PSYCHOLOGICAL NEEDS AND WELL-BEING  1 An examination of Dweck’s psychological needs model in relation to exercise-related well-being Colin M. Wierts, MSc1 Bruno D. Zumbo, PhD1 Ryan E. Rhodes, PhD2 Guy Faulkner, PhD1Mark R. Beauchamp, PhD11University of British Columbia 2University of Victoria Author Note Colin Wierts, Guy Faulkner, and Mark Beauchamp are with the School of Kinesiology, The University of British Columbia, Vancouver, British Columbia, Canada. Bruno Zumbo is with the Department of Educational and Counseling Psychology and Special Education at The University of British Columbia, Vancouver, British Columbia, Canada. Ryan Rhodes is with the School of Exercise Science, Physical and Health Education, University of Victoria, Victoria, British Columbia, Canada. This research was supported by a graduate scholarship awarded to Colin Wierts by the Social Sciences and Humanities Research Council of Canada. The authors would like to acknowledge Allison McVicar for assistingwith the focus groups.  Correspondence should be addressed to Colin M. Wierts, colin.wierts@ubc.ca or School of Kinesiology, War Memorial Gym, University of British Columbia, 122–6081 University Blvd., Vancouver, BC, V6T 1Z1, Canada. Citation: Wierts, C. M., Zumbo, B. D., Rhodes, R. E., Faulkner, G., & Beauchamp, M. R. (2021). An examination of Dweck’s psychological needs model in relation to exercise-related well-being. Journal of Sport & Exercise Psychology, 43(4), 323–334. https://doi.org/10.1123/jsep.2021-0026 © 2021, Human Kinetics, Inc. This paper is not the copy of record and may not exactly replicate the final, authoritative version of the article. The final article is available via its DOI: https://doi.org/10.1123/jsep.2021-0026 PSYCHOLOGICAL NEEDS AND WELL-BEING  2  Abstract 1 This two-part study examined Dweck’s psychological needs model in relation to exercise-related well-2 being, and particularly focused on the basic need for optimal predictability, and compound needs for 3 identity and meaning.  In Part 1 (N = 559), using exploratory factor analysis, scores derived from items 4 assessing optimal predictability (prediction of affect and instrumental utility in exercise) were 5 empirically distinct from scores derived from items assessing competence, relatedness, and autonomy.  6 In Part 2, participants from Part 1 (N = 403) completed measures of exercise-related well-being four 7 weeks after baseline assessment.  Prediction of affect was the most consistent predictor of subsequent 8 exercise-related well-being.  An implication of these findings is that optimal predictability (primarily 9 prediction of affect) represents a unique experience that may be necessary for thriving in the context of 10 exercise.  Prediction of affect should be targeted in experimental designs to further understand its 11 relationship with exercise-related well-being. 12 Key words: psychological need satisfaction, physical activity, optimal predictability, meaning, identity, 13 subjective vitality 14 15 PSYCHOLOGICAL NEEDS AND WELL-BEING  3  Just as humans have physical needs for food and water to maintain physiological functioning 1 (Hull, 1943), humans have psychological needs that maintain the integrity and functioning of the psyche 2 (Baumeister & Leary, 1995; Deci & Ryan, 2000; Dweck, 2017; Sheldon, 2011).  The study of 3 psychological needs has a long history, with different conceptualizations (Pittman & Zeigler, 2007) and 4 new models of psychological needs regularly proposed (e.g., Dweck, 2017; Sheldon, 2011).  5 Psychological needs can be broadly conceptualized as innate, universal psychosocial requirements for 6 well-being and long-term psychological health and development that also play a functional role in 7 shaping motivation and behaviour (Baumeister & Leary, 1995; Deci & Ryan, 2000; Dweck, 2017; 8 Maslow, 1943; Sheldon, 2011).   9 Arguably, the most frequently used model of psychological needs corresponds to basic 10 psychological need theory (Ryan & Deci, 2002, 2017) that is subsumed within self-determination theory 11 (SDT; Ryan & Deci, 2002, 2017).  SDT is a macro theory of human motivation, well-being, and 12 personality development, with competence, relatedness, and autonomy identified as basic, universal, and 13 fundamental psychological needs that need to be fulfilled in order for humans to thrive.  Competence 14 refers to feeling a sense of mastery and effectiveness in one’s environment while having the opportunity 15 to expand and build upon one’s abilities (Ryan & Deci, 2017; White, 1959).  Relatedness refers to feeling 16 connected, cared for, and a sense of belonging among others in one’s social milieu (Baumeister & Leary, 17 1995; Ryan & Deci, 2017).  Finally, autonomy refers to feeling a sense of volition, self-endorsement, and 18 choice over one’s actions (de Charms, 1968; Ryan & Deci, 2017).  Deci and Ryan (1991) proposed that 19 these three needs constitute the necessary psychosocial experiences for maintaining intrinsically 20 motivated behaviour (engaging in activities because they are inherently interesting and rewarding), and 21 the capacity to internalise and integrate external social and cultural values as one’s own in order to act as 22 a self-determined agent in society.  Intrinsic motivation and integration of psychosocial experiences are 23 considered natural, organismic growth processes of the self (Deci & Ryan, 1991; Ryan, 1995), and 24 PSYCHOLOGICAL NEEDS AND WELL-BEING  4  because psychological needs support these natural processes, Deci and Ryan (2000) propose they are 1 necessary for well-being.   2 Research that has applied BPNT in exercise and health promotion settings has had some success 3 explaining variability in exercise and physical activity related well-being (Gunnell et al., 2013; Mack et 4 al., 2017; Sylvester et al., 2012; Wilson et al., 2009; Wilson, Longley, et al., 2006). There are, however, 5 at least two caveats associated with this research that should be noted.  First, patterns of relationships 6 between these three ostensive needs have been notably inconsistent, with several studies failing to find 7 support for the predictive utility of one or more of those needs in relation to both positive and negative 8 well-being outcomes (e.g., Gunnell et al., 2014; McDonough & Crocker, 2007).  Second, in light of the 9 small-to-medium sized relationships between those needs and putative well-being outcomes (e.g., Wilson 10 et al., 2008) researchers in social psychology (Sheldon, 2011) and exercise psychology (Wilson, Longley, 11 et al., 2006) have suggested that other psychological experiences should be explored.  For example, 12 studies, in the context of exercise, examining perceived variety (Sylvester et al., 2014) and self-13 actualization and physical thriving (Wilson, Longley, et al., 2006) have explained additional variance in 14 exercise-related well-being above and beyond the three SDT needs.   15 A promising psychological needs model that may be particularly useful in the context of exercise 16 is that proposed by Dweck (2017), which provides the foundation for a theory of motivation, personality, 17 and development.  Dweck began with the assumption that psychological needs energize need-satisfying 18 goals and support psychological well-being and health, and proposed there are three basic psychological 19 needs present from birth (competence, acceptance, optimal predictability) and four emerging compound 20 needs that arise from the combination of the basic needs (self-esteem/status, control, trust, self-21 coherence).  See Figure 1 for a visual representation of Dweck’s psychological need model.  By applying 22 Baumeister and Leary's (1995) criteria of basic psychological needs, Dweck (2017) suggested that a 23 psychological need (basic and compound) should have high universal value and contribute to well-being 24 and ongoing psychological development.  A basic need should not be derived from other needs or 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  5  motives, and should be present from, or shortly after, birth (Dweck, 2017).  Dweck (2017) acknowledged 1 that within the basic needs set, competence and acceptance map directly onto SDT’s competence and 2 relatedness needs, respectively; acceptance being the relatedness that infants need.  Drawing from 3 motivational concepts such as Higgins' (2012) motive for truth and Stevens and Fiske's (1995) motive for 4 understanding, Dweck (2017) proposed the basic need for optimal predictability, which refers to the need 5 to understand and predict the relationships between events in one’s environment.  Moreover, Dweck 6 (2017) drew from the developmental literature, neuroscience, and animal studies to contend that (a) 7 infants are able to integrate relevant information for making predictions about their environment; (b) 8 predictable caregiving during infancy and childhood is necessary for well-being; (c) the brain naturally 9 encodes predictive models; and (d) animals prefer, and benefit from, predictable stimuli in their 10 environment.  Dweck included the word optimal in order to reflect the notion that too much predictability 11 is undesirable, and humans must engage with novel stimuli.  Of particular note, optimal predictability 12 represents a need that was not conceptualized in any form within SDT.  