Predicting change in middle school students’ leisure-time physical activity participation: A prospective test of the trans-contextual model

We applied the trans-contextual model (TCM) to examine the effects of middle school students’ perceived autonomy support from their physical education (PE) teachers on autonomous motivation toward PE in school and, critically, autonomous motivation toward, and actual participation in, leisure-time physical activity (PA). The research adopted a three-wave prospective design enabling the modeling of change in the TCM constructs over time. Middle school students (N = 248) aged from 12 to 16 years reported their perceived autonomy support, autonomous motivation in PE, autonomous motivation toward leisure-time PA, attitudes, subjective norms, perceived behavioral control (PBC), intentions for PA in leisure-time, and leisure-time PA participation. The psychological constructs and leisure-time PA were measured at baseline (T0) and at a first follow-up occasion (T1) 5 weeks later. Another measure of PA was taken at a second follow-up occasion (T2) a further 5 weeks later. A single-indicator structural equation model using residualized change scores revealed that perceived autonomy support predicted autonomous motivation in PE (β =.345), and autonomous motivation in PE predicted autonomous motivation for leisure-time PA (β =.484). Autonomous motivation toward leisure-time PA predicted attitudes (β =.425), subjective norms (β =.264), and PBC (β =.517). Autonomous motivation toward leisure-time PA (β =.376), attitude (β =.231), and subjective norms (β =.185) predicted intentions toward leisure-time PA, and intentions predicted PA (β =.198). Findings extend research on the TCM by demonstrating its efficacy in predicting change in middle school students’ autonomous motivation across PE and leisure-time contexts, and accounting for change in intentions toward, and actual participation in, leisure-time PA.

Despite these benefits, research has shown that young people do not participate in sufficient PA to confer health benefits (Guthold, Stevens, Riley, & Bull, 2020).
Given the insufficient levels of PA observed in young people (e.g., Kokko et al., 2016), development of effective campaigns, and interventions to promote increased PA participation in young people has been identified as a priority (Messing et al., 2019).
Researchers in behavioral science and applied psychology have, consequently, adopted psychological theories and models to predict and understand PA participation in young people, with the view of identifying the potential targets for intervention (Hagger, Cameron, Hamilton, Hankonen, & Lintunen, 2020;Hagger, Moyers, McAnally, & McKinley, 2020;Sheeran, Klein, & Rothman, 2017). In addition to identifying these targets, researchers have also been mindful of the key contexts, in which interventions to promote PA will have maximum benefit and reach (Messing et al., 2019).
Physical education (PE), for example, has been noted as a potentially viable existing network on which interventionists can capitalize to deliver PA interventions to a broad, and captive audience of young people (Finnish National Board of Education, 2014; Hagger & Chatzisarantis, 2016).
Considering the imperative of identifying factors that determine PA participation and the potential for the school context to intervene and motivate young people to participate in PA in their leisure-time, researchers have sought to identify the factors linked to young people's motivation toward PA both within (Standage, Duda, & Ntoumanis, 2003) and outside of school (Plotnikoff, Costigan, Karunamuni, & Lubans, 2013). Theories of motivation and belief-based decision-making have been identified as important in this regard. Prominent among these is the trans-contextual model (TCM), an integrated model of motivation that outlines the psychological factors that likely influence the children's motivation toward, and actual participation in, PA outside of school (Hagger, Chatzisarantis, Culverhouse, & Biddle, 2003). The model outlines how the quality of motivation toward PA in school relates to motivation toward, and actual participation in, out-of-school PA. The model has been shown to be effective in identifying the predictors of motivation and PA participation in multiple samples in many countries, and these findings have been supported in a meta-analysis of studies (Hagger & Chatzisarantis, 2016). However, to date, research applying the TCM has not modeled change in its constructs over time. The current study aimed to advance knowledge on the TCM by testing its effectiveness in accounting for change in its constructs over time, particularly the target outcomes of leisure-time autonomous motivation, intentions, and PA behavior.

