite effect in one condition – a greater mismatch was associated with a stronger increase in alpha power (Vossen et al., 2015). 128 Entrainment (online effects) and spike-timing-dependent plasticity (STDP) mediated plasticity are both considered possible mechanisms of action of tACS on natural brain oscillations (Liu et al., 2018; Vogeti et al., 2022). However, there are still mixed results, and the roles of different mechanisms underlying tACS remain unclear. In this study, we investigated the effects of 10 Hz alpha (vs. 41 Hz gamma) stimulation on alpha oscillations during a vigilance-oddball paradigm. We used a within-subject design where each participant underwent both alpha and gamma stimulation (active sham). We hypothesized that alpha stimulation would enhance alpha power compared to gamma stimulation. 6.2 Methods 6.2.1 Participants 99 participants (74 females; age range: 19-42 years; median age: 22 years) with corrected-to-normal vision participated in the experiment. All participants provided written, informed consent, and all experimental procedures were approved by the Human Ethics Committee at UBC, Vancouver. Participants were screened for eligibility to participate in the tACS procedure. Participants with a diagnosis potentially related to psychosis, history of neurological problems, history of migraines, metallic implants in the head, severe head injury, frequent or prolonged loss of consciousness, recent concussion, pregnancy, severe sleep disturbances, taking medication known to increase risk of stroke and/or seizure, and suffer from severe current substance dependence; were ineligible to participate in the study. 129 Out of 99 participants conducted, 25 participants were not considered for analyses because they either dropped out without completed two sessions of tACS (n=19) or their EEG data were corrupted (n=6). Data from only 74 participants, who had good EEG data for both sessions, were considered for further analyses. Out of the 74 participants, 52 performed the oddball paradigm, where their responses were laterally biased. Whereas, 22 participants performed a control experiment where their responses were unbiased (more details below). 6.2.2 Experimental paradigm 6.2.2.1 Experimental setup Participants performed the task in a dark room, with their heads positioned 60 cm away from the monitor on a chin rest. The task was presented on a 24.5-inch, contrast-calibrated LED monitor with a resolution of 1920x1080 at a 240 Hz screen refresh rate. A black background was maintained throughout the experiments, and stimulus presentation was performed using PsychoPy version 2021.2.1. 6.2.2.2 Study design In this study, 74 participants underwent alpha (10Hz) and gamma (41Hz) stimulation on separate days. During each session, participants performed three blocks of a behavioral task (see below) where either transcranial alternating current stimulation (tACS) was delivered or electroencephalogram (EEG) signals were recorded. The first block consisted of the task with simultaneous EEG recording (PRE), the second block involved either alpha or gamma stimulation (STIM), and the third block again involved EEG recording (POST), as shown in Figure 6.1. 130 Figure 6.1. Block diagram depicting the study design. Note: Schematic showing the three blocks of the experiment for gamma (41Hz, top) and alpha (10Hz, bottom) stimulation sessions. PRE – pre stimulation block; POST – post stimulation block; EEG – electroencephalography; tACS – transcranial alternating current stimulation; min = minutes; Hz = Hertz, unit for frequency. 6.2.2.3 Behavioral Task In each block, participants performed the vigilance-oddball task (Figure 6.2), where a white cross of a specified width in degrees of visual angle was continuously presented in the center of the screen. Participants were instructed to fixate on the white cross and respond to color changes using a button press on a keyboard. The color of the cross changed from white to either red or green for 100ms before reverting to white. One color change (red or green) occurred 80% of the time (DEFAULT color change), while the other occurred 20% of the time (ODDBALL color change). 131 The duration between two consecutive color changes was randomly selected from an exponential distribution ranging from 2000 to 4000ms. Figure 6.2. Task paradigm Note: The vigilance-oddball task performed in each block of the experiment. Briefly, participants were instructed to fixate on the white cross and respond to color changes to the cross using different button presses for different colors. 6.2.2.4 Participant Groups Fifty-two participants (out of 74) performed the vigilance-oddball task, whereas twenty-two participants performed the control experiment. For the oddball experiment, some participants (23 out of 52) were instructed to respond using their left-hand index finger to press the button ‘Z’ for the DEFAULT color change and their right-hand index finger to press the button ‘M’ for the ODDBALL color change. Conversely, the other participants (29 out of 52) used the opposite configuration to respond (i.e., right-hand for DEFAULT and left-hand for ODDBALL color change). These groups are referred to as the left-hand and right-hand biased groups, respectively 132 (Figure 6.3A). A control experiment was conducted where the red and green color changes were equally likely to occur. In this no-bias group (n=22), participants’ responses were not biased towards either the left or the right hands (Figure 6.3B). Figure 6.3. Schematic depicting participant groups Note: A. Participant group performing the oddball paradigm (n=52), where 23 were biased towards left-handed responses and 29 were biased towards right-handed responses. B. Participant group performing the control paradigm (n=20), where their responses are unbiased. 6.2.2.5 EEG recording and tACS During the pre- and post-stimulation blocks, EEG signals were recorded from participants’ scalps to monitor their brain activity. EEG recordings were made using the Electrical Geodesics Inc. Geodesic Transcranial Electrical Neuromodulation (EGI GTEN) with 256 electrodes to provide high-density data, capturing detailed information about electrical activity across the scalp. The 133 sampling frequency was set at 1000Hz, allowing for high temporal resolution and accurate tracking of rapid changes in brain activity. In the stimulation block, the GTEN system was used to deliver tACS. Alpha and gamma stimulation were delivered at 10Hz and 41Hz, respectively. The anode and cathode electrodes were placed at the medial occipital and central locations, respectively, as shown in the electrode montage in Figure 6.4A. A sinusoidal alternating current stimulation was delivered at a peak amplitude of 1.8mA. The simulated electric fields for the tACS montage, using the Realistic vOlumetric Approach to Simulate Transcranial electric stimulation (ROAST) MATLAB toolbox (Huang et al., 2018), are shown in Figure 6.4B. Figure 6.4. Electrode montage for tACS and simulated electric fields Note: C. The electrode montage used for tACS. Red and blue electrodes correspond to anodes and cathodes. The anodes and cathodes reverse every half cycle because the stimulation is alternating in nature. D. Simulated electric field for the tACS electrode montage at 1.8mA. 134 6.2.3 Data analysis 6.2.3.1 EEG preprocessing The EEG data recorded using the GTEN system was analyzed using in-house MATLAB scripts, with preprocessing conducted through FASTER (Fully Automated Statistical Thresholding for EEG Artifact Rejection) (Nolan et al., 2010). This method removes EEG artifacts based on statistical parameters. Fifty face electrodes out of the total 256 electrodes were rejected, leaving 206 electrodes for analysis. The EEG data from only the PRE and POST blocks were analyzed, as the data from the stimulation block was heavily contaminated by the tACS artifact. The EEG data were downsampled from 1000Hz to 250Hz after passing it through an anti-aliasing filter. Then, the data were filtered using an IIR bandpass filter with stop band frequencies at 1Hz and 55Hz. Noisy electrodes were identified and rejected based on three metrics: mean correlation with other electrodes, variance, and the Hurst exponent. Electrodes that deviated more than 2.5 standard deviations in any of these metrics were deemed noisy, rejected, and their activity interpolated based on neighboring electrodes. The EEG data were then average-referenced and epoched around the color change event, including data from 2 seconds before to 1 second after the color change. Noisy epochs were rejected based on deviations greater than 2.5 standard deviations in any of the following metrics: epoch's mean deviation from electrode means, epoch variance, and maximum amplitude range. Subsequently, Independent Component Analysis (ICA) was performed. Outlier components were identified and rejected based on the median gradient for high frequency, kurtosis of the spatial 135 map, and the Hurst exponent. Components classified as either eye or muscle artifacts by ICLabel (Pion-Tonachini et al., 2019) with a confidence greater than 70% were also rejected. Further cleaning was done by interpolating noisy channels within each epoch using parameters like median of consecutive difference, variance, range, and mean deviation from electrode mean. The cleaned data were then used for further analysis. 