Conceptually, however, optimal 13 predictability shares similarities with outcome expectancies, which reflect expectations that an outcome 14 will follow a given behaviour (Bandura, 1997). 15  According to Dweck (2017), as people mature psychologically and develop more complex 16 cognitive schemas, compound needs subsequently emerge.  The need for self-esteem/status (positive 17 personal evaluations and respect from others), according to Dweck (2017), derives from the satisfaction 18 of acceptance and competence needs.  The need for control, which includes autonomy (from SDT), self-19 control (the ability to self-regulate one’s actions and override impulses and agency; Tangney et al., 2004), 20 and agency (the perception that one can intentionally influence their functioning and life circumstances; 21 Bandura, 2006), is derived from the satisfaction of competence and optimal predictability.  Again, 22 according to Dweck’s (2017) model, the need for trust emerges from the satisfaction of the need for 23 acceptance and predictable caregiving.  Finally, within this framework, the need for self-coherence (a 24 stable and intact sense of self) is purported to emerge from the satisfaction of the basic and compound 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  6  needs described above.  Self-coherence is conceptualized as a superordinate need for meaning (sense of 1 congruence among events in one’s world) and identity (self-perceived social roles and competencies), 2 both of which are considered to bind one’s sense of self (Dweck, 2017).     3 An important point to be made about Dweck’s (2017) model is that it has key similarities and 4 differences with the predominant SDT model proposed by Deci and Ryan (2000).  As previously noted, 5 within Dweck’s (2017) basic need framework, competence and acceptance map directly onto the SDT 6 needs of competence and relatedness, respectively.  The key difference with Dweck’s (2017) model when 7 compared to SDT is the inclusion of optimal predictability, and the exclusion of autonomy, which is 8 considered by Dweck (2017) to be a facet of the compound need for control.  Given that competence, 9 relatedness, and autonomy (from SDT) have been studied extensively in relation to exercise behaviour 10 (Rhodes et al., 2019; Teixeira et al., 2012) and well-being (Wilson et al., 2008), the overall purpose of 11 this two-part paper was to examine whether optimal predictability (when operationalized as a basic 12 psychological need) accounts for unique variance in exercise-related well-being beyond those three SDT 13 needs.   14 Specifically, in Part 1, based on Dweck’s contentions that optimal predictability is a unique basic 15 psychological need, we tested the hypothesis that scores derived from items assessing optimal 16 predictability (in exercise) would be empirically distinct from scores derived from measures of 17 competence, relatedness, and autonomy satisfaction in exercise settings.  In Part 2, based on Dweck’s 18 contentions that optimal predictability has direct implications for well-being, we tested the hypothesis that 19 scores derived from measures of optimal predictability would explain unique variance in scores derived 20 from measures of exercise-related well-being (while simultaneously considering measures of competence, 21 relatedness, and autonomy).  Finally, based on Dweck’s contention that each basic and compound need 22 influences feelings of self-coherence (identity and meaning), which in turn influences well-being, we 23 tested the hypothesis that identity and meaning would mediate the relationships between the basic 24 psychological needs and exercise-related well-being.  This involved examining indirect effects between 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  7  putative predictors (needs for optimal predictability, competence, autonomy, and relatedness) and well-1 being via exercise-related meaning and exercise identity.  2 Part 1 3 Methods 4 Participants 5  Participants (N = 559) were a community sample of adults (i.e., 18 – 77 years of age).  The sample 6 (Mage = 32.33 years; SDage = 14.15 years) included 369 females, 189 males, and one individual who 7 selected ‘other’ for gender.  The majority of participants reported they were White or White/mixed race 8 (70.10%), residents of Canada (93.40%), a student (40.40%) or employed full time (41.30%), and 65.80% 9 of the sample reported an annual household income of less than $100,000.  Participants either completed 10 some high school (1.30%), a high school diploma (12.20%), some college/university (24.00%), a college 11 diploma/university degree (34.50%), some graduate school (5.50%) or a graduate degree (22.50%).  12 Participants also reported the number of times they engaged in mild, moderate, and vigorous exercise in 13 the past week using the Godin leisure time exercise questionnaire (Godin & Shephard, 1985), and the 14 average duration of mild, moderate, and vigorous exercise sessions (Courneya et al., 2004).  Consistent 15 with Courneya et al. (2004), we created an indicator of moderate-to-vigorous exercise minutes (in the past 16 week) for each participant using the following equation: (number of moderate exercise bouts x average 17 minutes per bout) + (number of vigorous exercise bouts x average minutes per bout).  After removing out 18 of range values (≥ 25 moderate and vigorous exercise sessions in the past week) and outliers with Z-19 scores above 3.29 (Tabachnick & Fidell, 1996), the mean minutes of moderate-to-vigorous exercise 20 behaviour was 253.86 minutes (SD = 210.85 minutes; median = 210.00 minutes; skewness = 1.25; and 21 kurtosis = 1.90).  In short, by most standards, the sample would be considered an active one. 22 Procedure 23  After receiving University of British Columbia institutional ethical approval for the study, adults 24 (18 years +) who were able to read, converse, and write in English were recruited for the study online 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  8  (social media posts, and advertisements) and in-person (university classes, local hiking trails, and 1 community events).  After providing informed consent, participants responded to an online survey 2 assessing demographics and psychological need measures.  Participants were entered into a prize draw to 3 win one of six $50 gift cards to compensate them for their time. 4 Measures    5 Optimal Predictability in Exercise  6 We used a two-step process, including item development and focus groups, to develop and refine 7 items that assess optimal predictability in the context of exercise.  First, we used Dweck’s (2017) 8 definition of optimal predictability and the exercise psychology literature to inform item development.  9 Dweck (2017) defines optimal predictability as “the desire to know the relationships among events and 10 among things in your world: what follows what, what belongs with what, or what causes what” (p. 692).  11 Two judgements/expectations that have been examined in exercise psychology are affective outcomes 12 (Will I feel good?), and instrumental utility (Will it be useful for my health?) of participating in exercise 13 (Gellert et al., 2012; Rhodes et al., 2009).  By operationalizing affective and instrumental 14 judgements/expectations, optimal predictability was assessed by asking participants to consider 15 exercising the following day and predict their affective experience (unsatisfying-satisfying, unpleasant-16 pleasant, unenjoyable-enjoyable, and boring-exciting) and the instrumental utility of exercise for their 17 health (useless-useful, unimportant-important, harmful-beneficial, worthless-valuable, not worthwhile-18 worthwhile) using a seven-point semantic differential scale (for example, extremely unsatisfying (1) , 19 moderately unsatisfying (2), slightly unsatisfying (3), neutral (4), slightly satisfying (5), moderately 20 satisfying (6), extremely satisfying (7)).  The semantic differential descriptors were adopted from Conner 21 et al. (2011). 22  Within Messick's (1995) integrative view of validity, gathering content and substantive evidence 23 is important for score interpretation.  Content validity refers to whether the elements of a measure 24 adequately represent, and are relevant for, the construct of interest (Messick, 1995).  The elements of 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  9  measures refer to question items, instructions, item framing, and administration (Sireci, 1998).  The 1 substantive aspect of construct validity refers to the degree to which individuals interact with a measure in 2 a manner that is expected based on the theory of the construct purported to be assessed (Messick, 1995).  3 Thus, in the second step of item development, focus groups were conducted to ensure the items were 4 clear, interpreted appropriately by members of the target population (i.e., adults), and appropriate for the 5 context of exercise. 6 After receiving University of British Columbia institutional ethical approval, four focus groups (N 7 = 11; Mage = 27.36 years; SDage = 9.30 years; 54.54% females) were conducted.  A modified ‘retrospective 8 think-aloud’ protocol (Oremus et al., 2005) was used to understand how participants interpret and provide 9 responses to the items.  