| The TCM
The TCM is a multi-theory integrated model that specifies how students' perception of their PE teacher's support for their motivation toward physical activities relates to their in school motivation toward PA and, importantly, their motivation, intentions, and actual PA behavior outside of school in their leisure-time (Hagger et al., 2003).
The model draws its hypotheses from three motivational theories: self-determination theory (SDT; Deci & Ryan, 1985), the theory of planned behavior (TPB; Ajzen, 1991), and the hierarchical model of intrinsic and extrinsic motivation (Vallerand & Ratelle, 2002). Next, we outline the predictions of the model derived from the premises of the component theories.
Central to the model is autonomous motivation. Consistent with the predictions of SDT, autonomous motivation reflects engaging in activities and tasks out of a sense of volition, choice, and interest, and to attain self-endorsed goals. Autonomous motivation is important because it has been consistently shown to relate to behavioral persistence in multiple populations, behaviors, and contexts, and in the absence of external contingencies and reinforcement Teixeira, Carraça, Markland, Silva, & Ryan, 2012). It is, therefore, important for fostering self-regulation of behaviors, as individuals who are autonomously motivated are more likely to persist with behaviors without the need for consistent, intensive prompts and interventions. According to the theory, social agents in the environment, such as teachers in school contexts, have the capacity to foster autonomous motivation by displaying autonomy-supportive behaviors. Research in educational contexts has demonstrated that the students of teachers displaying autonomy supportive behaviors in school contexts are more likely to report autonomous motivation and display greater engagement and persistence on tasks (Reeve & Cheon, 2020;Reeve, Jang, Carrell, Jeon, & Barch, 2004).
Furthermore, students that perceive their teachers as autonomy supportive are more likely to report autonomous motivation in class (Hagger, Chatzisarantis, Barkoukis, Wang, & Baranowski, 2005). This forms the first premise of the TCM: Students perceiving that their teacher supports their autonomy in their PE classes will report autonomous motivation toward physical activities in class.
A key prediction of the TCM is that students' autonomous motivation toward PA in school will transfer to autonomous motivation toward physical activities outside of school in their leisure-time. This prediction is based on Vallerand and Ratelle's (2002) hierarchical model of intrinsic and extrinsic motivation. The hierarchical model proposes interplay between types of motivation across contexts.
The rationale behind this "transfer" of motivation is that individuals who view activities as autonomously motivating in a given context will also seek out further opportunities to experience autonomous motivation in other contexts. The primary drivers behind this process are basic psychological needs. Self-determination theory suggests that satisfaction of three fundamental needs for autonomy, competence, and relatedness is essential for optimal functioning, with the need for autonomy, that is, the need to experience actions as chosen and self-endorsed, the foremost need (Ryan & Deci, 2017).
Individuals who experience behaviors as autonomous, are likely to internalize such behaviors as those that satisfy their need for autonomy. Consistent with the hierarchical model, individuals will also be motivated to pursue need-satisfying behaviors elsewhere. This process forms the second premise of the TCM: Students experiencing physical activities in PE as autonomously motivating are more likely to report autonomous motivation toward PA outside of school in their leisure-time.
Consistent with SDT, individuals experiencing an activity as autonomously motivating are likely to seek out further opportunities to engage in that activity in the future, and will strategically bring their beliefs and intentions toward that activity in line in order to do so (Deci & Ryan, 1985;Hagger et al., 2014). This is because individuals are motivated to seek out behaviors likely to satisfy their psychological needs. The formation of beliefs, therefore, outlines how individuals' motives lead to future participation in need-satisfying behavior. In the TCM, this is the process by which autonomous motivation in leisure-time leads to subsequent PA behavior. The TCM utilizes the TPB, a social cognition theory that identifies the belief-based determinants of intentions and behavior, as a means to model these relations (Chan, Zhang, Lee, & Hagger, 2020;). The theory suggests that intentions are the most proximal predictor of behavior, a critical relationship in many social cognition theories (Orbell, 2004;Sheeran & Webb, 2016).
Intentions are proposed to mediate the effects of three belief-based constructs, attitudes, subjective norms, and perceived behavioral control, on behavior. Research has demonstrated that these beliefs mediate relations between autonomous motivation and leisure-time PA participation (Chan et al., 2020;).
These findings form the basis of the third premise of the TCM: Autonomous motivation toward leisure-time PA will predict PA participation mediated by attitudes, subjective norms, PBC, and intentions.
Research adopting the TCM has supported its predictions in multiple samples and in different national groups (Chan, Hagger, & Spray, 2011;González-Cutre, Sicilia, Beas-Jiménez, & Hagger, 2014;Hagger & Chatzisarantis, 2016;Hagger, Sultan, Hardcastle, & Chatzisarantis, 2015). Specifically, research has demonstrated that the key premises hold: students' perceived autonomy support predicts their autonomous motivation toward PA in school; students' in school autonomous motivation predicts their autonomous motivation toward PA in leisure-time; autonomous motivation toward leisure-time PA predicts subsequent participation in leisure-time PA mediated by the belief-based constructs and intentions from the TPB.
Primary research and meta-analytic findings have indicated small-tomedium sized effects for the direct effects that comprise the three key premises, with a small indirect effect of autonomous motivation on PA participation (Hagger & Chatzisarantis, 2016). In addition, intervention research has also suggested that provision of autonomy support by PE teachers or social agents affects leisure-time PA through the mediation of the model variables Mavropoulou, Barkoukis, Douka, Alexandris, & Hatzimanouil, 2019;Wallhead, Hagger, & Smith, 2010).