6.2.3.2 Region of interest (ROI) analysis Preprocessed EEG data from the one-second window before the color change were considered for this analysis. This window is selected because it is unlikely to contain motor artifacts from the response button press or other motion artifacts post-response. Spectral analysis was performed independently for each electrode in the selected time window using a single Slepian taper to obtain peak alpha power in the range of 8-14Hz. The peak alpha power data were z-scored based on the mean and standard deviation of powers in the PRE block, for each session and participant. These normalized powers were then averaged over all the electrodes in the specified ROI and across all epochs in a block. This process resulted in calculating the average peak of alpha power for each block, session, and participant within the specified ROI. 6.2.3.3 Joint decorrelation analysis Preprocessed EEG data from the one-second window before the color change were considered for the JD analysis (de Cheveigné & Parra, 2014). A detailed explanation of JD can be found in Chapter 2. Briefly, JD estimates latent dimensions that maximize the difference between two covariance matrices—one containing only the signal (C1) and the other containing both the signal 136 and noise (C0). In this case, the covariance matrix of the full spectrum EEG is C0, and the covariance matrix of the EEG data filtered in the alpha band (8-14Hz) is C1. Thus, JD estimates latent dimensions that maximize the covariance in C1 while suppressing the overall covariance in C0. The data used for this analysis contained EEG activity from 206 electrodes for one second, for approximately 150 trials in each block (pre- and post-stimulation) for each participant. We computed 206x206 covariance matrices for the full spectrum EEG (C0) and the filtered EEG (C1) for each one-second epoch. We averaged the covariance matrices across all epochs and participants and performed a single joint decorrelation analysis for all participants. The joint decorrelation analysis provided component loadings or weights for latent dimensions that best explain the alpha signal. The full spectrum EEG data were then projected onto the JD weights to obtain the JD components. 6.3 Results 6.3.1 Behavioral effects of tACS In this section, we examine the behavioral effects of tACS. In the oddball paradigm (n=52), the accuracy of default responses was significantly greater than oddball responses (mean +/- std. dev.; default: 93.67 +/- 7.02%; oddball: 89.77 +/- 7.73%; t-test, p<0.001). Moreover, the reaction times for default correct responses were lesser than oddball correct responses (mean +/- std. dev.; default: 372.3 +/- 71.7ms; oddball: 434.9 +/- 80.2ms; t-test, p<0.001). A three-way ANOVA was conducted on all behavioral measures with blocks (pre vs. stim vs. post) and stimulation sessions 137 (alpha vs. gamma) as fixed effects. The interaction between blocks and stimulation sessions was also included in the model, with participants treated as random effects. For accuracy in default trials, no significant interaction was found between blocks and stimulation sessions (F(2, 306) = 0.03, p = 0.975), nor were there significant main effects for either blocks (F(2, 306) = 1.39, p = 0.250) or stimulation sessions (F(1, 306) = 1.74, p = 0.188). Similarly, for accuracy in oddball trials, no significant interaction was observed between blocks and stimulation sessions (F(2, 306) = 0.12, p = 0.888), and there were no significant main effects for blocks (F(2, 306) = 2.34, p = 0.098) or stimulation sessions (F(1, 306) = 2.24, p = 0.136). For reaction time in default trials, there was no significant interaction between blocks and stimulation sessions (F(2, 306) = 0.01, p = 0.991), and no main effects were found for blocks (F(2, 306) = 0.72, p = 0.489) or stimulation sessions (F(1, 306) = 1.80, p = 0.181). The same was true for reaction times in oddball trials, where no significant interaction was found between blocks and stimulation sessions (F(2, 306) = 0.03, p = 0.971), and no main effects were observed for blocks (F(2, 306) = 2.19, p = 0.114) or stimulation sessions (F(1, 306) = 1.06, p = 0.304). In the control paradigm with unbiased response group (n=22), the response accuracy and reaction times were computed by combining responses from both hands. For accuracy, there was no significant interaction between blocks and stimulation sessions (F(2, 126) = 0.21, p = 0.814), and no main effects were found for blocks (F(2, 126) = 1.69, p = 0.188) or stimulation sessions (F(1, 126) = 0.00, p = 0.951). The same was true for reaction times, where no significant interaction was 138 found between blocks and stimulation sessions (F(2, 126) = 0.07, p = 0.930), and no main effects were observed for blocks (F(2, 126) = 0.37, p = 0.689) or stimulation sessions (F(1, 126) = 1.03, p = 0.717). In summary, no behavioral effects of tACS were observed. 6.3.2 Electrophysiological effects of tACS In this section, we examine the effects of tACS on EEG oscillations, specifically focusing on the frequencies around the stimulation frequency. We have two stimulation conditions in this experiment: alpha stimulation at 10Hz and gamma stimulation at 41Hz. Here, we present only the results concerning alpha power, as no significant effects on gamma power were observed. Our aim is to determine whether alpha tACS, compared to gamma tACS, modulates alpha power (8-14Hz). Henceforth, for examining the effects on alpha power, alpha stimulation will be considered the active stimulation, and gamma will serve as the sham stimulation. For this analysis, we calculated peak alpha power (8-14Hz) in a one-second window before the color change occurred. This captures the alpha power during the anticipatory period when the participant is waiting for the color change to occur. Using this time-window minimizing motor artifacts from the response button press and other post-response motion artifacts. Since we record EEG from 206 scalp electrodes (out of 256 total electrodes; with an additional 50 electrodes on the face), analyzing this high-dimensional data can be cumbersome. Studies typically employ one of two methods to address this issue of high dimensionality. One method involves selecting regions of interest (ROIs) based on literature or well-defined rationale and examining the 139 effects within these ROIs. The other method uses a data-driven approach to extract low-dimensional latent components of EEG and analyze the effects on these components. In this study, we employ both approaches. First, we test whether alpha power in selected ROIs is affected by tACS, and then we test the same in data-driven components of alpha oscillations. 6.3.2.1 ROI analysis Alpha oscillations are known to be dominant in the posterior electrodes. Thus, our electrical montage for stimulation was positioned in the posterior region. For the ROI analysis, we first check whether tACS affects alpha power in the regions where the electrical stimulation was delivered. These regions include the medial occipital and central electrodes, as shown in Figure 6.4A. Additionally, we examine the effects of tACS on alpha power in the left and right posterior electrodes, as studies have shown that alpha oscillations are lateralized during various cognitive paradigms. 6.3.2.1.1 tACS does not affect alpha power in medial electrodes We examined whether alpha tACS, compared to gamma tACS, modulates alpha power in the electrodes used for stimulation. In this regard, we computed the enhancement of alpha power as the change in alpha power from pre-stimulation to post-stimulation (Δ = POST - PRE). The enhancement of alpha power for gamma stimulation and alpha stimulation across all participants is shown in Figure 6.5. Panels A and B present the results for the medial occipital and central ROIs, respectively. We also estimated the Cohen’s d effect size using non-parametric estimation statistics. We observed that the enhancement in alpha power for alpha stimulation was not different 140 from gamma stimulation for both the medial occipital (Figure 6.5A, Paired Cohen’s d=0.0625 [95.0%CI -0.235, 0.384], p=0.681) and central (Figure 6.5B, Paired Cohen’s d=0.000 [95.0%CI -0.295, 0.327], p=0.998) clusters of electrodes used for stimulation. This suggests that, in our experiment, alpha tACS (compared to gamma tACS) does not affect alpha power at the stimulation electrodes that are placed medially. Figure 6.5. Effects of tACS on medial electrodes Note: A. (left) The enhancement of alpha power (Δ alpha power = POST alpha power - PRE alpha power) due to gamma and alpha stimulation, for medial occipital electrodes. The orange and purple circles correspond to left and right-biased groups respectively. Black dot and error bar: mean and standard error. (top-right) Topographical plot depicting the medial occipital ROI used for this analysis. (bottom-right) Effect size plot. Black dot and error bar: Mean effect size as measured by Cohen’s d and 95% confidence interval, respectively, for the difference of Δ alpha power between gamma and alpha stimulation conditions. Gray histogram: bootstrap sampling distribution for paired Cohen’s d. Dashed horizontal line: Datum indicating zero effect size. B. Same as A, but for medial central electrodes. 