After participants provided informed consent, they were instructed to complete 10 questionnaire items independently and were then asked a series of questions to prompt their interpretation 11 and understanding of those items.  Participants were asked and responded to the following questions 12 verbally: (a) “What, in your own words, does the question mean to you?” (b) “Did the answer choices 13 include your answer?” (c) “Did you understand how to answer the questions?” and (d) “Did the 14 questionnaire leave anything out you felt was important?”  Immediately after each focus group was 15 finished, the interviews were transcribed and coded using a constant comparison approach (Corbin & 16 Strauss, 2008) to identify potentially problematic items, instructions, or response formats.  In total, four 17 focus groups were conducted.  Modifications were made after each focus group until no further changes 18 were necessary.   19 After item trimming and refinement (4 items for prediction of affect; 5 items for prediction of 20 instrumental value for one’s health), the phrase “When answering the following questions, please think 21 about the exercise you typically perform and your personal health” was added to the instructions.  An 22 instrumental prediction item (how ‘useful’ exercise was predicted to be) was deleted, and an affective 23 prediction item (how ‘exciting’ exercise was predicted to be) was changed to ‘fun.’  These revisions 24 resulted in four prediction of affect items and four prediction of instrumental utility for health items (see a 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  10  full list of items in Table 1).  Also, see Table S1 in the Supplementary Online Materials for a complete 1 outline of changes made to the items, instructions, and scales of the optimal predictability items.   2 Competence, Autonomy, and Relatedness Satisfaction in Exercise 3 Competence was measured using five items from the competence subscale embedded in the 4 Intrinsic Motivation Inventory (IMI; McAuley et al., 1989; Ryan, 1982).  Autonomy was assessed using 5 the six-item autonomy subscale from the Psychological Need Satisfaction in Exercise Scale (PNSE; 6 Wilson, Rogers, et al., 2006).  Relatedness was assessed using the six-item Relatedness to Others in 7 Physical Activity Scale (ROPAS; Wilson & Bengoechea, 2010).  The ROPAS was modified for exercise 8 participation by exchanging the word ‘physical activity’ for ‘exercise’ in the instructional stem preceding 9 the items (see below). 10 The decision to not use the competence and relatedness subscales from the PNSE (Wilson, 11 Rogers, et al., 2006) was based on their item content.  Each item in the PNSE-competence subscale refers 12 to the concept of challenge.  Challenge may not be relevant for all people participating in exercise for 13 leisure purposes and health benefits, and we sampled participants from the community ranging in age and 14 exercise participation.  We decided to use the IMI-competence subscale because the items reflect general 15 perceptions of competence, and have been used in various samples including adult women ranging from 16 23 to 80 years in age (Markland & Tobin, 2010; Cronbach's alpha = .86), and university students (Wilson 17 & Bengoechea, 2010; Cronbach's alpha = .90).  Furthermore, there is external validity evidence for scores 18 derived from the IMI-competence subscale, as scores have been found to explain unique variance in 19 scores derived from various indices of well-being (Wilson & Bengoechea, 2010) and scores derived from 20 autonomous motivation for exercise (Markland & Tobin, 2010).  As for the PNSE-relatedness subscale 21 (see Wilson, Rogers, et al., 2006), the items assume participants interact with others in structured exercise 22 settings (example item: “I feel attached to my exercise companions because they accept me for who I 23 am”).  Again, because we sampled individuals from the community, as opposed to exercise classes or 24 exercise groups specifically, we could not assume that participants predominantly exercised alone or with 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  11  others.  The ROPAS was designed to measure perceptions of belonging in general physical activity 1 settings without the assumption that participants would be exercising in structured settings (Wilson & 2 Bengoechea, 2010).  There is also content, structural, and external validity evidence to support the 3 interpretation of scores derived from the ROPAS (Wilson & Bengoechea, 2010).  Therefore, we 4 considered the ROPAS items appropriate for our sample.  Items for all three sets of measures were 5 prefaced by: “The following statements represent different feelings people have when they engage in 6 exercise.  Please answer the following questions by considering how you typically feel when participating 7 in exercise using the scale provided.” Exemplar items of the scales included “I think I am pretty good at 8 exercising” (competence), “I am included by others” (relatedness), and “I feel like I am the one who 9 decides what exercises I do” (autonomy).  Responses were anchored on 6-point scales with higher scores 10 reflecting greater satisfaction of the corresponding need in the context of exercise. 11 Data Analysis 12  To examine whether scores derived from items assessing optimal predictability (prediction of 13 affect and the instrumental utility for one’s health) are empirically distinct from scores derived from items 14 assessing competence, autonomy, and relatedness, we conducted an exploratory factor analysis.  Models 15 with different factor structures were compared to determine the best fit when simultaneously analyzing 16 items assessing optimal predictability and competence, relatedness, and autonomy.  Based on Dweck’s 17 (2017) theorizing that optimal predictability is a distinct psychological need, and that items assessing 18 affective and health-related outcome expectancies load on separate factors (e.g., Gellert et al., 2012), we 19 expected scores from items assessing prediction of affect and prediction of instrumental utility for health 20 to load on two distinct factors (affect and instrumental prediction), and scores from items assessing 21 competence, relatedness, and autonomy to load on three distinct factors, ultimately producing a five-22 factor model.   Based on the three empirically-established psychological need factors of competence, 23 relatedness, and autonomy (Vlachopoulos & Michailidou, 2006; Wilson, Rogers, et al., 2006), the five-24 factor model was compared with a four- and three-factor model.  A four-factor model was examined to 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  12  determine whether the scores from optimal predictability items loaded on one factor (affect and 1 instrumental items loading on a single factor), and the scores from items assessing competence, 2 relatedness, and autonomy loaded on their own distinct factors.  A three-factor model was examined to 3 determine whether the scores from items used to assess optimal predictability could be subsumed by one 4 or more of the three known factors of competence, autonomy, and relatedness (Vlachopoulos & 5 Michailidou, 2006; Wilson, Rogers, et al., 2006).   6 The exploratory factor analysis was conducted using Mplus (Version 8.4; Muthén & Muthén, Los 7 Angeles, CA).  First, assumptions (outliers, missing data, normality) for the analysis were examined 8 (Tabachnick & Fidell, 1996). Due to measuring the variables with Likert-like categorical scales, we first 9 addressed the possibility of analyzing the data using the polychoric correlation matrix (Zumbo et al., 10 2007).  There was evidence of data sparseness in the multiway frequency data table, so we treated the 11 data as continuous for all subsequent analyses (in Part 1 and 2). The three different factor models were 12 estimated using robust maximum likelihood (RML) estimation and Geomin oblique rotation to account 13 for the correlations among psychological needs in exercise settings (Vlachopoulos & Michailidou, 2006; 14 Wilson, Rogers, et al., 2006).  To determine the best fitting model, we analyzed multiple goodness of fit 15 statistics (GOFS) alongside the χ2 test (Marsh, 2007).  The comparative fit index (CFI), Tucker Lewis 16 index (TLI), and root mean square error of approximation (RMSEA) were examined for each of the 17 proposed factor models, with higher CFI and TLI values (values closer to 1 along a 0-1 continuum) and 18 lower RMSEA values (values closer to 0 along a 0 to 1 continuum) signifying better model fit (Marsh, 19 2007).  We also examined the interpretability of factor loadings for the extracted factors.  20 Results 21  There were no missing data on any variables included for the analysis, as we used survey logic 22 (via Qualtrics, Qualtrics, Provo, UT) to inform participants that they needed to complete each question to 23 progress (same for Part 2).  No outliers were present as all values were in the expected range. The five-24 factor model had superior fit indices (χ2 (185) = 274.51, p < .01, CFI = .985, TLI = .975, RMSEA = .029, 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  13  90% confidence interval (CI) [.022-.037]) compared with a four-factor (χ2 (206) = 782.59, p < .01, CFI = 1 .902 , TLI = .857, RMSEA = .071, 90% CI [.066-.076]) and three-factor (χ2 (228) = 1470.31, p < .01, CFI 2 = .788, TLI = .721, RMSEA = .099, 90% CI [.094-.104]) model.  