Young children’s motivations and social cognitions toward swimming : Testing direct and moderation effects of sport competence in two large-scale studies

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Young children’s motivations and social cognitions toward swimming : Testing direct and moderation effects of sport competence in two large-scale studies © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Published version Chan, Derwin King Chung; Lee, Alfred Sing Yeung; Tang, Tracy Chor Wai; Leung, Kiko; Chung, Joan Sau Kwan; Hagger, Martin S.; Hamilton, Kyra Chan, D. K. C., Lee, A. S. Y., Tang, T. C. W., Leung, K., Chung, J. S. K., Hagger, M. S., & Hamilton, K. (2023). Young children’s motivations and social cognitions toward swimming : Testing direct and moderation effects of sport competence in two large-scale studies. Journal of Sports Sciences, 41(9), 859-873. https://doi.org/10.1080/02640414.2023.2241782 2023 Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=rjsp20 Journal of Sports Sciences ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/rjsp20 Young children’s motivations and social cognitions toward swimming: Testing direct and moderation effects of sport competence in two large-scale studies Derwin King Chung Chan, Alfred Sing Yeung Lee, Tracy Chor Wai Tang, Kiko Leung, Joan Sau Kwan Chung, Martin S. Hagger & Kyra Hamilton To cite this article: Derwin King Chung Chan, Alfred Sing Yeung Lee, Tracy Chor Wai Tang, Kiko Leung, Joan Sau Kwan Chung, Martin S. Hagger & Kyra Hamilton (2023): Young children’s motivations and social cognitions toward swimming: Testing direct and moderation effects of sport competence in two large-scale studies, Journal of Sports Sciences, DOI: 10.1080/02640414.2023.2241782 To link to this article: https://doi.org/10.1080/02640414.2023.2241782 © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Published online: 27 Jul 2023. Submit your article to this journal Article views: 230 View related articles View Crossmark data SPORT AND EXERCISE PSYCHOLOGY Young children’s motivations and social cognitions toward swimming: Testing direct and moderation effects of sport competence in two large-scale studies Derwin King Chung Chan a , Alfred Sing Yeung Lee a , Tracy Chor Wai Tang a , Kiko Leung a , Joan Sau Kwan Chung a , Martin S. Hagger b,c,d and Kyra Hamilton b,c,d a Faculty of Education and Human Development, The Education University of Hong Kong, Hong Kong, China; b Department of Psychological Sciences, University of California, Merced, CA, USA; c Faculty of Sport and Health Sciences, University of Jyväskylä, Jyväskyla, Finland; d School of Applied Psychology, Griffith University, Griffith, Australia ABSTRACT Direct and moderation effects of swimming competence using an integrated model of self-determination theory (SDT) and theory of planned behaviour (TPB) were examined in two large-scale studies among young children. Specifically, we examined whether swimming competence had direct and moderation effects on social psychological variables of perceived need support, autonomous motivation, TPB social cognition constructs, and intention. In Study 1, using a cross-sectional survey of 4959 primary school children, swimming competence formed significant positive relationships with all model variables (β =.061 to.330, p < .05) except intention (β = -.009, p > .05), and its moderation effect on model parameters were small in size or not statistically significant. In Study 2, using a pre-post-test quasi-experiment among 1,609 primary school children, improvement of swimming competence was associated with changescores in all model variables (β =.046 to.230, p < .05) except subjective norm (β =.049, p > .05). Swimming competence did not significantly moderate the parameter estimates of the integrated model (p > .05) at the change-score level. Findings indicate that swimming competence is associated with higher autonomous motivation; TPB social cognitions of attitude, subjective norm, and perceived behavioural control; and intention. However, swimming competence did not moderate the parameter estimates of the integrated model. ARTICLE HISTORY Received 5 May 2022 Accepted 20 July 2023 KEYWORDS Swimming ability; social cognition; theoretical integration; self-efficacy; theory of planned behaviour; self-determined motivation Swimming is one of the most popular sports and leisure-time exercises that has been shown to have important health and social value (Barnsley et al., 2017). It