141 6.3.2.1.2 tACS affects alpha power in lateral electrodes Next, we examined whether alpha tACS modulated alpha power in the left and right posterior electrodes. The rationale for focusing on these lateral electrodes is two-fold. Firstly, the responses in the oddball task are lateralized. Secondly, lateralized alpha oscillations are known to be involved in cognitive tasks such as attention and decision-making. In the electrodes contralateral to the default response hand (the hand used for the 80% DEFAULT color change response), we observed that the enhancement in alpha power (Δ = POST - PRE) was greater for alpha stimulation than for gamma stimulation, showing a small to medium effect size (Figure 6.6B, Paired Cohen’s d=0.372 [95.0% CI 0.000, 0.711], p=0.048). In contrast, for ipsilateral electrodes, the enhancement in alpha power for alpha stimulation trended lower than for gamma stimulation, showing a small effect (Figure 6.6A, Paired Cohen’s d=-0.259 [95.0%CI -0.506, -0.010], p=0.084). Furthermore, the difference in the enhancement in alpha power between alpha and gamma stimulation (ΔΔ = alpha stim - gamma stim) was significantly higher for the contralateral electrodes as compared to ipsilateral electrodes, showing a medium effect size (Figure 6.6C, Paired Cohen’s d=0.514 [95.0%CI 0.282, 0.705], p<0.001). In summary, alpha stimulation, compared to gamma stimulation, modulated the enhancement of alpha power in the lateral posterior electrodes but not in the medial occipital and central electrodes used for stimulation. The contralateral electrodes showed a greater enhancement for alpha stimulation, whereas the ipsilateral electrodes showed a lower enhancement. Since the only lateralized part of the experiment is the response during the task, this suggests that the effects of tACS are likely driven by the motor planning aspects involved in the task paradigm. 142 Figure 6.6. Effects of tACS on lateral electrodes Note: A. (left) The enhancement of alpha power (Δ alpha power = POST alpha power - PRE alpha power) due to gamma and alpha stimulation, for ipsilateral electrodes. The orange and purple circles correspond to left and right-biased groups respectively. Black dot and error bar: mean and standard error. (top-right) Schematic and topographical plot depicting the ROI ipsilateral to the default response hand. (bottom-right) Effect size plot. Black dot and error bar: Mean effect size as measured by Cohen’s d and 95% confidence interval, respectively, for the difference of Δ alpha power between gamma and alpha stimulation conditions. Gray histogram: bootstrap sampling distribution for paired Cohen’s d. Dashed horizontal line: Datum indicating zero effect size. B. Same as A but for contralateral electrodes. C. The difference in the enhancement of alpha power for gamma and alpha stimulation (ΔΔ alpha power) for ipsilateral vs contralateral electrodes. Other legends are the same as panels A and B but for ΔΔ alpha power. *p < 0.05, ***p < 0.001. 6.3.2.1.3 Control experiment In the oddball paradigm, participants were biased to either left-hand or right-hand responses. In this cohort, we observed that alpha stimulation led to a greater enhancement of alpha power in the electrodes contralateral to the response hand and a lower enhancement in the ipsilateral electrodes. 143 This suggests that the effects of tACS are likely driven by the motor planning aspects involved in the task paradigm. To further validate this hypothesis, we conducted a control experiment where red and green color changes were equally likely to occur. In this no-bias group (n=22), participants' responses were not biased towards either the left or right hand. If our hypothesis that the effects of tACS depend on the motor planning aspect of the task is correct, we should see systematic changes for different response groups. For the left-biased group, the difference in alpha enhancement between alpha and gamma stimulation (ΔΔ alpha power) was greater for the right posterior electrodes compared to the left posterior electrodes (Figure 6.7, left; Paired Cohen’s d = 0.721 [95% CI 0.335, 1.000], p = 0.001). Conversely, for the right-biased group, the difference in alpha enhancement was greater for the left posterior electrodes (Figure 6.7, right; Paired Cohen’s d = -0.347 [95% CI -0.635, -0.081], p = 0.037). And there was no significant difference in the alpha enhancement between the left and right posterior electrodes for the unbiased group (Figure 6.7, center; Paired Cohen’s d = 0.108 [95% CI -0.23, 0.424], p = 0.566). Moreover, the differences in enhancements between the left and right electrodes show a significant linear group effect for left-biased, unbiased, and right-biased groups (one way ANOVA: F(2, 73) = 7.74, p < 0.001). In summary, we observe a systematic gradation in the difference of alpha enhancement: the left-biased group showed a greater difference for the right electrodes, the right-biased group showed a greater difference for the left electrodes (i.e., the difference is greater for contralateral electrodes), 144 and the unbiased group showed no difference. This supports the idea that the effects of tACS are task-dependent. Figure 6.7. Group effects for ROI analysis Note: A. The difference in the enhancement of alpha power for gamma and alpha stimulation (ΔΔ alpha power) for left vs right electrodes for left-biased (left), unbiased (center), and right-biased (right) groups. B. Effect size as measured by Cohen’s d for the difference of ΔΔ alpha power between left and right electrodes. Black dot and error bar: Mean effect size and 95% confidence interval, respectively. Histogram: bootstrap sampling distribution for paired Cohen’s d. Horizontal line: Datum indicating zero effect size. *p < 0.05, ***p < 0.001. 145 6.3.2.2 Joint decorrelation (JD) analysis In this section, instead of selecting regions of interest (ROIs) and performing analysis on them, we use a data-driven approach to extract latent dimensions of EEG activity within a specific frequency band. We employ a supervised dimensionality reduction technique called joint decorrelation, or denoising source separation, to extract components in the alpha band (8-14Hz). Briefly, joint decorrelation identifies latent dimensions in the high-dimensional EEG data that maximize the signal-to-noise ratio of power in the alpha frequencies (8-14Hz) while suppressing power in other frequencies. More details regarding the joint decorrelation analysis can be found in the methods section on JD analysis. 6.3.2.2.1 JD alpha components We performed joint decorrelation analysis on all 72 participants to extract latent dimensions that maximize power in the alpha band (8-14Hz). The scree plot obtained is shown in Figure 6.8. Based on the scree plot, we selected the top three components and performed a varimax rotation to obtain more interpretable components. The topographical plots for JD component loadings and the power spectrum of the corresponding EEG time series for the three extracted components are shown in Figure 6.9. We observed that all the alpha components have high component loadings or weights in the posterior electrodes, indicating that the alpha signal predominantly originates from these electrodes, which aligns with findings in the literature. Additionally, we found that component 1 is right-lateralized, component 3 is left-lateralized, and component 2 has approximately medial loadings. 146 Figure 6.8. JD Scree plot Note: The scree plot obtained from the joint decorrelation (JD) analysis. Based on this plot, the top three components, which explain the maximum variance, were selected for further analyses. 147 Figure 6.9. JD components Note: D. The power spectrum for the EEG timeseries for joint decorrelation (JD) component 1. The purple line and shaded area correspond to the mean and standard error of mean of power spectrum across all participants (n=74). (inset) topographical map depicting component loadings for JD component 1. E. Same as A, but for component 2. F. Same as A, but for component 3. 6.3.2.2.2 JD alpha components have better SNR than PCA Next, we verify whether these components better represent alpha oscillations than unsupervised methods like principal component analysis (PCA). To do this, we perform PCA on the same EEG data used for JD analysis. We select the top three components and perform a varimax rotation, similar to the JD analysis. The topographical plots for PCA component loadings and the power spectrum of the corresponding EEG time series for the three extracted components are shown in Figure 6.10. 148 We then compute the alpha power signal-to-noise ratio (SNR) for PCA and JD components for all participants. SNR is defined as the log ratio (in dB) of mean power in the alpha frequencies (8-14Hz) to power in the remaining frequencies. The mean SNR, across all components, for PCA and JD analyses are plotted in Figure 6.11. We observed that JD provides a 1.65dB (1.5x) higher SNR than PCA (mean SNR difference = 1.65dB, [95% CI 1.36, 2.05], p<0.001). Thus, JD analysis estimates components with significantly higher alpha SNR than PCA. Figure 6.10. PCA components Note: A. The power spectrum for the EEG timeseries for principal component 1 obtained using PCA. The purple line and shaded area correspond to the mean and standard error of mean of power spectrum across all participants (n=74). (inset) topographical map depicting component loadings for JD component 1. B. Same as A, but for component 2. C. Same as A, but for component 3. 149 Figure 6.11. SNR comparison between PCA and JD Note: (left) Alpha power signal-to-noise ratio (SNR) for PCA and JD analyses. The orange, green, and purple circles correspond to left, unbiased, and right-biased groups respectively. Black dot and error bar: mean and standard error. (right) Effect size plot. Black dot and error bar: Mean effect size as measured by paired mean difference and 95% confidence interval, respectively, for the difference of SNR between JD and PCA conditions. Gray histogram: bootstrap sampling distribution for paired mean difference. Dashed horizontal line: Datum indicating zero effect size. 6.3.2.2.3 tACS does not affect the medial JD component Out of the three JD components, the second component appears to have loadings along the medial electrodes. Similar to the ROI analysis, we examined whether alpha tACS, compared to gamma tACS, modulates alpha power in this medial JD component. We computed the enhancement of alpha power as the change in alpha power from pre-stimulation to post-stimulation (Δ = POST - PRE). The enhancement of alpha power for gamma stimulation and alpha stimulation across all participants for the medial JD component is shown in Figure 6.12. 