For the five-factor model, the items 3 loaded (> .3) on the specified a priori factors, and there was evidence of relatively small cross loading of 4 items (< .3) with other factors (Kline, 1994).  The pattern coefficients and estimated communalities (h2) 5 of the five-factor model are reported in Table 1.  The inter-factor correlations in the five-factor model 6 were also small to moderate in size (i.e., .22 ≤ r ≤ .54) suggesting the five factors are related but distinct 7 from one another (see Table 2 for inter-factor correlations).   8 Part 2 9 Methods 10 Procedure 11 A prospective observational design was used.  Participants who completed the assessments from 12 Part 1 (operationalized as Time 1 in this study) were invited via email to complete measures of exercise-13 related well-being exactly four weeks after their baseline assessment (Time 2).  To be included in the 14 study, participants needed to complete the Time 2 measure of exercise-related well-being within 10 days 15 of receiving the invitation email. We examined whether participants who were included in the sample at 16 Time 2 (N = 403) were different from those who dropped out of the study after completing measures at 17 Time 1 (N = 156) on relevant variables. Participants did not differ in age, t(557) = -1.69, p = .09, or Time 18 1 observed mean levels of prediction of affect, t(557) = .63, p = .53, prediction of instrumental utility for 19 health, t(557) = -.21, p = .83, competence, t(557) = 1.32, p = .19, relatedness, t(557) = -.12, p = .90, 20 autonomy, t(557) = 1.83, p = .07, exercise-related meaning, t(557) = .82, p = .41, and the gender 21 distribution was similar between individuals included at Time 2 (33.25% male, 66.50% female) and 22 individuals who dropped out after completing Time 1 measures (35.26% male, 64.74% female). There 23 was a statistically significant difference in observed mean levels of exercise identity, t(557) = 2.27, p = 24 PSYCHOLOGICAL NEEDS AND WELL-BEING  14  .02, d = .21, such that individuals who completed Time 2 measures (M = 4.50) reported, on average, 1 higher exercise identity compared to individuals who dropped out at Time 2 (M = 4.20).  2 Participants 3 A total of 403 participants (Mage = 31.70 years; SDage = 14.42 years) completed both Time 1 (from 4 Part 1) measures of psychological needs and Time 2 (4 weeks later) measures of exercise-related well-5 being.  Seventeen individuals were removed from the analysis due to completing the follow up measures 6 eleven days or more after receiving the follow up email.  The sample included 268 females, 134 males, 7 and one individual who selected ‘other’ for gender.  8 Measures 9 Optimal Predictability, Competence, Autonomy, and Relatedness 10 The optimal predictability items utilized in Part 1 were operationalized in Part 2.  The Composite 11 Reliabilities (CRs) for the prediction of affect and instrumental utility scores were 0.83 and 0.87, 12 respectively.  Measures of competence (IMI; McAuley et al., 1989; Ryan, 1982), autonomy (PNSE 13 autonomy subscale; Wilson, Rogers, et al., 2006), and relatedness (ROPAS; Wilson & Bengoechea, 14 2010) were those that were operationalized in Part 1.  The CRs for scores derived from the competence, 15 relatedness, and autonomy subscales were .90, .86, and .90, respectively. 16 Exercise-Related Meaning 17 To our knowledge, no measure of exercise-related meaning exists, and therefore we used a two-18 step process, including item adaption from a previous scale that has produced scores with validity 19 evidence, and focus groups, to generate and refine items to assess exercise-related meaning.  First, seven 20 items were adapted from the positive meaning subscale and the meaning making through work subscale 21 of the Work and Meaning Inventory (WAMI; Steger et al., 2012).  The positive meaning subscale (4 22 items) assesses an individual’s perception that their work is significant and meaningful, whereas the 23 meaning making through work subscale (3 items) assesses the degree to which an individual perceives 24 their work as contributing to their life’s meaning.  Although the items were adapted from two distinct but 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  15  correlated subscales of meaningful work, the items were adapted for the current investigation to assess 1 one dimension of meaningful exercise engagement. 2 Second, the seven adapted items from the WAMI were assessed in focus groups, with different 3 participants in each of the focus groups, to assess their interpretability, clarity, and appropriateness for the 4 context of exercise.  In total, three focus groups were conducted (N = 10; Mage = 30.90 years; SD = 9.24 5 years; 80.00% females).  The same ‘retrospective think-aloud’ procedures, as per Part 1, were used to 6 understand how participants interpret and provide responses to the exercise-related meaning items with 7 the addition of providing participants with the definition of exercise-related meaning (“the subjective 8 experience that exercising has personal significance, it matters, and it is meaningful”) and the interview 9 questions: “Did the items reflect exercise-related meaning?” and “Are the items appropriate for the 10 context of exercise?” After item trimming and refinement, two items were deleted, and two items were 11 refined to improve their clarity and relevance for the context of exercise, resulting in five items assessing 12 exercise-related meaning (see Table S2; Supplementary Online Materials for outline of changes made to 13 the items).  The final five items (see Table S3; Supplementary Online Materials) were prefaced by: 14 “Exercise can mean a lot of different things for different people.  The following items ask about how you 15 see the role of exercise in your own life.  Please honestly indicate how true each statement is for you and 16 your exercise.”  Responses to items were provided on a 6-point Likert-type scale anchored by 1 (False) to 17 6 (True) with higher scores reflecting greater perceptions of exercise-related meaning (exemplar item: “I 18 have found a type of exercise that is meaningful to me”).  Scores derived from the exercise-related 19 meaning measure had a CR value of .87. 20 Exercise Identity 21  Exercise identity was assessed with the Exercise Identity Scale (EIS; Anderson & Cychosz, 1994).  22 The EIS was originally designed to assess the degree to which an individual considers exercise an 23 important aspect of their self-concept (Anderson & Cychosz, 1994).  However, Wilson and Muon (2008) 24 provided evidence that EIS scores are better represented by two dimensions; a role-identity dimension 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  16  and exercise beliefs dimension using confirmatory factor analysis.  Wilson and Muon suggested that the 1 role identity dimension was considered to assess the degree to which an individual integrates the social 2 role of being an exerciser (example item: “I consider myself an exerciser”), whereas the exercise beliefs 3 dimension assessed more general beliefs about exercising (example item: “For me, being an exerciser 4 means more than just exercising”).  In this study, using confirmatory factor analysis, the two-factor 5 model, χ2 (26) = 105.11, CFI = .951, TLI = .931, RMSEA = .087, 90% CI [.070-.105] had superior fit to 6 the one-factor model, χ2 (27) = 159.68, CFI = .917, TLI = .889, RMSEA = .110, 90% CI [.094-.127].  The 7 two factors were also highly correlated (Φ = .89) in the two-factor model, so we only used the role 8 identity factor in the mediation model to ensure model parsimony.  The decision to use the items 9 representing the role identity factor as opposed to the items representing the exercise beliefs factor was 10 based on two considerations.  First, Dweck (2017) conceptualized identity as “people’s social roles, social 11 categories, and areas of self-perceived competence – things that define and situate them” (p. 695); this 12 definition is more in line with the role identity dimension.  Second, the role identity items represent the 13 original content domain (i.e., role identity) that was intended by Anderson and Cychosz (1994).  14 Consistent with the other psychological need measures in this study, participants responded to the EIS 15 using a six-point Likert-type scale anchored by 1 (False) to 6 (True) with higher scores reflecting a 16 stronger exercise identity.  Participants were presented with the following stem before responding to the 17 items: “The following questions concern your personal beliefs about exercise.  Please indicate the degree 18 to which each statement is true for you when thinking about your exercise participation.” The CR of 19 scores derived from the three role identity items was 0.90. 20 Exercise-Related Well-Being 21 Well-being was assessed with the Scale of Positive and Negative Experience (SPANE; Diener et 22 al., 2010) and the Subjective Vitality Scale (SVS; Ryan & Frederick, 1997).  The SPANE is a 12-item 23 general measure of positive and negative experiences and feelings, with six items for each of the positive 24 and negative experiences subscales, respectively.  Participants were provided with the following 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  17  instructional stem adapted for the context of exercise: “Please think about what exercise you have been 1 doing and experiencing during the PAST 4 WEEKS.  