is particularly important for young children to learn swimming at an early age as it may prevent them from drowning (World Health Organization, 2014). Being able to swim is also often regarded as an entry requirement for many aquatic sports (e.g., rowing, canoeing, windsurfing and water polo). Many countries (e.g., United Kingdom, Australia and Jersey Islands) have hence implemented free learn-to-swim programmes to improve the swimming competence of young children (Australia, 2020; Safe, 2021). However, the literature within sport and exercise psychology has not provided a clear picture of the role of swimming competence in the motivational and social cognition patterns of swimming (Kowal & Fortier, 1999). Given the importance of swimming competence to drowning prevention and uptake of aquatic sports, understanding the role of competence in changing the nature of individuals’ motivations and beliefs of swimming behaviour may be valuable. This study addresses this knowledge gap in two large-scale studies with samples of almost 7,000 primary school students. Specifically, we examined the role of competence on the psychological constructs underpinning the motivational and social cognition factors of swimming intentions among young children using an integrated model of self-determination theory (SDT; Deci & Ryan, 1985) and theory of planned behaviour (TPB; Ajzen, 1985). The integrated model of SDT and TPB This research adopted an integrated model of SDT and TPB used in previous research (Hagger & Chatzisarantis, 2009) that accounts for both the motivational and social cognition processes of human self-regulatory actions. The model and its theoretical predictions have been well supported in the context of sport and exercise (Hagger & Chatzisarantis, 2009, 2014; Hagger et al., 2005, 2009; Hamilton et al., 2012). In the model, it is proposed that supporting individuals’ psychological needs (i.e., the basic needs of autonomy, competence, and relatedness) is fundamental to the quality of motivation in a given behaviour. Autonomous motivation is regarded in SDT as the most adaptive motivational pattern, which is characterised by having intrinsic interests and personal values as primary reasons guiding action (Hagger & Hamilton, 2021). This form of motivation, according to the integrated model, is proposed to have a direct and positive influence on the TPB psychological constructs of attitude (i.e., personal evaluation of the behaviour), subjective norm (i.e., perceived social appropriateness and pressure to undertake the behaviour), and perceived CONTACT Derwin King Chung Chan [email protected] Faculty of Education and Human Development, The Education University of Hong Kong, Hong Kong, China JOURNAL OF SPORTS SCIENCES https://doi.org/10.1080/02640414.2023.2241782 © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. behavioural control (PBC; i.e., perceived control over executing the action and considered to be synonymous to self-efficacy) (Hagger & Chatzisarantis, 2009, 2014; Pasi et al., 2021). These TPB social cognition constructs, in turn, are proposed to be directly and positively related to intention (i.e., the extent to which an individual plans to perform the action), and mediate the autonomous motivation-intention-behaviour relationships. This is because autonomous motivation is suggested to foster social cognition beliefs, leading to improved intentions and, thus, behavioural action (Hagger & Chatzisarantis, 2009, 2014; Pasi et al., 2021). The existing body of literature has provided strong evidence to support the pathways of the integrated model (i.e., psychological need support → autonomous motivation → TPB social cognition variables → intention; see Figure 1). However, current literature using the integrated model has primarily focused on more general physical activity as the target behaviour (Hagger & Chatzisarantis, 2009, 2014) or tested the model in other health-related behaviours (e.g., preventive measures for COVID-19 (Hagger et al., 2020; Wan et al., 2022), healthy diet (Vayro & Hamilton, 2016), and injury management (Lee et al., 2020)). Limited studies have tested the psychological pathways of the integrated model among athletes/sport participants in certain sports, although a greater number of studies have tested the tenets of SDT and TPB among specific sporting types (e.g., wheelchair basketball, netball; Palmer et al., 2005; Perreault & Vallerand, 2007). No studies to date, to the authors’ knowledge, have tested the integrated model in the context of children’s swimming nor tested the role of competence on model pathways. Direct and moderation effects of competence in the integrated model Based on prior theory and research integrating SDT and the TPB, it is possible that competence would have important effects in the integrated model. Specifically, according to the basic needs sub-theory of SDT (Ryan & Deci, 2008), perceived support for the psychological need of competence may help to foster autonomous motivation and, indirectly, the sets of beliefs that directly underpin intentions towards, and actual participation in, subsequent behaviour. Thus, within the integrated model, it might be expected that competence would have direct effects on autonomous motivation, and indirect effects on the TPB social cognition constructs of attitudes, subjective norms, and PBC, as well as on intentions and behaviour (Hagger & Chatzisarantis, 2009, 2014; Pasi et al., 2021). Specifically, in the current context of swimming, children who perceive their social environment to support their need for competence might be more likely to report autonomous motivation towards swimming and, as a consequence, report beliefs and intention to participate in swimming in future (Hagger & Chatzisarantis, 2009, 2014). Prior research has also identified constructs related to competence as candidate moderators of the effects of beliefs and other motivation-related constructs on intentions to perform a given behaviour in future. For example, a key prediction of the TPB is that PBC, a construct that is conceptually close to perceived competence, has been proposed as a moderator of beliefs such as attitudes and subjective norms on intentions, as well as the effect of intentions on behaviour (Ajzen, 1985). Such a prediction suggests that individuals who cite high competence in being able to perform a particular behaviour have greater intention to act as this is consistent with their beliefs, as well as enacting their intentions. However, a synthesis of research examining these effects demonstrated that although PBC moderated the intention-behaviour relationship, there was no evidence for the moderation of beliefs on intention (Hagger et al., 2022). As a consequence, we predicted that competence would have direct effects on autonomous motivation (consistent with SDT), and on the belief-based constructs and intentions (consistent with the TPB), but competence would not moderate the psychological pathways of the integration between the SDT and TPB. Despite support for the integrated model in the sports, exercise, and health psychology literature (Chan & Hagger, 2012b; Chan, Dimmock, et al., 2015; Chan, Zhang, et al., 2020; Hamilton et al., 2017; Jacobs et al., 2011; Lee et al., 2020; Standage et al., 2012), few studies have tested the moderating effects of competence on model constructs by either Figure 1. The proposed integrated model. 2D. K. C. CHAN ET AL. longitudinally monitoring the changes in competence in sports or manipulating one’s psychological need support (e.g., competence enhancement). Intervention studies based on the integrated model exist (Jacobs et al., 2011; Schneider et al., 2020), however the primary focus has been on promoting autonomy support only and sample sizes are often small with restricted variance of individuals’ sport competence. It is not surprising therefore that such studies have been unable to provide strong evidence to demonstrate whether the variables of the integrated model could be promoted by competence training. In addition, these prior studies did not formally examine whether the pathways of the integrated model would remain consistent if individuals had higher (or lower) sport competence. Thus, support for the moderating effects of competence on constructs in the integrated model remains unclear. Other research gaps of competence in sports Perceived competence versus actual competence Previous studies did not evaluate the actual competence level of individuals when applying the integrated model to explain behaviours in physical activity or exercise contexts. It is plausible as physical activity or exercise is typically not competitive in nature, so researchers tended to focus on the volume of the activity rather than the competence or skill level (Kalajas-Tilga et al., 2020; Shen et al., 2018). It is important to note that competence-based psychological variables, such as perceived competence, competence