| Modeling change in the TCM
Despite growing support for the premises of the model, numerous limitations and critiques of the model exist. At the forefront of these critiques has been the "static" approach to test the model (Hagger & Chatzisarantis, 2016). The three-wave prospective design, typically used to test the predictive validity of the model is limited as it does not account for change in the various model components over time. This is problematic because such models do not account for potential changes in both the predictor and predicted variables of the model that occur in the interim between measurements. Such changes may occur for multiple reasons, such as new information becoming available that influences the students' beliefs. For example, the introduction of a new teacher with a different interpersonal approach in PE lessons, the increased availability of opportunities to perform PA, or a series of positive or negative experiences may all change constructs in the model. A means to account for such change is to measure all model variables at each time point, which permits the explicit modeling of change in variables over time. Such an approach accounts for the relative temporal variability or stability in each construct over time, and allows the researcher to evaluate how well changes in antecedent constructs, such as perceived autonomy support and autonomous motivation in PE, predict changes in dependent constructs, such as autonomous motivation, beliefs, intentions, and behavior in leisure-time. Modeling change provides a more stringent test of the predictive validity of the model; if the model is able to account for change in constructs over time, then it will be more relevant to guiding interventions which focus on manipulating model constructs (e.g., perceived autonomy support) in order to affect change in key outcomes (e.g., leisure-time PA intentions and behavior.

| The present study
The purpose of the present study was to test the predictive validity of the TCM using change scores for each model construct in a sample of middle school students. Previous applications of the TCM have tested the predictive validity of the model using prospective designs, which use absolute values for model constructs to estimate the hypothesized relations among them. However, no previous study has shown whether the key premises of the model hold when it is used to predict change in its constructs over time. We applied a three-wave design to include measures of all model constructs at two data collection occasions separated by a 5-week interval, with a further follow-up measure of leisuretime PA behavior, 5 weeks after the second occasion. This design enabled modeling of change in study constructs using residualized change scores. In terms of specific predictions, we expected to find support for the three premises of the model in our changescore model: (i) changes in students' perceived autonomy support from teachers in PE were proposed to be positively related to changes in autonomous motivation toward PE; (ii) changes in autonomous motivation in PE were proposed to be positively related to changes in autonomous motivation for leisure-time PA outside of school; and (iii) changes in autonomous motivation for leisure-time PA were proposed to be positively related to changes in intentions toward, and actual participation in, leisure-time PA through changes in the immediate antecedents of intentions from the TPB.

| Participants and design
A convenience sample of middle-school students (N = 292) aged from 12 to 16 years was recruited from two schools in the city of Kouvola, Finland. Schools were identified through PE teachers with established links with the University, and approval from the principals of both schools was secured in advance of data collection. The study protocol was approved by the research ethics committee of the University of Jyväskylä. Students' participation in the study was voluntary. Guardians of the eligible students were required to complete informed consent forms prior to participation via letters sent home with the students using an opt-out strategy. The study employed a three-wave prospective correlational design with measures of all TCM variables and PA behavior collected at two initial data collection occasions and a further follow-up comprising a behavioral measure only. Data were collected during regular school lessons and students who did not participate in the study were provided with an alternative writing task. In the first (T0) and second (T1) data collection occasions, separated by 5 weeks, self-report measures of students' perceived autonomy support by teachers, autonomous motivation for PE, autonomous motivation for leisure-time PA, TPB constructs, and self-reported PA were administered. Five weeks after the second data collection occasion, participants self-reported their PA participation for a third time (T2).