Then report how much you experienced each of the 2 following feelings, during exercise, using the scale below.  For each item, select a number from 1 to 5.” 3 The SPANE includes a Likert-type response format ranging from 1 (Very Rarely or Never) to 5 (Very 4 Often or Always).   5  The SVS was used to assess the degree to which participants feel they have energy and vitality 6 when exercising.  Based on the psychometric analysis of the SVS conducted by Bostic et al. (2000), the 7 six-item version of the SVS was used (the negatively worded item was deleted) in the current study.  8 Participants were provided with the instructional stem adapted for the context of exercise: “Please 9 respond to each of the following statements by indicating the degree to which the statement is true for you 10 when you engage in exercise.”  Participants provided ratings to the items along a Likert-type scale 11 ranging from 1 (Not at All True) to 7 (Very True).  The CR values for scores derived from the exercise-12 related subjective vitality, positive exercise experiences, and negative exercise experiences scales were 13 .90, .88, and .77, respectively. 14 Data Analysis 15  First, assumptions (outliers, missing data, normality) for the analysis were examined (Tabachnick 16 & Fidell, 1996).  Structural equation modelling with RML estimation was used to examine the degree to 17 which optimal predictability (along with competence, relatedness, and autonomy) at Time 1 explained 18 unique variance in exercise-related well-being at Time 2.  Prediction of affect, prediction of the 19 instrumental utility for health, and ratings of competence, relatedness, and autonomy satisfaction were 20 specified as latent independent (exogenous) predictor variables.  Each exercise-related well-being 21 variable (subjective vitality, positive exercise experiences, and negative exercise experiences) was 22 simultaneously included in the structural model as dependent (endogenous) variables. 23  The structural model was analyzed in Mplus (version 8.4).  Based on the recommendations of 24 Marsh (2007), we used multiple Goodness-of-Fit statistics (GOFS) that included the CFI, TLI, and 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  18  RMSEA alongside the χ2 statistic (Marsh, 2007).  Applying Marsh’s (2007) general guidelines of 1 assessing model fit with GOFS, CFI and TLI values greater than .95 and .90 were considered to represent 2 excellent and acceptable fit, respectively.  RMSEA values less than .05 and .08 were considered to 3 represent close and reasonable fit, respectively.  To assess the internal consistency of scores produced by 4 each scale, CR values were calculated using confirmatory factor analysis and RML estimation.  We also 5 examined the relative importance of each predictor in the structural model by calculating relative Pratt 6 indices (Thomas et al., 1998) or each independent variable as per Zumbo (2007).  The relative pratt 7 indices were calculated by multiplying the standardized beta (β) weight by the raw correlation, and the 8 resultant sum was divided by the variance explained in the model (i.e., R2).  An index less than 1/ (2 × 9 number of predictor variables) is determined to be unimportant (Thomas, 1992), and the cutoff was .10 10 (i.e., 10.00% variance explained). 11 Finally, exploratory analyses were conducted to examine whether a latent exercise-related 12 meaning variable and a latent exercise identity variable (Time 1) mediated the relationship between the 13 predictors (i.e., Time 1 optimal predictability, relatedness, competence, and autonomy) and outcomes 14 (i.e., Time 2 positive and negative exercise experiences and subjective vitality).  In order to test 15 mediation, a parallel multiple mediator model was estimated by examining the relationships between (a) 16 predictors and mediators, (b) mediators and outcomes controlling for predictors, and (c) predictors and 17 outcomes while controlling for mediators (Hayes, 2013).  The indirect effects of prediction of affect, 18 prediction of instrumental utility for health, competence, relatedness, and autonomy on Time 2 well-being 19 outcomes (positive exercise experiences, negative exercise experiences, and subjective vitality) through 20 exercise-related meaning and exercise identity were calculated using bootstrapping (k = 5000 samples) to 21 produce bias-corrected confidence intervals (BCCIs) as per Preacher and Hayes (2008).  RML estimation 22 is not available when conducting bootstrapping in Mplus software, and so the mediation model was 23 estimated using Maximum Likelihood (ML) estimation. 24 Results 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  19  There were no missing data on any variables included in the analysis. No outliers were present as 1 all values were in the expected range.  The structural model of the candidate psychological needs and 2 well-being outcomes had adequate model fit, χ2 (832) = 1271.64, p < .01, CFI = .95, TLI = .94, RMSEA 3 = .036, 90% CI [.032-.040].  With respect to the raw interfactor correlations (See Table S4; 4 Supplementary online materials) among predictors and outcomes in the model, all five predictors were 5 significantly correlated (i.e., p < .01) with each of the three well-being outcomes, and ranged from small 6 to large in magnitude (rs = -.17 to .59).  All correlations were in the expected direction, as each predictor 7 was positively correlated with positive exercise experiences and subjective vitality, and negatively 8 correlated with negative exercise experiences. 9 Positive Exercise Experiences 10 The complete model, including prediction of affect, prediction of instrumental utility for health, 11 competence, relatedness, and autonomy satisfaction explained 39.10% of the variance in the latent 12 variable positive exercise experiences.  Prediction of affect (β = .456, p < .01) and relatedness (β = .155, p 13 < .05) were significant prospective correlates.  Prediction of instrumental utility for health (β = .032, p = 14 0.600), competence (β = .097, p = .174), and autonomy (β = .047, p = .403) were not significantly related 15 to positive exercise experiences.  Of the 39.10% variance explained by the model, prediction of affect, 16 relatedness, and competence each accounted for 68.23%, 15.62%, and 10.77% of the explained variance, 17 respectively.   18 Negative Exercise Experiences   19 The complete model, including prediction of affect, prediction of instrumental utility for health, 20 competence, relatedness, and autonomy satisfaction explained 15.50 % of the variance in the latent 21 variable negative exercise experiences.  Prediction of affect (β = -.193, p < .05) and autonomy (β = -.177, 22 p < .01) were significant prospective correlates, whereas prediction of instrumental utility for health (β = -23 .070, p = .296), competence (β = -.123, p = .144), and relatedness (β = .036, p = .629) were not 24 significantly related to negative exercise experiences.  Of the 15.50% variation explained by the model, 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  20  prediction of affect, autonomy, and competence accounted for 38.73%, 32.55%, and 22.93% of the 1 explained variance in negative exercise experiences.   2 Subjective Vitality   3 The complete model, including prediction of affect, prediction of instrumental utility for health, 4 competence, autonomy, and relatedness explained 30.10% of the variance in the latent subjective vitality 5 variable.  Prediction of affect (β = .240, p < .01), prediction of instrumental utility for health (β = .132, p 6 < .05), competence (β = .167, p < .05), and relatedness (β = .166, p < .05) were significant prospective 7 correlates, while autonomy was not significantly related to subjective vitality (β = .056, p = .350).  Of the 8 30.10% variation explained by the model, prediction of affect, competence, relatedness, and prediction of 9 instrumental utility for health accounted for 35.80%, 23.75%, 21.45%, and 13.90% of the explained 10 variance, respectively.  11 Mediation Model 12 The mediation model including exercise-related meaning and exercise identity as mediators 13 between the predictors and Time 2 well-being outcomes had adequate GOFS, χ2 (1179) = 2104.876, p < 14 .01, CFI = .93, TLI = .92, RMSEA = .044, 90% CI [.041-.047].  The direct effects in the mediation model 15 are presented in Figure 2 (significant effects) and Table S5 (Supplementary Online Materials). With 16 respect to the mediation effects, exercise identity did not mediate any of the relationships between the 17 predictors and well-being outcomes.  Based on the p values for the mediation effects, exercise-related 18 meaning did not mediate any relationships between the predictors and outcomes (all ps > .05).  However, 19 based on the BCCIs, prediction of affect (β = .025, 95% BCCI [.002 - .073], p = .15), prediction of 20 instrumental utility for health (β = .036, 95% BCCI [.004 - .096], p = .09), relatedness (β = .023, 95% 21 BCCI [.001 - .075], p = .17), and competence (β = .066, 95% BCCI [.003 - .154], p = .08), were indirectly 22 related to subjective vitality via exercise-related meaning (i.e., BCCIs did not contain zero).  The 23 inconsistencies between the BCCIs and p values means that it remains inconclusive whether exercise-24 related meaning was a substantive mediator.  