satisfaction, self-efficacy, selfconcepts, or PBC, do not fully reflect actual competence itself (Barnett et al., 2015; Moran et al., 2012; Pesce et al., 2018). Previous research in swimming has shown that self-concepts of swimming only accounted for approximately 10% of the variance in swimming performance among world-class swimmers (Marsh & Perry, 2005), and a similar study among gymnastic beginners also reported consistent findings (Marsh et al., 2006). In sum, due to limitations in conceptualising and assessing competence in sport, previous studies were unable to provide solid evidence to reveal whether improving one’s actual competence could have any effects on the motivation and decision-making factors in a particular physical activity or exercise setting. Swimming as a unique type of physical activity/exercise As different types of physical activity have different performance indicators, standardising measures and attributing a single indicator of overall performance is difficult. Similarly, determining a measurement of competence in a single type of exercise, such as swimming, is not without challenges or limitations. Swimming has received comparatively little attention in exercise and health-related research despite the popularity of swimming as a leisure-time physical activity (Moran et al., 2012). This may, in part, be due to the measurement of swimming competence or skill level, which has traditionally been inconsistent or labour intensive (Chan, Lee, Macfarlane, et al., 2020) with limited validity evidence. Recently, a measurement tool for swimming competence, the Swimming Competence Scale, has been developed and found support for its psychometric properties and validity (Chan, Lee, Macfarlane, et al., 2020). The Swimming Competence Scale evaluates the actual competence of swimming in terms of one’s furthest swimming distance (without resting) and one’s basic swimming skills (e.g., holding a breath in the water and treading water). The scoring of the scale correlated significantly with objective measurement of swimming competence by swimming coaches (Chan, Lee, & Hamilton, 2020), supporting the ability of the selfreport instrument to measure one’s actual competence in swimming. Further, the tool allows for the identification of children’s high, low, and improvement in swimming competence, thus making it feasible to test direct and moderation effects of competence on constructs in the integrated model adopted in this study. The present investigation The present investigation aimed to examine the direct and moderation effects of competence on constructs in the integrated model in two large-scale datasets examining the swimming intentions of young children. This forms part of a larger study that has previously published two papers using the datasets to examine the psychometric properties of the Swimming Competence Scale (Chan, Lee, Macfarlane, et al., 2020) and report the descriptive findings of children’s swimming competence (Chan, Lee, & Hamilton, 2020). This study reports on a unique research question and tests the pathways of the proposed integrated model. Study 1 used the dataset from a population-representative crosssectional survey of swimming competence involving nearly 5,000 primary school students. Capturing a broad spectrum of competence information in a population-representative sample allowed the investigation and testing of moderation analyses for swimming competence. This data allowed us to compare the robustness of the model against children with higher or lower swimming competence. It also allowed natural variances of demographic variables (e.g., age, gender) to be accounted for when testing the effects of competence on young children’s swimming patterns, as recommended by previous studies (Nicholls, 1984; Weiss & Williams, 2004). Given that testing moderation effects in a cross-sectional study is somewhat limited, Study 2 used another dataset from an intervention study whereby swimming competence was measured in approximately 1,600 primary school students before and after a structured learn-to-swim intervention programme. In this pre-post-test experiment, we examined the proposed moderation of swimming competence at a changescore level. That is, whether the improvement of swimming competence after a learn-to-swim programme would successfully moderate the changes in the variables and parameter estimates in the integrated model. These two studies allowed us to examine the proposed moderations