Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.
Andreas Stenling, Andreas Ivarsson, Urban Johnson and Magnus Lindwall
Katherine A. Tamminen, Patrick Gaudreau, Carolyn E. McEwen and Peter R.E. Crocker
Efforts to regulate emotions can influence others, and interpersonal emotion regulation within teams may affect athletes’ own affective and motivational outcomes. We examined adolescent athletes’ (N = 451, N teams = 38) self- and interpersonal emotion regulation, as well as associations with peer climate, sport enjoyment, and sport commitment within a multilevel model of emotion regulation in teams. Results of multilevel Bayesian structural equation modeling showed that athletes’ self-worsening emotion regulation strategies were negatively associated with enjoyment while other-improving emotion regulation strategies were positively associated enjoyment and commitment. The team-level interpersonal emotion regulation climate and peer motivational climates were also associated with enjoyment and commitment. Team-level factors moderated some of the relationships between athletes’ emotion regulation with enjoyment and commitment. These findings extend previous research by examining interpersonal emotion regulation within teams using a multilevel approach, and they demonstrate the importance of person- and team-level factors for athletes’ enjoyment and commitment.
Rosemary A. Arthur, Nichola Callow, Ross Roberts and Freya Glendinning
understanding of the nature of coaching of PS. Study 2 involved questionnaire development using the qualitative findings, and then testing of the questionnaires’ factor structure via a Bayesian structural equation modeling (BSEM) approach to confirmatory factor analysis. Finally, in Study 3, we confirmed the
Derwin K.C. Chan, Andreas Ivarsson, Andreas Stenling, Sophie X. Yang, Nikos L.D. Chatzisarantis and Martin S. Hagger
Consistency tendency is characterized by the propensity for participants responding to subsequent items in a survey consistent with their responses to previous items. This method effect might contaminate the results of sport psychology surveys using cross-sectional design. We present a randomized controlled crossover study examining the effect of consistency tendency on the motivational pathway (i.e., autonomy support → autonomous motivation → intention) of self-determination theory in the context of sport injury prevention. Athletes from Sweden (N = 341) responded to the survey printed in either low interitem distance (IID; consistency tendency likely) or high IID (consistency tendency suppressed) on two separate occasions, with a one-week interim period. Participants were randomly allocated into two groups, and they received the survey of different IID at each occasion. Bayesian structural equation modeling showed that low IID condition had stronger parameter estimates than high IID condition, but the differences were not statistically significant.
Ben Jackson, Daniel F. Gucciardi and James A. Dimmock
Drawing from a three-factor model of organizational commitment, we sought to provide validity evidence for a multidimensional conceptualization designed to capture adolescent athletes’ commitment to their coach–athlete relationship or their team. In Study 1, 335 individual-sport athletes (M age = 17.32, SD = 1.38) completed instruments assessing affective, normative, and continuance commitment to their relationship with their coach, and in Study 2, contextually modified instruments were administered to assess interdependent-sport athletes’ (N = 286, M age = 16.31, SD = 1.33) commitment to their team. Bayesian structural equation modeling revealed support for a three-factor (in comparison with a single-factor) model, along with relations between commitment dimensions and relevant correlates (e.g., satisfaction, return intentions, cohesion) that were largely consistent with theory. Guided by recent advancements in Bayesian modeling, these studies provide a new commitment instrument with the potential for use and refinement in team- and relationship-based settings and offer preliminary support for a conceptual framework that may help advance our understanding of the factors underpinning individuals’ engagement in sport.
Isaac Estevan, Javier Molina-García, Gavin Abbott, Steve J. Bowe, Isabel Castillo and Lisa M. Barnett
Bayesian Structural Equation Modeling Results for the PMSC for the Sample ( n = 247) Model Priors Specification No. of Free Parameters 2.5% PP Limit 97.5% PP Limit PP p No. of Iterations (Runtime) 1 Three factor (6-6-6); non-informative 75 87.155 195.11 <.001 60,000 (10 s) 2 Three factor (6
Alex J. Benson and Mark Eys
that cover a range of socialization tactics that can occur in sport teams and evaluate their content validity. The second objective was to test the STSTQ’s factor structure by moving from exploratory structural equation modeling (ESEM; Studies 2–3) to Bayesian structural equation modeling (BSEM; Study
Eleanor Quested, Nikos Ntoumanis, Andreas Stenling, Cecilie Thogersen-Ntoumani and Jennie E. Hancox
. , Muthén , B. , & Morin , A. ( 2015 ). Bayesian structural equation modeling with cross-loadings and residual covariances: Comments on Stromeyer et al . Journal of Management, 41 , 1561 – 1577 . doi:10.1177/0149206315591075 10.1177/0149206315591075 Bartholomew , K. , Ntoumanis , N. , Ryan , R
Lennart Raudsepp and Eva-Maria Riso
b013e3180616aa2 10.1249/mss.0b013e3180616aa2 Niven , A.G. , & Markland , D. ( 2016 ). Using self-determination theory to understand motivation for walking: instrument development and model testing using Bayesian structural equation modelling . Psychology of Sport and Exercise, 23 , 90 – 100
Collin A. Webster, Diana Mindrila, Chanta Moore, Gregory Stewart, Karie Orendorff and Sally Taunton
Sage handbook of quantitative methodology for the social sciences (pp. 345 – 368 ). Thousand Oaks, CA : Sage . Muthén , B. , & Asparouhov , T. ( 2010 ). Bayesian structural equation modeling: A more flexible representation of substantive theory . Psychological Methods, 17 ( 3 ), 313