Finally, it should be noted that the direct effect between 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  21  exercise-related meaning and subjective vitality was not statistically significant at p < .05 (β = .167, 95% 1 BCCI [.001 - .344],  p = .06), but the BCCI did not contain zero.  See Table S5 (Supplementary online 2 material) for all total and specific indirect effects. 3 Discussion 4  In this two-part study, we (a) developed measures to assess the need for optimal predictability in 5 the context of exercise (prediction of affect and prediction of instrumental utility for health); (b) 6 examined the extent to which scores from items assessing optimal predictability are empirically distinct 7 from scores produced by items assessing competence, relatedness, and autonomy in exercise; (c) 8 examined the extent to which measures of optimal predictability (prediction of affect, prediction of 9 instrumental utility for health) prospectively explained unique variance in exercise-related well-being; (d) 10 adapted items to assess exercise-related meaning; and (e) examined the degree to which exercise-related 11 self-coherence (meaning and identity) mediated the effects of optimal predictability, competence, 12 autonomy, and relatedness satisfaction on exercise-related well-being.  To our knowledge, this is the first 13 investigation to empirically examine Dweck’s (2017) psychological needs model in the context of 14 exercise behaviour.  Our findings support Dweck’s (2017) notion that optimal predictability is a unique 15 psychological experience that has implications for future well-being outcomes, but failed to support 16 exercise-related meaning and identity as mediators between the basic needs and well-being outcomes. 17  We conducted an exploratory factor analysis to test the hypothesis that scores derived from 18 measures of prediction of affect and instrumental utility (in exercise) would be empirically distinct from 19 scores derived from items assessing competence, relatedness, and autonomy satisfaction in exercise.  The 20 five-factor model represented the best fitting model based on model fit and interpretability of factor 21 loadings for the three-, four-, and five-factor models.  The five-factor model included distinct factors for 22 competence, relatedness, autonomy, and two distinct factors for the prediction of affect and prediction of 23 instrumental utility for health.  These results support Dweck’s (2017) contentions that optimal 24 predictability is a distinct psychological experience from competence, relatedness, and autonomy in the 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  22  context of exercise.  It also provides discriminant validity evidence for the two-dimensional measure of 1 the prediction of affect and prediction of instrumental utility for health.   2 Upon examination of the interfactor correlations of the five-factor model, it was apparent that 3 factors of optimal predictability had small to medium-sized correlations with competence, relatedness, 4 and autonomy factors.  Prediction of affect was most strongly correlated with competence (r = .47, p < 5 .01) and relatedness (r = .34, p < .01), and to a lesser extent autonomy (r = .23, p < .01).  When compared 6 to prediction of affect, prediction of instrumental utility for health was correlated to a lesser extent with 7 competence (r = .22, p < .01), relatedness (r = .22, p < .01), and autonomy (r = .23, p < .01).  These 8 small-to-medium-sized correlations also support Dweck’s (2017) notions that these psychological needs 9 are related but distinct constructs.  These findings are consistent with previous investigations of 10 psychological need measurement in the context of exercise behaviour, such that competence, relatedness, 11 and autonomy satisfaction generally have moderately sized correlations with one another (Sylvester et al., 12 2014; Wilson, Rogers, et al., 2006).  Finally, the finding that the prediction of affect had stronger 13 relationships with competence and relatedness compared to autonomy is in line with Dweck’s model, 14 such that optimal predictability, competence, and relatedness represent the basic needs within Dweck’s 15 psychological needs model, whereas autonomy does not.  16  In order to test the hypothesis that optimal predictability (in exercise) would explain unique 17 variance in exercise-related well-being, we used structural equation modelling to examine whether the 18 two optimal predictability factors (prediction of affect and instrumental utility for health) prospectively 19 explained unique variance in exercise-related well-being, four weeks later, alongside measures of 20 competence, relatedness, and autonomy.  Among the five exogenous variables, prediction of affect was 21 the most consistent prospective correlate with exercise-related well-being, as it was the only variable to 22 explain unique variance in each of the three well-being outcomes.  Prediction of instrumental utility for 23 health, competence, relatedness, and autonomy also explained variance in at least one well-being 24 outcome.  Prediction of affect also accounted for the most variance in each of the well-being outcomes 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  23  indicated by the Pratt indices.  These results support the hypothesis that optimal predictability in exercise 1 explains unique variance in exercise-related well-being.  Relative to competence, relatedness, and 2 autonomy, predicting how one will feel when engaging in exercise appears to be a robust prospective 3 correlate of experiencing exercise-related well-being.  The fact that prediction of affect was more 4 important than prediction of instrumental utility for health in explaining variance in exercise related well-5 being is consistent with the current exercise psychology literature.  For example, affective judgements 6 appear to be a better predictor of exercise behaviour than instrumental judgements (Rhodes et al., 2009).   7  We also used structural equation modelling to test the hypothesis that exercise-related meaning 8 and identity would mediate the relationships between the a priori psychological needs and well-being 9 outcomes.  Based on BCCIs, exercise-related meaning partially accounted for the effects of prediction of 10 affect and relatedness on subjective vitality, and fully accounted for the effects of prediction of 11 instrumental utility for health and competence on subjective vitality.  However, the p values of the 12 mediation effects were not significant at p < .05.  When these findings are taken together, it remains 13 inconclusive whether exercise related meaning acted as a substantive mediator in this instance.  More 14 research is needed to determine what role (if any) exercise-related meaning plays in contributing to 15 exercise-related well-being.  16 There was no evidence to support exercise identity as a mediator between any of the predictors 17 and well-being outcomes.  This is interesting, as there is evidence that exercise-related integrated-18 regulation (i.e., exercising because it is part of one’s identity), a conceptually similar construct to exercise 19 identity, is related to indices of well-being such as physical self-concept (Wilson, Rodgers, et al., 2006) 20 and subjective vitality (McLachlan et al., 2011).  In a recent study, greater exercise identity-behavioural 21 consistency (i.e., perception that exercise behaviour is in line with one’s exercise identity) was also 22 associated with life satisfaction and vitality (Guérin et al., 2019).  However, these studies did not control 23 for psychological need variables.  In the current study, exercise identity was significantly correlated with 24 positive (r = .43, p < .01) and negative (r = -.20, p < .01) exercise experiences, and subjective vitality (r = 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  24  .42, p < .01).  These effects were negligible after controlling for psychological need variables.  Taken 1 together, a strong exercise identity may be more important in regulating an individual’s behaviour 2 (Rhodes et al., 2016) but is less important for how one feels in the context of exercise. 3  The implications of these findings are that optimal predictability (particularly related to affective 4 outcomes) represents an additional experience, beyond the psychological needs subsumed within SDT, 5 that individuals need in order to thrive in the context of exercise.  However, it is necessary to conduct 6 controlled designs such as randomized experiments and interventions that target change in optimal 7 predictability before it is considered a necessary experience for thriving in the context of exercise.  In 8 related research, telling individuals that people experience positive feelings after exercise (vs not 9 providing any information) had a positive effect on ratings of subsequent post-exercise mood (Helfer et 10 al., 2015).  Helfer et al. (2015) also reported that participants who reflected on the exercise-affect 11 relationship experienced improvements in ratings of post-exercise positive feeling two weeks later.  12 Asking individuals to focus on the positive affective experiences of exercise may enhance their prediction 13 of positive affective outcomes, and in turn, their well-being.  