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 is with the Department of Psychology, Umeå University, Umeå, Sweden. Andreas Ivarsson is with the Center of Research on Welfare, Health and Sport (Centrum för Forskning om Välfärd, Hälsa och Idrott), Halmstad University, Halmstad, Sweden, and with Department of Psychology, Linnaeus University, Växjö, Sweden. Urban Johnson is with the Center of Research on Welfare, Health and Sport (Centrum för Forskning om Välfärd, Hälsa och Idrott), Halmstad University, Halmstad, Sweden. Magnus Lindwall is with Department of Food and Nutrition, and Sport Science & Department of Psychology, University of Gothenburg, Gothenburg, Sweden.