| Measures
Participants completed questionnaires containing previously validated self-report measures of the TCM constructs and self-report measures of behavior. Details of the measures are provided in the next section, and complete study measures are available in Appendix A (Supporting Information).

| Students' perceived autonomy support from their PE teacher
Perceived autonomy support from the students' PE teacher was measured using items from the perceived autonomy support scale for exercise settings (PASSES; Hagger et al., 2007). The scale comprised 12 items (e.g., "I feel that my PE teacher provides me with choices and options to …") with responses provided on 7-point scales (1 = strongly disagree and 7 = strongly agree). The scale has demonstrated adequate construct validity and reliability statistics in previous research (Hagger et al., 2007).

| Autonomous motivation toward in school and out-of-school PA
Autonomous motivation toward in school and out-of-school physical activities was measured using items from the perceived locus of causality questionnaire (Ryan & Connell, 1989). Two items measured identified regulation (e.g., "I do PE/PA because it is important to me to do well in PE/PA") and two items measured intrinsic motivation (e.g., "I do PE/PA because it is fun"). Responses were provided on 7-point scales (1 = not true for me and 7 = very true for me). For each of the PE and out-of-school contexts, a composite autonomous motivation score was computed by averaging scores on the identified regulation and intrinsic motivation items. Measures of autonomous motivation have demonstrated satisfactory construct validity and internal consistency in previous studies ).

| Theory of planned behavior constructs
Measures of students' attitudes, subjective norms, PBC, and intentions with respect to their future participation in PA were measured using scales developed according to reported guidelines (Ajzen, 2002). Attitudes were measured on three items in response to a common stem: "Participating in PA in the next five weeks will be…" with responses made on 7-point scales (e.g., 1 = unenjoyable and 7 = enjoyable). Subjective norms (e.g., "Most people who are important to me think I should do active sports and/or vigorous physical activities during my leisure-time in the next five weeks"), PBC (e.g., "I am confident I could do active sports and/or vigorous physical activities during my leisure-time in the next 5 weeks"), and intentions (e.g., "I intend to do active sports and/or vigorous physical activities during my leisure-time in the next five weeks") were measured using two items each with responses provided on 7-point scales (e.g., 1 = strongly disagree and 7 = strongly agree). Previous research has supported the construct validity and internal consistency of these measures within the TCM ).

| Physical activity behavior
PA behavior was measured using a modified version of the leisuretime exercise questionnaire (Godin & Shephard, 1985). The meas-

| Data analysis
Study hypotheses were estimated using single-indicator structural equation models using scale reliabilities to provide estimates of the measurement errors of the latent variables as advocated by Savalei (2019). Models were estimated using the Mplus software version 8.0 (Muthén & Muthén, 2002). Given the number of variables and the complexity of the model, we opted not to use an autoregressive path analytic model. Instead, change in model constructs was estimated using residualized change scores, which is a useful means to control for change while minimizing parameterization (Castro-Schilo & Grimm, 2018).
Standardized residualized change scores for psychological constructs were computed by regressing scores for each variable taken at the first follow-up occasion (T1) on its score at the baseline data collection occasion (T0). We also included scores for leisure-time PA taken at T0 as an independent predictor of each psychological construct, which effectively controlled for past behavior. We used the same process to  1989) formula. We opted for a single-indicator structural equation model over the more traditional multiple-indicator model because of the difficulty of fitting models comprising constructs indicated by large numbers of items with data, particularly on relatively small sample sizes (Hsiao, Kwok, & Lai, 2018;Savalei, 2019). Model fit was evaluated using multiple goodness-of-fit indices: the model chi-square, the comparative fit index (CFI), the standardized root mean square of the residuals (SRMR), and the root mean error of approximation (RMSEA). A nonsignificant chi-square, a CFI value that approaches or exceeds .95, a SRMR value of less than .08, and a RMSEA value of .05 or less, are indicative of good fit of the model with the data (Hu & Bentler, 1999). Model effects were expressed as standardized parameter estimates. This makes assessment of effect sizes easy because each effect has the same scale ranging from 0 to 1.00. However, because effect sizes for indirect effects are products of one or more direct effects, effect sizes of standardized coefficients should be interpreted differently. Researchers have suggested that indirect effect sizes of .075 or larger are non-trivial in size while effect sizes < .075 are small or trivial in size (Hagger, Koch, Chatzisarantis, & Orbell, 2017;Seaton, Marsh, & Craven, 2010). The data file, Mplus syntax, and output files for the analyses are available online: https://osf.io/py2g7 /.