150 We also estimated the Cohen’s d effect size using non-parametric estimation statistics (Ho et al., 2019). We observed that the enhancement in alpha power for alpha stimulation was not different from gamma stimulation for the medial JD component (Figure 6.12, Paired Cohen’s d=0.119 [95.0%CI -0.254, 0.467], p=0.526). This result is similar to what was observed in the ROI analysis, indicating that in our experiment, alpha tACS (compared to gamma tACS) does not affect alpha power medially. Figure 6.12. Effects of tACS on medial JD component Note: (left) The enhancement of alpha power (Δ alpha power = POST alpha power - PRE alpha power) due to gamma and alpha stimulation, for medial JD component. The orange and purple circles correspond to left and right-biased groups respectively. Black dot and error bar: mean and standard error. (top-right) Topographical plot depicting the component loadings for medial JD component. (bottom-right) Effect size plot. Black dot and error bar: Mean effect size as measured 151 by Cohen’s d and 95% confidence interval, respectively, for the difference of Δ alpha power between gamma and alpha stimulation conditions. Gray histogram: bootstrap sampling distribution for paired Cohen’s d. Dashed horizontal line: Datum indicating zero effect size. 6.3.2.2.4 tACS affects alpha power in lateral JD components Next, we examined whether alpha tACS modulated alpha power in the left and right lateral JD components. In the JD component contralateral to the default response hand (the hand used for the 80% DEFAULT color change response), we observed that the enhancement in alpha power (Δ = POST - PRE) for alpha stimulation trended greater than for gamma stimulation, showing a small effect size (Figure 6.13B, Paired Cohen’s d=-0.251 [95.0%CI -0.509, 0.0798], p=0.111). In contrast, for ipsilateral electrodes, the enhancement in alpha power for alpha stimulation trended lower than for gamma stimulation, also showing a small effect (Figure 6.13A, Paired Cohen’s d=0.248 [95.0%CI -0.118, 0.58], p=0.172). These trends are consistent with the findings from the ROI analysis. Furthermore, the difference in the enhancement in alpha power between alpha and gamma stimulation (ΔΔ = alpha stim - gamma stim) was significantly higher for the contralateral electrodes compared to ipsilateral electrodes, showing a medium effect size, just like the ROI analysis (Figure 6.13C, Paired Cohen’s d=0.413 [95.0%CI 0.156, 0.677], p=0.003). In summary, although the JD components showed a weaker trend than the ROI analysis, the contralateral electrodes still showed a greater enhancement for alpha stimulation, whereas the ipsilateral electrodes showed a lower enhancement. The difference in enhancement in alpha power 152 was significantly greater for contralateral than for ipsilateral JD components. These results align with the hypothesis that the effects of tACS are likely driven by the motor planning aspects involved in the task paradigm. Figure 6.13. Effects of tACS on lateral JD components Note: A. (left) The enhancement of alpha power (Δ alpha power = POST alpha power - PRE alpha power) due to gamma and alpha stimulation, for ipsilateral JD component. The orange and purple circles correspond to left and right-biased groups respectively. Black dot and error bar: mean and standard error. (top-right) Schematic and topographical plot depicting the loadings for the JD component ipsilateral to the default response hand. (bottom-right) Effect size plot. Black dot and error bar: Mean effect size as measured by Cohen’s d and 95% confidence interval, respectively, for the difference of Δ alpha power between gamma and alpha stimulation conditions. Gray histogram: bootstrap sampling distribution for paired Cohen’s d. Dashed horizontal line: Datum indicating zero effect size. B. Same as A but for contralateral electrodes. C. The difference in the enhancement of alpha power for gamma and alpha stimulation (ΔΔ alpha power) for ipsilateral vs contralateral JD components. Other legends are the same as panels A and B but for ΔΔ alpha power. **p < 0.01. 153 6.3.2.2.5 Control experiment In the ROI analyses, we validated the hypothesis that the effects of tACS are likely driven by the motor planning aspects involved in the task paradigm. We showed systematic differences in enhancement for left and right lateral electrodes for different response groups—i.e., greater enhancement in the right electrodes for the left-biased group, no difference in enhancement for either of the lateral electrodes for the unbiased group, and greater enhancement in the left electrodes for the right-biased group. We tested whether similar effects could be observed in JD components. Using JD components, for the left-biased group, the difference in alpha enhancement between alpha and gamma stimulation (ΔΔ alpha power) was greater for the right JD component compared to the left JD component (Figure 6.14, left; Paired Cohen’s d = 0.804 [95.0%CI 0.324, 1.26], p=0.004), showing a large effect size, similar to the ROI analysis. However, the unbiased group shows a trend for greater enhancement for the right JD component than the left (Figure 6.14, middle; Paired Cohen’s d = 0.264 [95.0%CI -0.125, 0.621], p=0.208), and the difference in alpha enhancement was not different between the left and right components for the right-biased group (Figure 6.14, right; Paired Cohen’s d = -0.173 [95.0%CI -0.496, 0.0886], p=0.311). Although the results for JD components differed for the unbiased and right-biased groups, the differences in enhancements between the left and right JD components show a significant linear group effect for left-biased, unbiased, and right-biased groups (one-way ANOVA: F(2, 73)=4.35, p=0.016), similar to the ROI analysis results. In summary, we observe a systematic gradation in 154 the difference of alpha enhancement similar to the ROI analysis. This is in line with the idea that the effects of tACS are task-dependent. Figure 6.14. Group effects for JD analysis Note: A. The difference in the enhancement of alpha power for gamma and alpha stimulation (ΔΔ alpha power) for left vs right JD components for left-biased (left), unbiased (center), and right-biased (right) groups. 155 B. Effect size as measured by Cohen’s d for the difference of ΔΔ alpha power between left and right JD components. Black dot and error bar: Mean effect size and 95% confidence interval, respectively. Histogram: bootstrap sampling distribution for paired Cohen’s d. Horizontal line: Datum indicating zero effect size. **p < 0.01. 6.4 Discussion In this study, we investigated the effects of 10 Hz alpha (vs. 41 Hz gamma) stimulation on alpha oscillations during a vigilance-oddball paradigm. Similar tasks, presumably unrelated to EEG oscillations but involving sustained attention, have been used to study the effects of tACS on electrophysiology and behavior (Zaehle et al., 2010; Vossen et al., 2015). We observed that the enhancement in alpha power was greater for alpha stimulation than gamma stimulation, but this effect was only significant for the contralateral electrodes to the response hand during the DEFAULT color change condition, not for the ipsilateral electrodes. Moreover, the difference in the enhancement of alpha power between alpha and gamma stimulation (ΔΔ = alpha stim - gamma stim) showed a systematic gradation for left-biased, unbiased, and right-biased groups. Specifically, the enhancement of alpha was greater on the contralateral electrodes. Our findings reveal that alpha tACS enhances alpha power, but this enhancement is more pronounced in the electrodes contralateral to the dominant hand involved in the task. It is noteworthy that this lateralized effect is observed even though our tACS electrode montage was not lateralized. This implies that the effect is likely driven by the motor planning aspects involved during the task paradigm (Deiber et al., 2012), suggesting that the effects of tACS on electrophysiological signals depend on the nature of the task being performed. 156 A few studies have shown posterior alpha to be involved in motor planning (Deiber et al., 2012; Miasnikova & Franz, 2022). However, the current experimental paradigm cannot distinguish whether the effects of tACS on posterior alpha are due to motor planning or to the attention-based inhibitory control required for the oddball task. To differentiate between these possible mechanisms, future experiments should conduct similar studies without using the oddball paradigm. Instead, participants should respond to only one color change using either their left or right hand. In such an experiment, if a lateralized effect of tACS on alpha is observed, it would indicate that the effect is likely due solely to motor planning. Conversely, if no lateralized effect of tACS is observed, this would suggest that the attention and inhibitory control required by the oddball paradigm are necessary to produce a lateral effect on posterior alpha through tACS. Although our results somewhat align with our hypothesis that alpha tACS would affect alpha oscillations, we observed that tACS influences different brain regions differently depending on the task being performed. In our study, we used a vigilance/oddball paradigm where participants were biased to respond with one hand and only occasionally responded with the other. This experiment involves inhibiting the default response, and alpha oscillations are known to play a role in such inhibitory control (Klimesch et al., 2007). The interaction between the inhibitory action of alpha oscillations and tACS likely led to the lateralized enhancement of alpha oscillations. This observation underscores the importance of considering the task context when designing and interpreting tACS studies. Moreover, it may pave the way for tACS to be used alongside behavioral therapies to enhance the efficacy of therapeutic interventions. 