of competence on the integrated model in both a cross-sectional study (i.e., testing moderation in cross-sectional relationships) and a quasiexperimental study (i.e., testing moderation at the changescore level). Based on the tenets of the integrated model in the prediction of physical activity and other health behaviours JOURNAL OF SPORTS SCIENCES 3 (Chan & Hagger, 2012b; Chan, Dimmock, et al., 2015; Hamilton et al., 2017; Jacobs et al., 2011; Standage et al., 2012), as well as the evidence regarding the adaptive role of psychological support of competence (Bagøien & Halvari, 2005; Gunnell et al., 2014), we hypothesised that swimming competence would not moderate the parameter estimates of the integrated model and, instead, expected only direct, positive effects of competence on model variables consistent with the integrated model. Study 1 Study 1 examined the integrated model on children’s swimming as well as direct and moderating effects of swimming competence on model constructs. Due to the crosssectional design of Study 1, we examined the following hypotheses: H1 The pathways between psychological need support, autonomous motivation, TPB social cognition constructs, and intention would be consistent with the tenets of the integrated model of SDT and TPB: ●H1a Psychological need support would be significantly and positively associated with autonomous motivation. ●H1b Autonomous motivation would be significantly and positively associated with attitude, subjective norm, and PBC. ●H1c Attitude, subjective norm, and PBC would be significantly and positively associated with intention. H2 The psychological pathways of the integrated model would hold when including effects of swimming competence; namely, the direct effects of swimming competence (H2a) and the interactions between swimming competence and the variables of the integrated model (H2b). H3 Swimming competence would be significantly and positively associated with all model constructs. In other words, children with higher swimming competence would have higher psychological need support, autonomous motivation, TPB social cognition constructs, and intention. H4 The interaction terms representing the moderation effect of swimming competence on effects of model constructs on outcomes would be trivial in size 1 (Hagger, Koch, Chatzisarantis, & Orbell, 2017; Seaton, Marsh, & Craven, 2010), or no different from zero, consistent with the predictions of the integrated model. Methods of study 1 Participants and procedure The study was approved by the Institutional Review Board of The University of Hong Kong (no. UW16–407). Invitations were sent to 520 local primary schools in Hong Kong, and 28 schools across 15 districts (out of a total of 18 districts) agreed to participate in the study. Participants were eligible for Study 1 if they were enrolled in a local primary school. No exclusion criteria were applied in the recruitment. Participants were recruited from November 2016 to May 2017. A final sample of 4,959 primary school students (M age = 8.632, SD = 1.686; age range = 5 to 14 years; female = 54.547%) and their parents/ guardians provided informed consent and agreed to take part in the study. After consent was obtained, student participants were asked to complete a paper-based questionnaire with the assistance of their parents/guardians. On average, participants reported that they started swimming at the age of 6.116 years (SD = 1.772) and had 2.786 years (SD = 1.990) of swimming experience. It was also reported that they swam 2.876 times (SD = 3.246) per month and undertook 74.920 minutes (SD = 37.228) of swimming activity per session. Other than swimming and demographic information, participants were given questionnaires that measured the current study’s variables. All the measures included in the questionnaires are presented in the Supplemental Material (Appendix A), and available online on the Open Science Framework platform (https://osf.io/n6b9u/). Measures Psychological need support Participants’ perception of psychological need support from their significant others in the swimming context was measured using the six-item Chinese version of the Health Care Climate Questionnaire (HCCQ; Williams et al., 1996) developed in previous research (Chan et al., 2009). Participants responded to the items with reference to “the most important person who teaches you swimming” on a seven-point Likert scale (1 = not at all true and 7 = very true). The Chinese version of the scale showed good score reliability in previous studies (α = .93; Chan et al., 2011). Autonomous motivation The 12-item Chinese version (Chan et al., 2011) Behavioural Regulation in Sport Questionnaire (Lonsdale et al., 2008) was used to measure participants’ autonomous motivation in swimming. Participants’ responses were rated on a seven-point Likert scale (1 = not at all true and 7 = very true). The scale showed good internal consistency (α =.93) in previous studies (Chan & Hagger, 2012a, 2012b). 