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UBC Theses and Dissertations

Exploring the mathematical equations and empirical properties for maximal reliability and factor determinacy in bifactor models Li, Sijia

Abstract

Bifactor models gained increasing popularity across different areas of psychology in the past two decades. Methodologists proposed that omega reliability indices, maximal reliability (i.e., coefficient H) and factor determinacy can be used for evaluating the quality of total scale and subscales, as well as whether the general and group factors are well-defined by item (sub)set in the bifactor model. However, previous literature directly imported the formula for coefficient H derived from unidimensional models, which is incorrect for bifactor models. Additionally, no previous study explored the mathematical connections between maximal reliability and factor determinacy and empirical performances in bifactor models. Therefore, I proved that coefficient H formula is incorrect for latent variables in bifactor models, and derived the correct formula for maximal reliability in bifactor models. I also proved that in bifactor models, the mathematical relationships between omega reliability, maximal reliability and factor determinacy are consistent with their relationships in unidimensional models. With the bifactor-derived formulas, I illustrated how to compute and interpret maximal reliability, factor determinacy, optimal and regression weights for general and group factors in the empirical bifactor model reported by Watts et al. (2019). In empirical bifactor models, regression factor total scores are more reliable than regression factor subscores, and regression factor scores are more reliable than sum scores. Additionally, a substantive proportion of negative regression weights are found on positively loaded items, which compromised the interpretability of regression factor scores. [An errata to this thesis was made available on 2025-01-15.]

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Attribution-NonCommercial-NoDerivatives 4.0 International