157 Moreover, our findings revealed that the effect sizes were greater for participants in the left-hand bias group. Specifically, the left-hand biased group showed a much more significant lateral difference in the enhancement of alpha power, whereas the right-hand biased group showed a relatively weaker effect. This could be because around 88% of our participants indicated that they are right-handed. This bias is significant because handedness can affect brain lateralization and the organization of neural circuits, potentially influencing the outcomes of neurostimulation studies. Future research should aim to include a more balanced representation of left- and right-handed participants to better understand the impact of handedness on tACS outcomes. These results offer possible solutions to a common challenge in tACS research, which is that to induce large electric fields, the anode and cathode must be placed far apart. However, this placement can lead to non-localized electric fields spreading throughout much of the brain. We addressed this issue by placing the anode and cathode far apart to ensure that the induced electric fields were sufficient to induce changes (see Table 1.1). In this regard, we prioritized achieving a greater electric field over a more localized effect, and our findings suggest that the non-localized electric fields spreading throughout much of the brain associated with this greater electric field can be localized by using specific tasks that engage the desired brain areas. If these results can be generalized, it suggests that tasks can be used to funnel the effects of tACS to target brain regions, enhancing the precision and effectiveness of the stimulation. 158 Chapter 7: Conclusion In this dissertation, I explore two applications of supervised dimensionality reduction techniques: one for identifying cognitive correlates of psychiatric symptoms (chapters 3 and 4), and the other for estimating latent EEG dimensions to investigate the effects of transcranial alternating current stimulation (tACS, chapters 5 and 6). 7.1 Comparisons between CPCA and JD In this dissertation, I applied constrained principal component analysis (CPCA) to find cognitive correlates of psychiatric symptoms (Chapters 3 and 4) and joint decorrelation (JD) to extract latent EEG dimensions to study the effects of tACS on them (Chapters 5 and 6). There are many similarities between these two supervised dimensionality reduction techniques – CPCA and JD. Both methods enhance the representation of the desired features in the raw data before performing dimensionality reduction. In CPCA, the variance in the criterion variable (Z) is constrained to the variance explained by the predictor variable (G) (mathematically, Z is projected onto G), while in JD, the variance in the data is selectively enhanced using a bias filter. Mathematically, both methods bias the data using linear transformations. Then, both methods use PCA (or eigen decomposition) on the biased (or constrained) data to estimate the latent dimensions. However, there are a few differences between CPCA and JD. The main difference is that the data in JD is whitened before the application of the bias filter. Then, eigen decomposition is used on the covariance matrix of the biased data to estimate the weights to transform the raw data from 159 observed space to latent space. These weights are used to project the raw data onto the latent space to estimate the latent components (scores), without using the bias filter again. In contrast, in CPCA, there is no whitening of the data before constraining it, and singular value decomposition is used to decompose the constrained data into component loadings and component scores. It is important to note that although the main difference between the two methods is the whitening of the data, mathematically, both methods optimize different objectives. In CPCA, latent dimensions are estimated by performing eigen decomposition on the covariance matrix of the constrained data, whereas in JD, latent dimensions are estimated based on the eigen decomposition of the ratio of the covariance matrix of the biased data to the covariance matrix of the raw data. That is, CPCA estimates latent components that best explain the constrained variance, whereas JD estimates latent components that enhance the biased variance while suppressing the overall raw variance. This leads to the latent components being estimated by decomposing the constrained data in CPCA, whereas in JD, they are obtained by projecting the raw data onto the latent space. The rationale for using CPCA for finding cognitive correlates of symptoms and JD for extracting latent dimensions is that CPCA is better suited to explain the overlap between cognition and psychiatric symptoms (the constrained data), whereas JD is better suited to extract latent EEG components. The reasoning is as follows - CPCA could be used for EEG analysis, and this would be equivalent to bandpass filtering the data in the desired frequency bands and performing PCA on the filtered data. However, such an approach limits the EEG signal to only the given frequency band, and thus does not allow further exploration of the latent dimensions such as the influence of cross-frequency coupling. Also, JD could also be used to find cognitive components related to 160 symptoms, but although JD latent components will minimize the variance unrelated to predictor variables, it’s overlap with the predictor variables won’t be optimized, as the latent components will still contain some variance unrelated to the predictor variables. Future studies are required to test the extent of similarities and differences by data simulation and comparative analysis. 7.2 Findings from identifying cognitive correlates of psychiatric symptoms In Chapter 3, I employed constrained principal component analysis (CPCA), a supervised dimensionality reduction technique, on data from an international multisite study involving non-clinical participants. The analysis focused on the overlap between two multivariate sets of variables—one assessing cognition and the other measuring hallucinatory experiences—at the individual item level. To mitigate overfitting, I developed a three-step analysis pipeline incorporating a series of reliability tests to minimize the reporting of spurious results. Although I obtained novel insights into the overlap between the variables, certain parts of the analysis pipeline required improvement. The major issue was the challenge of matching components across independent runs of CPCA in each iteration, which led to the use of many arbitrary thresholds throughout the analyses. In chapter 4, I mitigated the issues in the three-step CPCA pipeline used in chapter 3. To avoid the possible mismatch of components across iterations and selecting multiple arbitrary thresholds throughout the analyses, I estimated a common set of component loadings for all iterations, thereby preventing the need for arbitrary thresholds to determine whether components across iterations are matched. Additionally, I used the Benjamini-Hochberg correction for multiple comparisons. I 161 applied this improved pipeline, referred to as iterative CPCA, to identify links between cognition and symptoms within the schizophrenia spectrum disorder. This approach also provided a nuanced, multimodal understanding of psychiatric symptoms but without the limitations of 3-step CPCA. 7.2.1 Implications The use of aggregate scores in many studies has prevented the discovery of novel nuanced associations at the level of individual items. The approach in Chapter 3 revealed that the overlap between hallucinatory experiences (HEs) and cognition variables can be conceptualized as bi-dimensional. Specifically, two distinct mechanisms were identified: psychosis-spectrum distortions (including voices) underpinned by a liberal criterion for signal detection in cognition, and dissociation-spectrum sensation overload underpinned by reduced laterality in cognition. These mechanisms suggest multiple pathways for the development of HEs in different individuals. For instance, hallucinations involving psychosis-spectrum experiences may be linked to a liberal criterion for signal detection, whereas dissociation-spectrum experiences, such as vivid daydreams and sensory overload, may be associated with reduced laterality of attention. In Chapter 4, analysis revealed two distinct symptom clusters within the schizophrenia spectrum disorder: firstly, disorganized communication, language and thought disorders were associated with verbal memory deficiencies. Secondly, motor impoverishment was associated with working memory deficit. This demonstrates how using aggregate scores for HEs can obscure more nuanced dimensional associations, highlighting the value of studying items at the individual level. 