1 In this case, it is important to define what a “trivial” effect means in this context. Interpreting effect sizes of interaction terms as well as mediation effects in path analytic models is more complex than interpreting direct effects even when considering standardized coefficients. As a rule of thumb, and consistent with previous research (e.g., Hagger et al., 2017; Seaton et al., 2010), we adopted a standardized coefficient below .10 as representing a small effect size. In the case of the current study, effect sizes for the interaction terms fell well short of this standard. 4D. K. C. CHAN ET AL. TPB social cognition constructs The TPB social cognition constructs of attitude (5 items), subjective norms (3 items), PBC (5 items), and intention (3 items) were measured using the Chinese versions of the TPB scale that were constructed according to TPB published guidelines (Ajzen, 2002). Participants’ responses were reported on a seven-point Likert scale (1 = strongly disagree and 7 = strongly agree). Similar methods have been applied in other studies examining physical activity and sportsrelated behaviours (Chan, Zhang, et al., 2020; Lee et al., 2020, 2021), with acceptable scale score reliabilities reported (ω = .717–.919). Swimming competence The Swimming Competence Questionnaire (Chan, Lee, Macfarlane, et al., 2020) was used to measure participants’ actual swimming competence. This 11-item scale is a selfreport measure that aims to evaluate children’s swimming competence through the maximum swimming distance of various swimming strokes (i.e., front crawl, breaststroke, backstroke, and butterfly) and swimming ability in six basic skills (i.e., swimming underwater, holding breath underwater, floating, poolside kicking, kickboard kicking, and treading water). Validation of the scale reported strong support of the factor structure, convergent validity, concurrent validity, criterion validity, predictive validity, test-retest reliability, inter-rater reliability, and ecological validity of the scale, showing that the scale is applicable to primary school children from 5 to 14 years old (Chan, Lee, & Hamilton, 2020; Chan, Lee, Macfarlane, et al., 2020). To ease interpretation, participants’ responses in the items of swimming distance and basic swimming skill were converted to a swimming competence index following a specific algorithm developed in the validation study (Chan, Lee, Macfarlane, et al., 2020). A swimming competence index ranging from 0 (i.e., “incompetent”) to 100 (i.e., “competent”) may reflect the overall swimming competence of children. Data analysis We calculated descriptive statistics, zero-order correlations among the matrix of the integrated model constructs, reliability coefficients of the scales, and collinearity diagnostics using the Statistical Package for the Social Sciences (SPSS) v26. Structural equational modelling (SEM) was conducted to test study hypothesis using Mplus (version 8.4). Prior to SEM analysis, we conducted a confirmatory factor analysis (CFA) measurement model that consisted of the study variables (i.e., psychological need support, autonomous motivation, and TPB social cognition constructs of attitude, subjective norm, PBC, and intention). The convergent and discriminant validity of the scales were examined in the measurement model (Kline, 2015). For convergent validity, we estimated correlations between the integrated model variables. For discriminant validity, we estimated the shared variance between the factors and average variance extracted (AVE) for each factor. We tested H1 to H4 in three separate models. In Model 1, we tested the psychological pathways of the integrated model (i.e., psychological need support → autonomous motivation → attitude, subjective norm, PBC → intention). In Model 2, we added swimming competence as the predictor of all the variables of Model 1. In Model 3, we created the latent variable interactions between swimming competence and each of the