It would also be useful to determine the 14 factors that explain individual difference in prediction of affective outcomes.  There is evidence that 15 experiencing more positive affect during exercise is associated with positive affective judgements 16 (Rhodes & Kates, 2015).  Manipulating exercise (e.g., managing intensity) to produce more positive 17 affect is one method that may enhance an individual’s prediction of positive affective outcomes for future 18 exercise.     19  Although the current investigation has many strengths, there are limitations that should be 20 addressed.  First, this study used an observational design, which ultimately limits causal claims.  21 Although there was time separation between the predictors and outcomes, an observational design does 22 not permit one to claim that any of the predictors are causally linked to the outcomes.  Moreover, we 23 tested mediation effects in the context of an observational design.  Mediation models are fundamentally 24 directional causal models (Wu & Zumbo, 2008), such that the predictors are theorized to cause the 25 PSYCHOLOGICAL NEEDS AND WELL-BEING  25  outcome by having an effect on the mediating variable(s).  Due to the observational design, the mediation 1 effects should not be interpreted from a directional/causal perspective, but rather interpreted as testing 2 indirect relationships between predictors and outcome variables.  3 The second limitation corresponds to the assessment of optimal predictability.  Dweck’s 4 conceptualization of optimal predictability as the need to understand and predict events in one’s world is 5 open-ended and general.  With the intent of developing clear and specific items, we chose two highly 6 relevant outcomes in the context of exercise for individuals to make predictions – their affective 7 experiences and the instrumental utility of exercise for one’s health.  However, doing so could result in 8 construct underrepresentation (i.e., the assessment is narrower than the full conceptual bandwidth of the 9 construct), which represents a source of invalidity (Messick, 1995).  Individuals may make a number of 10 predictions when exercising (e.g., performance, social interactions with other exercisers) and future 11 research should examine these predictions and their implications for well-being.  Future research should 12 also examine the link between prediction of affect and more distal outcomes such as exercise behaviour to 13 further support the predictive utility of optimal predictability in exercise.  Finally, an additional 14 component of predicting outcomes refers to people’s perceived certainty (or uncertainty) in an outcome 15 occurring (see Windschitl & Wells, 1996).  Future research should examine whether the certainty of an 16 individual’s prediction explains additional variance in well-being outcomes or influences the relationship 17 between those predictions and exercise-related well-being.   18 In conclusion, our results provide partial and initial support for Dweck’s (2017) model of 19 psychological needs.  Specifically, we provide support for the importance of predicting affective 20 outcomes for experiencing well-being when exercising.  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The model includes three basic needs (optimal predictability, acceptance, and competence), three compound needs (self-esteem/status, control, and trust), and the superordinate need for self-coherence at the epicenter of all needs within the model. Copyright © 2017 American Psychological Association. Reproduced with permission. Dweck, C.S. From needs to goals and representations: Foundations for a unified theory of motivation, personality, and development. Psychological Review, 124(6), 689–719.  PSYCHOLOGICAL NEEDS AND WELL-BEING  36  Figure 2  Structural model of the relationships between prediction of affect, prediction of instrumental utility for health, competence, relatedness, exercise-related meaning, and exercise identity at Time 1, and exercise-related well-being at Time 2.  Only significant standardized path coefficients are shown   Note. **p < .01*p < .05   PSYCHOLOGICAL NEEDS AND WELL-BEING  37  Table 1  Part 1 EFA Communalities and Geomin Rotated Pattern Coefficients of the Five-Factor Solution Scale and Item h2 I II    III IV V Prediction of affect       If you were to exercise tomorrow, please predict how satisfying it would be .28 0.31  0.12  0.04  0.19  0.06 If you were to exercise tomorrow, please predict how pleasant it would be .62 0.78 -0.03 -0.04  0.02  0.08 If you were to exercise tomorrow, please predict how enjoyable it would be .88 0.96  0.00 -0.02 -0.04 -0.00 If you were to exercise tomorrow, please predict how fun it would be .57 0.64  0.16  0.12  0.03 -0.08 Prediction of instrumental utility for health        If you were to exercise tomorrow, please predict how beneficial it would be for your health .48  0.06 0.66 -0.01  0.06 -0.04 If you were to exercise tomorrow, please predict how important it would be for your health .63 -0.03 0.81  0.01 -0.07  0.01 If you were to exercise tomorrow, please predict how valuable it would be for your health .87 -0.01 0.94 -0.00 -0.01  0.00 If you were to exercise tomorrow, please predict how worthwhile it would be for your health .57  0.04 0.72 -0.02   0.03  0.04 ROPAS - Relatedness         I am included by others .71 -0.02  0.00 0.88  -0.08   0.06  I am part of a group who share my goals .48  0.07 -0.01 0.69  0.01 -0.21 I am supported by others in this activity .43 -0.01  0.06 0.65  0.01 -0.01 Others want me to be involved with them .50 -0.14  0.00 0.72  0.04  0.01 I have developed a close bond with others .56  0.01 -0.01 0.74  0.02 -0.06 I fit in well with others .48  0.13 -0.02 0.58  0.08  0.06 IMI - Competence       I think I am pretty good at exercising .83 -0.02  0.02  0.01  0.92 -0.04 I think I do pretty well at exercising compared with others .72  0.02 -0.01 -0.01  0.85  0.01 After working at exercise for a while, I feel pretty competent .45  0.02  0.16  0.19  0.41  0.13 I am satisfied with my performance when exercising .49  0.16 -0.02  0.08  0.53  0.09 I am pretty skilled at exercising .79 -0.01 -0.01 -0.01  0.91 -0.02 PNSE - Autonomy       I feel free to exercise in my own way .62  0.00 -0.03 -0.02  0.17 0.73 I feel free to make my own exercise program decisions .68 -0.03  0.01  0.01  0.03 0.82 I feel like I am in charge of my exercise program decisions .67  0.05 -0.01  0.02 -0.01 0.81 I feel like I have a say in choosing the exercises that I do .68 -0.01  0.04  0.01  0.00 0.81 I feel free to choose which exercises I participate in .56  0.08  0.03  0.03  0.02 0.70 I feel like I am the one who decides what exercises I do .62 -0.02 -0.00  -0.01 -0.04 0.81 Note. N = 559. ROPAS = Relatedness to Others in Physical Activity Scale; IMI = Intrinsic Motivation Inventory; PNSE = Psychological Need Satisfaction in Exercise Scale.  Pattern coefficients in bold represent primary factor loadings of each item retained in the final solution. PSYCHOLOGICAL NEEDS AND WELL-BEING  38  Table 2  Part 1 Interfactor Correlations of the Five-Factor Solution  Variable 1 2 3 4 5 1. Prediction of affect --     2. Prediction of instrumental utility for health 0.37 --    3. Relatedness 0.34 0.22 --   4. Competence 0.47 0.22 0.54 --  5. Autonomy  0.23 0.23 0.22 0.36 -- Note. All ps < .01  PSYCHOLOGICAL NEEDS AND WELL-BEING  39  Supplementary Online Materials   Table S1  Findings from the Retrospective Think-Aloud Focus Groups Concerning the Optimal Predictability Items.  Examples of Problems and Alterations to Items Measure Component Concern/suggestion Examples Action Taken Instructions The type of exercise is important when responding to the items FG 1 “When I was thinking about this, I was thinking about the tough ones (exercise sessions), the ones that are not so pleasant.”  FG 1“If you have a different mindset and you’re thinking of something fun (exercise) then it changes how you say how pleasant it would be, enjoyable it will be, depends on what you’re thinking”  Included the instruction: “When answering the following questions, please think about the exercise you typically perform and your personal health”    Prediction of instrumental utility for health items Participant indicated they were using general health knowledge as opposed to thinking about their own health when answering the instrumental health items FG 1 “All the way to question 4 (affective items) like 4 was still personal from 5 and 6 it was more like general knowledge. Do you think exercise is good for you? Yeah Included the instruction: “When answering the following questions, please think about the exercise you typically perform and your personal health” FG 1 and 3 “if you were to exercise tomorrow, please indicate how useful it would be for your health” Redundancy of the term ‘useful’ and ‘beneficial’ FG 1 “useful and beneficial was very similar in my understanding”  FG 3 “I thought of that one (beneficial) as exactly the same as useful, it (beneficial) meant the same thing as useful so I answered it in the same way”  Removed the item that used the term useful PSYCHOLOGICAL NEEDS AND WELL-BEING  40  FG 1 “if you were to exercise tomorrow, please indicate how exciting it would be” Interpreting ‘exciting’ as before exercise as opposed to the experience while exercising.   FG 1 “Just how much I look forward to it.”  FG 1 “just how much you are looking forward to it.”    