162 7.2.2 Limitations One significant limitation of the iCPCA approach is the lack of cross-validation. Although I employed rigorous split-half and permutation testing, cross-validation, which is considered the gold standard for assessing generalizability (Arlot, 2017), was not conducted. This would involve using component loadings from a training set of data to estimate scores for a test set, thereby validating the reliability of predictor loadings in the held-out dataset. Incorporating cross-validation in future studies would provide a more robust validation of my findings and enhance the generalizability of the associations identified. One could argue that a limitation of item-level analysis is that individual questionnaire items can be noisy, requiring the use of summary scores or subscales to reliably measure symptoms. However, using supervised multivariate techniques does not necessarily mean interpreting data at the level of individual items but rather at the level of components. The main difference between using summary scores and components derived from a supervised method is that summary scores assume equal weighting for all items within a subscale. In contrast, components do not require this assumption; instead, the optimal weight for each item is estimated for each component. By performing a multivariate item-level analysis, one rejects the assumption that a group of items is uniformly important in predicting another set of measures and instead relies on a data-driven approach to estimate the importance of each item within a component. Therefore, instead of simply averaging a set of items (and assuming uniform importance) to reduce the noise of individual items, multivariate methods reduce noise by calculating a weighted average of the items. 163 Another limitation is the need for a comprehensive comparison with other dimensionality reduction techniques. While I focused on constrained principal component analysis (CPCA), it is essential to evaluate how CPCA performs relative to other techniques using the same iterative pipeline. Some candidate methods for comparison are canonical correlation analysis (CCA), partial least squares (PLS), and machine learning approaches like random forests (D. G. Lee et al., 2021; Okutucu et al., 2023; S. Vieira et al., 2024; Zhuang et al., 2020). Conducting a data simulation and comparative analysis would help determine the strengths and weaknesses of my approach and provide a broader context for interpreting the results. 7.2.3 Future directions The use of supervised approaches to detect individual item-level associations is exploratory in nature. In the future, these item-level hypotheses could be tested by pre-registering these findings as hypotheses, ensuring that the exploratory research is followed by a confirmatory approach. This would enhance the credibility and replicability of the results. Moreover, using iCPCA is not limited to finding cognitive correlates to symptoms. It can be applied to link any two sets of variables. Future research should also focus on collecting various measures such as neuroimaging data (e.g., electroencephalography (EEG) and functional magnetic resonance imaging (fMRI)), personality traits, cognitive assessments, daily functioning, demographics, brain activity, and other general measures of mental and physical health. By linking each set of variables with the others, researchers can gain a comprehensive understanding of subjective experiences and behaviors and how they relate to neurobiology. 164 One potential application of my method is in the development of new questionnaire items and recommended subscales. Most questionnaires have established subscales that group items into specific categories or divide them into meaningful subgroups. For example, the Scale for the Assessment of Negative Symptoms (SANS) includes five recommended subscales, such as affective flattening, alogia, avolition, anhedonia, and attention. In this dissertation, I demonstrate that item-level analysis can identify optimized components or sets of items that differ from the recommended subscales and are better suited for correlating with other measures. Thus, future developers should consider not only the subscales that explain the internal structure of questionnaire items but also additional subscales that are best suited to be linked with other measures. For instance, questionnaire items could have additional subscales that best correlate with cognition, neuroimaging data, or health data from wearable devices. The key takeaway message for future researchers is twofold. Firstly, perform individual item-level analysis to uncover nuanced associations that might be obscured by aggregate scores. Secondly, use supervised approaches that enable novel exploration of associations, because pre-defined factors (from unsupervised methods) generate suboptimal associations. 7.3 Findings from neuromodulation studies The overarching goal of the neuromodulation studies is to identify conditions in which tACS reliably affects electrophysiology and behavior. In Chapter 5, I investigated whether tACS influences 40Hz auditory steady-state responses (ASSRs) when their frequencies are matched. To achieve this, I used joint decorrelation (JD), a supervised dimensionality reduction technique, to 165 extract latent EEG oscillations corresponding to the 40Hz ASSR signal. I observed that the ASSR component obtained using JD had a higher signal-to-noise ratio than the components obtained from PCA. However, the ASSR components were unaffected by tACS (as compared to sham and 11Hz tACS). In Chapter 6, I addressed some of the possible reasons for tACS not affecting the EEG signal in Chapter 5. The major issue with the previous paradigm was that the anodes and cathodes were placed very close together, like in a high-density stimulation setup, resulting in induced electric fields that were too weak to induce changes. To rectify this, I separated the anode and cathode to ensure that the induced electric fields in the brain were sufficient to induce changes (see Table 1.1). Thus, I prioritized achieving a greater electric field over a more localized effect. Additionally, I targeted alpha oscillations rather than evoked oscillations, as their magnitude is significantly higher. Lastly, I introduced a simple behavioral paradigm before, during, and after stimulation to standardize brain states across participants. In this study, I investigated the effects of tACS on alpha oscillations. I extracted alpha oscillations using both ROI and JD analyses. I hypothesized that tACS at 10Hz (as compared to 40Hz) would increase alpha power, and I observed that tACS did indeed increase alpha power, but only in the contralateral electrodes. This suggested that the lateralized effect of tACS could be due to the lateral bias in responses in the behavioral paradigm. To further test this hypothesis, I conducted a control experiment with unbiased responses. I observed a systematic gradation in the difference in alpha enhancement due to 10Hz tACS between left and right lateral electrodes for left-biased, unbiased, and right-biased groups. These results suggest that the effects of tACS on alpha oscillations are task-dependent. 166 7.3.1 Implications My findings suggest that tACS influences different brain regions differently depending on the task being performed. In the study, participants engaged in a vigilance/oddball paradigm, where they were biased to respond with one hand and only occasionally with the other. This task involves inhibiting the default response, a process in which alpha oscillations are known to play a role (Deiber et al., 2012; Klimesch et al., 2007). The interaction between the inhibitory action of alpha oscillations and tACS likely led to the lateralized enhancement of alpha oscillations. This underscores the importance of considering task context when designing and interpreting tACS studies and suggests that tACS could be used alongside behavioral therapies to enhance therapeutic interventions. Additionally, my results provide insights into a common challenge in tACS research: inducing large electric fields often requires placing the anode and cathode far apart, which can lead to non-localized electric fields spreading throughout much of the brain. By placing the anode and cathode far apart, I ensured sufficient induced electric fields to induce changes, prioritizing a greater electric field over localization. However, my findings suggest that the effects of tACS can be localized by using specific tasks that engage the desired brain areas. If these results can be generalized, tasks can be employed to direct the effects of tACS to target brain regions, enhancing the precision and effectiveness of the stimulation. 167 7.3.2 Limitations One of the main limitations in any tACS study is its replicability as tACS studies are notoriously challenging to replicate reliably. Despite having a relatively large sample size of n=74 participants, the robustness of the results should be cautiously considered pending replication. In my investigation, I found that using predefined Regions of Interest (ROIs) yielded more consistent tACS results as compared to using supervised dimensionality reduction techniques like joint decorrelation. While both approaches showed similar trends, the effect sizes from JD analyses were notably smaller than those from ROI analyses. This difference might be because the JD analysis was designed to maximize signal within the alpha band rather than differentiating between stimulation conditions. 