variables of the integrated model (e.g., psychological need support x swimming competence). Moreover, the interactions were added as additional predictors of Model 2 to determine whether swimming competence had any moderation effects on the parameter estimates of the integrated model (e.g., psychological need support x swimming competence → autonomous motivation). The interaction terms were created in Mplus using the XWITH command for the latent moderated structural equations (LMS) procedure (Muthén & Muthén, 2017). Demographic variables, including age, sex, parents’ income and highest education, and frequency, duration, and years of swimming, were included as covariates in all three models. Regarding the three models, H1 was tested in Model 1, H2a and H3 were tested in Model 2, and H2b and H4 were tested in Model 3. Conventional fit indices were used to assess model fit: the comparative fit index (CFI), Tucker‒Lewis index (TLI), root mean square error of approximation (RMSEA), and standardised root mean square residual SRMR (Hu & Bentler, 1999). Traditional cut-off criteria of CFI and TLI (i.e., >.90) and RMSEA and SRMR (i.e., <.08) were applied to indicate acceptable fit (Hu & Bentler, 1999). Maximum likelihood estimation with robust standard errors (MLR) was used as the estimator, which has been proven to be an effective method in handling missing data (Shin et al., 2017). Datasets and analytical scripts can be accessed online on the Open Science Framework platform (https://osf.io/n6b9u/). Results of study 1 Descriptive statistics Descriptive statistics, zero-order correlations, reliability coefficients, AVE, shared variance, and factor loadings are presented in Table 1. The scores of the study variables exhibited acceptable internal consistency (McDonald’s omega = .922 to .948). The measurement model showed excellent fit with the data, χ2 = 2555.394, CFI = .974, TLI = .967, and RMSEA = .033, 90% CI [.031, .034], and SRMR = .053. The integrated model variables were all positively associated with each other (r = .292 to .772), supporting the convergent validity. In general, the AVES of the factors (range = .524 to .852) were higher than the share variance with the study variables (range = .085 to .596), supporting the discriminant validity. Collinearity diagnostics did not reveal evidence of multicollinearity between any of the predictor variables included in the three models examined in this study (i.e., tolerance = .364 to .982; variance inflation factor = 1.018 to 2.751). Structural equation modelling In Model 1, the SEM analysis showed adequate fit with the data, χ2 = 6415.388, CFI = .941, TLI = .926, and RMSEA = .042, 90% CI [.041, .043], and SRMR = .068. All proposed paths of the integrated model were positive and significant (β = .189 to .684, p < .01). See Table 2. The model explained a significant proportion of the variance in the endogenous variables of the JOURNAL OF SPORTS SCIENCES 5 Table 1. Descriptive statistics and zero-order correlation matrix of the study variables (N = 4,959). Variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1. Psychological Need Support – 2. Autonomous Motivation .505** – 3. Attitude .383** .577** – 4. Subjective Norm .292** .484** .542** – 5. PBC .348** .516** .646** .722** – 6. Intention .298** .520** .632** .772** .765** – 7. Competence .113** .283** .325** .281** .403** .342** – Demographic Variables 8. Age −.063** −.086** −.009 −.091** .007 −.036* .346** – 9. Sex −.010 −.031* −.044** −.022 −.011 −.046** −.004 −.032* – 10. Parents’ Income .010 −.016 .022 .078** .098** .088** .200** −.007 −.074** – 11. Parents’ Highest Education .006 .004 .040** .085** .125** .102** .239** −.029* −.068** .419** – 12. Frequency of Swimming .118** .244** .284** .310** .338** .312** .457** .021 .047** .058** .024 – 13. Swimming Duration .058** .102** .082** .029 .039* .046** .128** .216** −.026 −.065** −.83** .123** – 14. Years of Swimming −.019 −.016 .086** .034 .128** .089** .497** .538** −.049** .133** .131** .103** .143** – Omega .939 .939 .922 .924 .942 .948 N/A N/A N/A N/A N/A N/A N/A N/A Mean 4.963 4.573 4.913 3.734 4.188 4.053 45.862 8.632 .453 7.393 2.160 2.876 74.920 2.786 Standard Deviation 1.458 1.340 1.594 2.011 1.927 2.097 32.761 1.686 .497 2.344 .942 3.246 37.228 1.990 Skewness −.56 −.44 −.61 .10 −.22 −.10 −.01 .01 .28 .65 .34 2.96 1.22 .79 Kurtosis −.17 −.02 −.35 −1.22 −1.11 −1.30 −1.31 −.84 −1.92 2.17 −.82 14.10 6.60 .84 AVE .630 .524 .563 .836 .705 .852 N/A N/A N/A N/A N/A N/A N/A N/A Range of Shared Variance .085–.255 .234–.333 .147–.417 .085–.596 .121–.585 .089–596 N/A N/A N/A N/A N/A N/A N/A N/A Range of Factor Loading .738–.856 .574–.938 .648–.877 .897–.938 .710–.932 .902–.938 N/A N/A N/A N/A N/A N/A N/A N/A Note. AVE = average variance extracted; N/A = not applicable; PBC = Perceived behavioural control. *p < .05 **p < .01. 