| Model effects
The proposed model exhibited adequate fit with the data according to the adopted goodness-of-fit indices, χ 2 (9) = 18.543, p = .029; CFI = Solid unidirectional arrowed paths represent statistically significant effects among the model variables, broken unidirectional arrowed paths represent nonsignificant effects. Variables depicted are residual change scores for the study variables calculated by regressing variable scores taken at the first follow-up occasion (T1) on scores for the same variable taken on the first data collection occasion (baseline, T0). Physical activity behavior measured at T0 was also included in computing the change score of each variable to control for past behavior. The change score for physical activity was calculated by regressing the physical activity score taken at the second-follow up occasion (T2) on physical activity scores taken at T1 and T0. All parameter estimates of the model and error variances presented in Appendix F. Correlations among study variables omitted for clarity. *p < .05. **p < .01. ***p < .001 TA B L E 1 Parameter estimates (β) with 95% confidence intervals for hypothesized effects from the single indicator structural equation model of the trans-contextual model

| D ISCUSS I ON
The present study applied the TCM to explain the process by which Specifically, perceived autonomy support predicted autonomous motivation in a PE context directly, and autonomous motivation in a Abbreviations: 95% CI = 95% confidence interval of path coefficient; Aut. mot. ( Research suggests that PE teachers can foster autonomous motivation in PE by displaying key autonomy supportive behaviors (e.g., listening, providing positive feedback, providing choice, providing a clear rationale, assisting setting of autonomous goals), and that such behaviors lead to increased perceptions of autonomy support in students (Cheon, Reeve, & Moon, 2012;Reeve & Cheon, 2020). If such behaviors are effective in changing perceptions of autonomy support, as indicated in the literature, they may lead to changes in school and out-of-school autonomous motivation according to the TCM. While the effects of such interventions need to be empirically verified, these findings may signpost a key strategy that may have utility in promoting positive changes in autonomous motivation and PA across contexts (Ntoumanis et al., 2020).
That changes in autonomous motivation toward PA in leisure-time were also related to the sets of beliefs (attitudes, subjective norms, and PBC) that underpin intentions to participate in PA, also supports a key process in the TCM, as well as previous correlational research demonstrating these relations (Chan et al., 2020). Furthermore, attitudes mediated the effects of autonomous motivation on intentions, as predicted by the model and previous integrative research on the TPB and SDT ). Importantly, current findings are consistent with previous research in an adult sample that has also demonstrated that changes in autonomous motivation lead to changes in beliefs and intentions (Jacobs, Hagger, Streukens, De Bourdeaudhuij, & Claes, 2011). What is the value of the inclusion of these beliefs as intermediary constructs between autonomous motivation and intentions? As Deci and Ryan (1985) suggest in their original specification of SDT, individuals holding autonomous motives toward behaviors will likely seek out those behaviors, primarily because they are associated with adaptive, self-referenced outcomes and fulfillment of psychological needs, and, in order to do so, they will strategically align their beliefs and intentions with their motives. The TCM formalizes these proposals and capitalizes on the TPB, a preeminent theory outlining the belief-based determinants of intentions and behavior, as a means to do so. Importantly, current findings provide further evidence to support this process by incorporating change processes. This suggests that these processes hold when accounting for naturally occurring changes in these constructs over time. They also may signpost that changes in autonomous motivation toward PA brought about by contexts that support autonomy may lead to changes in beliefs and intentions. This illustrates one of the additional, often overlooked, advantages of the TCM which is that it provides multiple potential targets for interventions across contexts. For example, significant others like parents and peers may provide support for students' autonomy toward PA in a leisure-time context, and interventions using autonomy support in these groups may be additional means to promote autonomous motivation and intentions toward PA (Teixeira et al., 2020).