7.3.3 Future directions These findings lead to several new questions for future research. One key question is whether the cognitive load imposed by an oddball task is necessary to observe tACS effects, or if the effect is solely dependent on the motor bias of responses (Deiber et al., 2012). To investigate this, conducting a similar experiment but replacing the oddball task with a task involving 100% responses on either the left or right side would dissociate the impact of cognitive load versus motor bias on the efficacy of tACS. There are many other avenues for researchers to explore - whether participants must actively perform the task during tACS stimulation to observe these effects? Do effects generalize to other 168 brain areas and frequency bands? Understanding this could expand the application of tACS to modulate behavior more broadly. Additionally, exploring the underlying mechanisms of these effects is crucial. Are the observed effects primarily due to the after-effects of entrainment during stimulation, or do they involve long-term plastic changes in neural circuits? Future research paradigms should aim to address these mechanistic questions to better understand the potential and limitations of tACS as a neuromodulation tool. 7.4 Conclusion In conclusion, this research showcased the versatile applicability of supervised dimensionality reduction techniques. I effectively utilized methods such as CPCA and JD across two distinct domains: identifying cognitive correlates of psychiatric symptoms and estimating EEG latent dimensions to study the effects of neuromodulation. 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Component reliability proportions Components 1 2 3 4 5 6 1.00 1.00 0.83 0.64 1.00 0.35 Note. To test the reliability of the PCA component loadings, we performed 1,000 iterations of a split-half reliability test. In each iteration, the data (Z and G) was divided randomly into two halves, GC was computed, PCA was carried out on GC for each half independently, and the split-half component loading solutions were Procrustes rotated to the full-sample loading solution to optimize the match. The two sets of component loadings (one from each split-half) were correlated, and component pairs with correlation coefficients >= 0.64 were considered reliable across split halves. Each reliable component pair was then attempted to be matched to one of the components from the full-sample PCA on CG, achieved by correlating the averaged component loadings for a reliable split-half pair (i.e., averaged over the two split halves) with the component loadings from the full-sample CPCA (again, a correlation >= 0.64 was used, this time to determine a match). The component reliability proportions presented here were computed separately for each full-sample CPCA component, and are the proportion of the 1,000 iterations for which component pairs were not only deemed reliable, but also passed our criteria for being declared a match to a component from the full sample. This process led to exclusion of component 6 from further interpretation due to low component reliability proportions (< 0.5). 215 Table A.3. Predictor loading reliability proportions for positive loadings (threshold >= 0.48). Components 1† 2† 3† 4† 5† 6 CAPS Questionnaire Items CAPS Item 1: Do you ever notice that sounds are much louder than they normally would be? 0.00 0.06 0.01 0.00 0.00 n/a CAPS Item 2: Do you ever sense the presence of another being, despite being unable to see any evidence? 0.00 0.53 0.00 0.00 0.00 n/a CAPS Item 3: Do you ever hear your own thoughts repeated or echoed? 0.00 0.00 0.04 0.00 0.00 n/a CAPS Item 4: Do you ever see shapes, lights or colours even though there is nothing really there? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 5: Do you ever experience unusual burning sensations or other strange feelings in or on your body? 0.00 0.00 0.00 0.00 0.02 n/a CAPS Item 6: Do you ever hear noises or sounds when there is nothing about to explain them? 0.00 0.00 0.02 0.00 0.00 n/a CAPS Item 7: Do you ever hear your own thoughts spoken aloud in your head, so that someone near might be able to hear them? 0.00 0.00 0.12 0.00 0.00 n/a CAPS Item 8: Do you ever detect smells which don't seem to come from your surroundings? 0.01 0.02 0.03 0.00 0.00 n/a CAPS Item 9: Do you ever have the sensation that your body, or a part of it, is changing or has changed shape? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 10: Do you ever have the sensation that your limbs might not be your own or might not be properly connected to your body? 0.00 0.15 0.00 0.07 0.00 n/a CAPS Item 11: Do you ever hear voices commenting on what you are thinking or doing? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 12: Do you ever feel that someone is touching you, but when you look nobody is there? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 13: Do you ever hear voices saying words or sentences when there is no-one around that might account for it? 0.00 0.91 0.00 0.00 0.00 n/a CAPS Item 14: Do you ever experience unexplained 0.00 0.03 0.00 0.00 0.00 n/a 216 tastes in your mouth? CAPS Item 15: Do you ever find that sensations happen all at once and flood you with information? 0.00 0.00 0.53 0.00 0.00 n/a CAPS Item 16: Do you ever find that sounds are distorted in strange or unusual ways? 0.00 0.03 0.00 0.00 0.00 n/a CAPS Item 17: Do you ever have difficulty distinguishing one sensation from another? 0.25 0.24 0.07 0.00 0.00 n/a CAPS Item 18: Do you ever smell everyday odours and think that they are unusually strong? 0.00 0.01 0.00 0.00 0.38 n/a CAPS Item 19: Do you ever find the appearance of things or people seems to change in a puzzling way, e.g. distorted shapes or sizes or colour? 0.00 0.21 0.00 0.00 0.00 n/a CAPS Item 20: Do you ever find that your skin is more sensitive to touch, heat or cold than usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 21: Do you ever think that food or drink tastes much stronger than it normally would? 0.00 0.00 0.00 0.01 0.00 n/a CAPS Item 22: Do you ever look in the mirror and think that your face seems different from usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 23: Do you ever have days where lights or colours seem brighter or more intense than usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 24: Do you ever have the feeling that of being uplifted, as if driving or rolling over a road while sitting quietly? 0.14 0.46 0.00 0.00 0.00 n/a CAPS Item 25: Do you ever find that common smells sometimes seem unusually different? 0.00 0.11 0.00 0.02 0.01 n/a CAPS Item 26: Do you ever think that everyday things look abnormal to you? 0.09 0.78 0.07 0.00 0.00 n/a CAPS Item 27: Do you ever find that your experience of time changes dramatically? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 28: Have you ever heard two or more unexplained voices talking with each other? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 29: Do you ever notice smells or odours that people next to you seem unaware of? 0.00 0.01 0.00 0.00 0.00 n/a CAPS Item 30: Do you ever notice that food or drink seems to have an unusual taste? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 31: Do you ever see things that other people cannot? 0.21 0.00 0.00 0.03 0.00 n/a CAPS Item 32: Do you ever hear sounds or music that 0.32 0.44 0.00 0.00 0.00 n/a 217 people near you don't hear? LSHS-E Questionnaire Scores LSHS-E Item 1: Sometimes a passing thought will seem so real that it frightens me 0.00 0.02 0.07 0.00 0.00 n/a LSHS-E Item 2: Sometimes my thoughts seem as real as actual events in my life 0.00 0.01 0.04 0.00 0.00 n/a LSHS-E Item 3: No matter how hard I try to concentrate on my work unrelated thoughts always creep into my mind 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 4: In the past, I have had the experience of hearing a person’s voice and then found that no one was there 0.00 0.33 0.00 0.00 0.00 n/a LSHS-E Item 5: The sounds I hear in my daydreams are generally clear and distinct 0.00 0.00 0.03 0.00 0.00 n/a LSHS-E Item 6: The people in my daydreams seem so true to life that I sometimes think that they are 0.00 0.00 0.41 0.00 0.00 n/a LSHS-E Item 7: In my daydreams I can hear the sound of a tune almost as clearly as if I were actually listening to it 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 8: I often hear a voice speaking my thoughts aloud 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 9: I have been troubled by hearing voices in my head 0.10 0.77 0.05 0.00 0.00 n/a LSHS-E Item 10: On certain occasions, I have seen the face of a person in front of me, but there was no one 0.00 0.00 0.44 0.00 0.00 n/a LSHS-E Item 11: Sometimes, immediately prior to falling asleep or upon awakening, I have had the experience of having seen or felt or heard something or someone that wasn’t there or the feeling of being touched even though no one was there 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 12: Sometimes, immediately prior to falling asleep or upon awakening, I have had a sensation of floating or falling or that I left my body temporarily 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 13: On certain occasions I have had the feeling of the presence of someone close who has deceased 0.00 0.00 0.07 0.00 0.00 n/a LSHS-E Item 14: In the past, I have smelt a particular odour when there was nothing there 0.00 0.00 0.34 0.00 0.00 n/a 218 LSHS-E Item 15: I have had the feeling of touching something or being touched and then found that nothing or no one was there 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 16: Sometimes I have seen things or animals when nothing was in fact there 0.00 0.00 0.00 0.00 0.00 n/a Note: †Components that were deemed reliable according to the component reliability proportions presented in Table A.2. Predictor loading reliability was performed only on reliable components. The positive predictor loading reliability proportion was computed as the proportion of the reliable components from the 1,000 iterations that showed positive predictor loadings >= 0.19 in both split-half solutions. Predictor loading reliability proportions >= 0.48 were used to interpret the predictor loadings, and are highlighted in bold font and cell borders. The proportions for unreliable component (comp 6) have been populated with ‘n/a’. 