6D. K. C. CHAN ET AL. integrated model, R 2 = .351 to .772, p < .01. The H1 (i.e., H1a, H1b, and H1c) was supported. Model 2 also exhibited adequate fit (χ2 = 6521.400, CFI = .939, TLI = .924, and RMSEA = .042, 90% CI [.041, .043], and SRMR = .074). The proposed paths of the integrated model were also positive and significant (β = .191 to .666, p < .01) after controlling for the effects of swimming competence and were consistent with H2a. Swimming competence had positive effects on all the integrated model variables (β = .061 to .330, p < .05) except intention (β = −.009, p > .05), so H3 was only partially supported. Model 2 significantly explained the variance of the endogenous variables in the integrated model, R 2 = .340 to .767, p < .01. See Table 2. In Model 3, all proposed paths of the integrated model were positive and significant (β = .166 to .604, p < .01), supporting H2b. Furthermore, we examined the moderation effects of swimming competence on all variables of the integrated model. The interaction terms of swimming competence did not identify any significant relationships with the model variables, except with subjective norms (β = .060, p < .001), PBC (β = .030, p < .05), and intention (β = .023, p < .05). Consistent with our hypothesis (H4), these interaction terms were either very small, falling short of the guideline effect size for a non-trivial effect, or were not statistically significant (see Table 2). The model explained a significant proportion of the variance in the endogenous variables of the integrated model, R 2 = .377 to .738, p < .01. Table 2. Parameter estimates for the proposed SEM in Study 1. 95%CI Model Paths B LB UB β a 1 Integrated Model Paths Psychological Need Support →Autonomous Motivation .574 .540 .607 .530** Autonomous Motivation →Attitude .761 .711 .811 .684** Autonomous Motivation →Subjective Norms .628 .565 .691 .458** Autonomous Motivation →PBC .747 .688 .806 .548** Attitude →Intention .222 .184 .259 .189** Subjective Norms →Intention .426 .391 .460 .448** PBC →Intention .448 .409 .487 .468** 2 Integrated Model Paths Psychological Need Support →Autonomous Motivation .535 .502 .568 .500** Autonomous Motivation →Attitude .742 .688 .795 .666** Autonomous motivation →Subjective Norms .606 .537 .674 .440** Autonomous motivation →PBC .697 .634 .761 .511** Attitude →Intention .223 .186 .261 .191** Subjective Norms →Intention .426 .391 .460 .450** PBC →Intention .447 .408 .487 .468** Swimming Competence Effects Swimming Competence →Psychological Need Support .224 .183 .266 .165** Swimming Competence →Autonomous Motivation .480 .424 .537 .330** Swimming Competence →Attitude .102 .023 .181 .063* Swimming Competence →Subjective Norms .122 .020 .223 .061* Swimming Competence →PBC .260 .161 .359 .131** Swimming Competence →Intention −.018 −.064 .028 −.009 3 Integrated Model Paths Psychological Need Support →Autonomous Motivation .616 .580 .652 .458** Autonomous Motivation →Attitude .637 .602 .673 .604** Autonomous Motivation →Subjective Norms .655 .607 .704 .449** Autonomous Motivation →PBC .679 .638 .720 .481** Attitude →Intention .222 .188 .256 .166** Subjective Norms →Intention .488 .451 .525 .504** PBC →Intention .411 .371 .451 .411** Swimming Competence Effects Swimming Competence →Autonomous Motivation .413 .364 .462 .307** Swimming Competence →Attitude .067 .016 .118 .047* Swimming Competence →Subjective Norms .131 .056 .206 .067** Swimming Competence →PBC .310 .241 .379 .163** Swimming Competence →Intention .024 −.023 .070 .013 Moderation Effects Psychological Need Support x Swimming Competence →Autonomous Motivation −.026 −.060 .007 −.020 Autonomous motivation x Swimming Competence →Attitude .010 −.012 .031 .009 Autonomous motivation x Swimming Competence →Subjective Norms .064 .034 .095 .060** Autonomous motivation x Swimming Competence →PBC .042 .013 .070 .030* Attitude x Swimming Competence →Intention .010 −.013 .032 .007 Subjective Norms x Swimming Competence →Intention −.011 −.026 .004 −.011 PBC x Swimming Competence →Intention .023 .007 .039 .023* Note. 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