FG 2 “I always think about how exciting it would be as a before thing” Changed the adjective from ‘exciting’ to ‘fun’ Question ordering Response sets – responding the same way FG 1 “The last questions at the end (instrumental items) I didn’t think much because it was like okay I got it Participants are presented with the affect and instrumental items in an alternating fashion Note: FG = Focus Group.  PSYCHOLOGICAL NEEDS AND WELL-BEING  41  Table S2  Findings From The Retrospective “Think-Aloud” Focus Groups Concerning Exercise-Related Meaning Items.  Examples Of Problems And Alterations To Items Item Concern/suggestion Examples Action taken  FG 5 “I understand how exercising contributes to my life’s meaning” Exercising is not the only thing that contributes to the meaning in one’s life. FG 5  “When you think of your life meaning you tend to think of one single purpose so then this is not my single purpose, not to exercise, but it still contributes in a meaningful way so I guess I wasn’t sure”  FG 5 “its how exercising contributes to part of my life’s meaning” “is this my sole purpose?” Adapted item to reflect that exercising is not the only source of meaning in one’s life: “I understand how exercising can contribute my life’s meaning” FG 5 “I feel that exercising helps me make sense of the world around me” Did not see the connection between exercising and making sense of one’s world “I feel like number 7, it’s hard to make the connection between exercising and what’s going on in the world. I didn’t really know what to make of that”  Adapted item: I feel that exercising helps me make sense of my life. Eventually deleted item (see below)  FG 6 “I feel that exercising helps me better understand myself”   “I feel that exercising helps me make sense of my life” Items not relevant to exercise FG 6 “But I don’t feel like the exercise itself is the thing that makes me better understand myself or make sense of my life”  Deleted both items  FG  6 “I have found exercise that is meaningful to me”       The use of ‘I have found exercise’        FG 6 “I found that it was related to the type of exercise. I have found exercise that is meaningful to me. Like I like doing Zumba because it’s fun so it’s meaningful to me or I accomplished a goal by doing a triathlon and that’s meaningful to  Item changed to: “I have found a type of exercise that is meaningful to me”     PSYCHOLOGICAL NEEDS AND WELL-BEING  42  me. So maybe it needs to be that I have found a type of exercise or an exercise activity?” Note: FG = Focus Group. PSYCHOLOGICAL NEEDS AND WELL-BEING  43  Table S3  Final Exercise-Related Meaning Items used in Part 2 Item 1. I have found a type of exercise that is meaningful to me 2. I understand how exercising can contribute to my life’s meaning   3. I have a good sense of what makes exercising meaningful 4. I have discovered exercise that has a satisfying purpose 5. I feel that exercising contributes to my personal growth   PSYCHOLOGICAL NEEDS AND WELL-BEING  44  Table S4  Part 2 Interfactor Correlations Among Latent Variables in Structural Equation Model  Variable 1 2  3 4 5 6 7 8 1. Prediction of Affect --        2. Prediction of Instrumental Utility for Health  .40 --       3. Relatedness  .36 .22  --      4. Competence  .50 .22   .54  --     5. Autonomy  .24 .27   .28  .42  --    6. Positive Exercise Experiences  .59 .28   .39  .43   .25  --   7. Negative Exercise Experiences -.31  -.21 -.17  -.30 -.29 -.56  --  8. Subjective Vitality   .45 .32   .40  .43  .27   .75 -.43 -- Note. All ps < .01 PSYCHOLOGICAL NEEDS AND WELL-BEING  45  Table S5  Part 2 Direct and  Indirect (Total and Specific) Effects in Mediation Model  Variables Standardized Estimate Standard Error  p-Value Bias Corrected Bootstrapped 95% Confidence Interval Direct Effects      Predictors to Exercise Identity   Prediction of Affect .065 .051 .202 [-.036, .162]   Prediction of Instrumental Utility  .002 .038 .948 [-.070, .083]   Relatedness .013 .049 .785 [-.080, .109]   Competence .862 .044 <.001 [.773, .947]   Autonomy -.048 .044 .277 [-.137, .035] Predictors to Exercise-Related Meaning   Prediction of Affect .151 .065 .019 [.024, .277]   Prediction of Instrumental Utility  .216 .055 <.001 [.110, .328]   Relatedness .137 .066 .037 [.010, .265]   Competence .396 .070 <.001 [.261, .538]   Autonomy .069 .056 .219 [-.042, .183] Predictors and Mediators to Positive Exercise Experiences   Prediction of Affect .435 .070  <.001 [.298, .570]   Prediction of Instrumental Utility  .001 .064 .982 [-.134, .119]   Relatedness .137 .069 .048 [.002, .277]   Competence .022 .148 .884 [-.256, .331]   Autonomy .039 .058 .499 [-.076, .155]   Exercise Identity  .020 .152 .893 [-.271, .314]   Exercise-Related Meaning .138 .084 .100 [-.024, .308] Predictors and Mediators to Negative Exercise Experiences   Prediction of Affect -.212 .081 .009 [-.368, -.050]   Prediction of Instrumental Utility  -.073 .076 .340 [-.223, .075]   Relatedness .031 .076 .682 [-.126, .173]   Competence -.363 .168 .030 [-.698, -.048]   Autonomy -.163 .074 .026 [-.303, -.016]   Exercise Identity  .278 .174 .110 [-.070, .617]   Exercise-Related Meaning .005 .101 .963 [-.192, .205] Predictors and Mediators to Subjective Vitality    Prediction of Affect .212 .071 .003 [.073, .357]   Prediction of Instrumental Utility  .096 .057 .094 [-.021, .201]   Relatedness .143 .071 .045 [.005, .284]   Competence .045 .152 .768 [-.242, .360]   Autonomy .048 .063 .450 [-.080, .169]   Exercise Identity  .061 .148 .679 [-.232, .351]   Exercise-Related Meaning .167 .088 .057 [.001, .344] Indirect Effects Prediction of Affect to Positive Exercise Experiences   Total Indirect Effects .022 .017 .193 [-.004, .065] PSYCHOLOGICAL NEEDS AND WELL-BEING  46      Specific Indirect Effects           Exercise Identity .001 .013 .919 [-.020, .038]       Exercise-Related Meaning .021 .016 .192 [-.001, .066] Prediction of Instrumental Utility to Positive Exercise Experiences   Total Indirect Effects .030 .021 .157 [-.004, .084]     Specific Indirect Effects           Exercise Identity .000 .006 .993 [-.012, .014]       Exercise-Related Meaning .030 .020 .144 [.000, .088] Relatedness to Positive Exercise Experiences   Total Indirect Effects .019 .017 .259 [-.004, .067]     Specific Indirect Effects           Exercise Identity .000 .007 .971 [-.013, .019]       Exercise-Related Meaning .019 .016 .223 [-.001, .067] Competence to Positive Exercise Experiences   Total Indirect Effects .072 .120 .547 [-.155, .308]     Specific Indirect Effects           Exercise Identity .018 .132 .894 [-.236, .273]       Exercise-Related Meaning .055 .035 .120 [-.008, .133] Autonomy to Positive Exercise Experiences   Total Indirect Effects .009 .015 .578 [-.018, .046]     Specific Indirect Effects           Exercise Identity -.001 .010 .919 [-.028, .015]       Exercise-Related Meaning .010 .011 .370 [-.003, .045] Prediction of Affect to Negative Exercise Experiences   Total Indirect Effects .019 .024 .434 [-.021, .078]     Specific Indirect Effects           Exercise Identity .018 .021 .380 [-.006, .081]       Exercise-Related Meaning .001 .017 .967 [-.031, .039] Prediction of Instrumental Utility to Negative Exercise Experiences   Total Indirect Effects .002 .025 .946 [-.048, .058]     Specific Indirect Effects           Exercise Identity .001 .013 .957 [-.021, .034]       Exercise-Related Meaning .001 .022 .963 [-.040, .050] Relatedness to Negative Exercise Experiences   Total Indirect Effects .004 .022 .840 [-.039, .047]     Specific Indirect Effects           Exercise Identity .004 .016 .820 [-.022, .046]       Exercise-Related Meaning .001 .015 .966 [-.030, .034] Competence to Negative Exercise Experiences   Total Indirect Effects .241 .143 .091 [-.031, .535]     Specific Indirect Effects           Exercise Identity .239 .154 .120 [-.057, .552]       Exercise-Related Meaning .002 .041 .964 [-.076, .086] Autonomy to Negative Exercise Experiences   Total Indirect Effects -.013 .021 .540 [-.072, .018]     Specific Indirect Effects     PSYCHOLOGICAL NEEDS AND WELL-BEING  47        Exercise Identity -.013 .018 .456 [-.074, .006]       Exercise-Related Meaning .000 .009 .971 [-.017, .023] Prediction of Affect to Subjective Vitality   Total Indirect Effects .029 .019 .117 [.001, .075]     Specific Indirect Effects           Exercise Identity .004 .013 .761 [-.013, .044]       Exercise-Related Meaning .025 .017 .147 [.002, .073] Prediction of Instrumental Utility to Subjective Vitality   Total Indirect Effects .036 .023 .113 [.000, .092]     Specific Indirect Effects           Exercise Identity .000 .006 .980 [-.011, .015]       Exercise-Related Meaning .036 .022 .094 [.004, .096] Relatedness to Subjective Vitality   Total Indirect Effects .024 .019 .209 [-.003, .076]     Specific Indirect Effects           Exercise Identity .001 .008 .919 [-.010, .026]       Exercise-Related Meaning .023 .017 .173 [.001, .075] Competence to Subjective Vitality   Total Indirect Effects .119 .117 .309 [-.115, .343]     Specific Indirect Effects           Exercise Identity .053 .129 .682 [-.204, .307]       Exercise-Related Meaning .066 .038 .080 [.003, .154] Autonomy to Subjective Vitality   Total Indirect Effects .009 .017 .616 [-.021, .049]     Specific Indirect Effects           Exercise Identity -.003 .010 .764 [-.037, .010]       Exercise-Related Meaning .012 .013 .358 [-.003, .052]