However, caution must be exercised when evaluating the effectiveness of the TCM in determining change in PA behavior. Current findings indicate that although intentions toward PA were related to actual participation in PA, the size of the effect was small, much smaller than the effect sizes identified in previous meta-analyses of the TCM (Hagger & Chatzisarantis, 2016) and integrated models of the TPB and SDT ). This suggests that intention change may not be very effective in accounting for change in PA participation, and that previous estimates of the size of the intention-behavior relationship based on "static" tests that do not account for change may be inflated, a finding that has been reported elsewhere (Webb & Sheeran, 2006 It is important to note that we found a statistically significant small-to-medium sized total effect of perceived autonomy support on PA behavior-this effect comprised the total indirect effect and the direct effect of perceived autonomy support. The direct effect of perceived autonomy support on PA behavior was expected to be zero, and accounted for by the motivational sequence offered by the model. Therefore, although neither the direct nor the indirect effect of perceived autonomy support on behavior was statistically significant, the combined effect was, and was non-trivial in size.
There may be a number of reasons for this pattern of effects. One reason may be limitations in the measures of the TCM constructs.
This means that these measures were not sufficient to account for the effect of perceived autonomy support change on PA behavior change. While reliability coefficients of these constructs were reasonable, some researchers have indicated that use of self-report measures reduce the precision of model tests (Fan et al., 2006).
Given that all constructs were measured using self-report, such imprecision may have introduced substantive method variance, which may have attenuated relations. Another possibility is that other unmeasured constructs may be responsible for explaining the relationship between perceived autonomy support and PA behavior. For example, the current study did not take into account psychological need satisfaction, another key mediator of perceived autonomy support (Fenner, Straker, Davis, & Hagger, 2013).
There is also the possibility that implicit motives that may represent more "automatic" or "non-conscious" effects are important in explaining model relationships (e.g., Hagger, Trost, Keech, Chan, & Hamilton, 2017;Keatley, Clarke, & Hagger, 2012). Nevertheless, the lack of mediation from autonomous motivation raises questions about the proposed process by which perceived autonomy support in PE translates to PA participation in leisure-time. or through interventions, such as an intervention to change autonomy support, and is a key avenue for future research Hagger, Cameron, et al., 2020). Third, related to the previous point, while the temporal ordering implied directional relations among constructs, causal effects are inferred only by theory and not the data. Again, experimental manipulations are paramount for such inferences. Finally, we also modeled change using two or, in the case of behavior, three time points. Future research should consider adopting multiple measures and assessing change using growth curve models, which has often been cited as the method of choice for effectively modeling change (Rogosa, Brandt, & Zimowski, 1982). However, such analyses involve a large number of parameters, and we had insufficient sample size to estimate such a model. Studies using larger samples and multiple time points are needed for a more fine-grained evaluation of change.

| CON CLUS ION
The TCM was applied to outline how changes in perceived autonomy support from PE teachers and autonomous motivation in school PE related to changes in autonomous motivation toward PA in a leisure-time context, and changes in beliefs, intentions, and future participation in PA. Although research supported the model in explaining change in autonomous motivation across contexts, including prediction of PA participation and total effects of perceived autonomy support on PA participation, effect sizes were small. Current findings suggest that the TCM does not account for substantial variance in change in PA intentions and behavior.
Nevertheless, it should be noted that even small changes in outcomes may translate to substantive changes when translated to the population level.

ACK N OWLED G M ENT
We thank Heidi Pasi-Turpiainen for her assistance in enabling the data collection; Jinyoung Choi, Maiken Hansen, Arto Laukkanen, Stina Seppänen, and Miika Tuominen for their assistance in collecting and processing data. We are also grateful to the the students, teachers, and rectors of the city of Kouvola for supporting the study.