219 Table A.4. Predictor loading reliability proportions for negative loadings. Components 1† 2† 3† 4† 5† 6 CAPS Questionnaire Items CAPS Item 1: Do you ever notice that sounds are much louder than they normally would be? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 2: Do you ever sense the presence of another being, despite being unable to see any evidence? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 3: Do you ever hear your own thoughts repeated or echoed? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 4: Do you ever see shapes, lights or colours even though there is nothing really there? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 5: Do you ever experience unusual burning sensations or other strange feelings in or on your body? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 6: Do you ever hear noises or sounds when there is nothing about to explain them? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 7: Do you ever hear your own thoughts spoken aloud in your head, so that someone near might be able to hear them? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 8: Do you ever detect smells which don't seem to come from your surroundings? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 9: Do you ever have the sensation that your body, or a part of it, is changing or has changed shape? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 10: Do you ever have the sensation that your limbs might not be your own or might not be properly connected to your body? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 11: Do you ever hear voices commenting on what you are thinking or doing? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 12: Do you ever feel that someone is touching you, but when you look nobody is there? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 13: Do you ever hear voices saying words or sentences when there is no-one around that might account for it? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 14: Do you ever experience unexplained tastes in your mouth? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 15: Do you ever find that sensations happen 0.00 0.00 0.00 0.00 0.00 n/a 220 all at once and flood you with information? CAPS Item 16: Do you ever find that sounds are distorted in strange or unusual ways? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 17: Do you ever have difficulty distinguishing one sensation from another? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 18: Do you ever smell everyday odours and think that they are unusually strong? 0.00 0.00 0.00 0.00 0.06 n/a CAPS Item 19: Do you ever find the appearance of things or people seems to change in a puzzling way, e.g. distorted shapes or sizes or colour? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 20: Do you ever find that your skin is more sensitive to touch, heat or cold than usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 21: Do you ever think that food or drink tastes much stronger than it normally would? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 22: Do you ever look in the mirror and think that your face seems different from usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 23: Do you ever have days where lights or colours seem brighter or more intense than usual? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 24: Do you ever have the feeling that of being uplifted, as if driving or rolling over a road while sitting quietly? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 25: Do you ever find that common smells sometimes seem unusually different? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 26: Do you ever think that everyday things look abnormal to you? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 27: Do you ever find that your experience of time changes dramatically? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 28: Have you ever heard two or more unexplained voices talking with each other? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 29: Do you ever notice smells or odours that people next to you seem unaware of? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 30: Do you ever notice that food or drink seems to have an unusual taste? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 31: Do you ever see things that other people cannot? 0.00 0.00 0.00 0.00 0.00 n/a CAPS Item 32: Do you ever hear sounds or music that people near you don't hear? 0.00 0.00 0.00 0.00 0.00 n/a 221 LSHS-E Questionnaire Scores LSHS-E Item 1: Sometimes a passing thought will seem so real that it frightens me 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 2: Sometimes my thoughts seem as real as actual events in my life 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 3: No matter how hard I try to concentrate on my work unrelated thoughts always creep into my mind 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 4: In the past, I have had the experience of hearing a person’s voice and then found that no one was there 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 5: The sounds I hear in my daydreams are generally clear and distinct 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 6: The people in my daydreams seem so true to life that I sometimes think that they are 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 7: In my daydreams I can hear the sound of a tune almost as clearly as if I were actually listening to it 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 8: I often hear a voice speaking my thoughts aloud 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 9: I have been troubled by hearing voices in my head 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 10: On certain occasions, I have seen the face of a person in front of me, but there was no one 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 11: Sometimes, immediately prior to falling asleep or upon awakening, I have had the experience of having seen or felt or heard something or someone that wasn’t there or the feeling of being touched even though no one was there 0.00 0.00 0.00 0.04 0.00 n/a LSHS-E Item 12: Sometimes, immediately prior to falling asleep or upon awakening, I have had a sensation of floating or falling or that I left my body temporarily 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 13: On certain occasions I have had the feeling of the presence of someone close who has deceased 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 14: In the past, I have smelt a particular odour when there was nothing there 0.00 0.00 0.00 0.00 0.00 n/a LSHS-E Item 15: I have had the feeling of touching something or being touched and then found that nothing or no one was there 0.00 0.00 0.00 0.00 0.00 n/a 222 LSHS-E Item 16: Sometimes I have seen things or animals when nothing was in fact there 0.00 0.00 0.00 0.00 0.00 n/a Note: †Components that were deemed reliable according to the component reliability proportions presented in Table A,2. Predictor loading reliability was computed only on reliable components. The negative predictor loading reliability proportion was computed as the proportion of the reliable components from the 1,000 iterations that showed negative predictor loadings <= -0.19 in both split-half solutions. No negative predictor loadings were deemed as reliable (predictor loading reliability proportions >= 0.48). The proportions for unreliable component (comp 6) have been populated with ‘n/a’. 223 Figure A.1. Histograms for cognitive measures Note: Z-score normalized histograms for the 18 cognitive measures used for CPCA (n=419). DL = Dichotic Listening; SMT = Source Memory Task; MR = Matrix Reasoning; DS = Digit Span; SgD = Auditory Signal Detection. 224 Figure A.2. Histograms for CAPS questionnaire items Note: Histograms for 32 questionnaire items (n=419) of Cardiff Anomalous Perceptions Scale (CAPS). Each item has a ‘Yes’ or ‘No’ response. ‘Yes’ is coded as 1 and ‘No’ is coded as ‘0’. The questionnaire questions are shortened for better visualization. The full questions can be found in Table 3.2. 225 Figure A.3. Histograms for LSHS-E questionnaire items Note: Histograms for 16 questionnaire items (n=419) of Launay-Slade Hallucination Scale – Extended (LSHS-E) hallucination scale. Each item has a 5-point Likert response from 0-4. The questionnaire questions are shortened for better visualization. The full questions can be found in Table 3.2. 226 Appendix B Figure B.1. Histograms for cognitive measures Note: Z-score normalized histograms for the 18 cognitive measures used for CPCA (n=206). 227 Figure B.2. Histograms for SANS items Note: Histograms for 25 items (n=206) of Scale for the Assessment of Negative Symptoms (SANS). Each item has a 6-point Likert response from 0-5. 228 Figure B.3. Histograms for SAPS items Note: Histograms for 33 items (n=206) of Scale for the Assessment of Positive Symptoms (SAPS). Each item has a 6-point Likert response from 0-5.
Thesis/Dissertation
eng
Bioinformatics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Woodward, Todd S.
Supervised dimensionality reduction applications in identifying cognitive correlates of psychiatric symptoms and extracting low-dimensional EEG signals to study the effects of tACS
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