Bayesian structural equation modeling in sport and exercise psychology.

Area of Science:

• Psychology
• Sport and Exercise Psychology
• Statistical Modeling

Background:

• Bayesian statistics is increasingly used in general psychology.
• Applications in sport and exercise psychology are limited.
• This paper introduces Bayesian analysis foundations.

Purpose of the Study:

• Illustrate Bayesian structural equation modeling in sport and exercise psychology.
• Contrast Bayesian estimation with maximum likelihood.
• Evaluate model fit for the Sport Motivation Scale II.

Main Methods:

• Confirmatory factor analysis of the Sport Motivation Scale II.
• Comparison of maximum likelihood (ML) and Bayesian estimation.
• Application of weakly informative priors for cross-loadings and correlated residuals in the Bayesian approach.

Main Results:

• The Bayesian approach with weakly informative priors yielded a well-fitting model.
• The maximum likelihood estimator resulted in a poorly fitting model.
• Discrepancies between the two estimation methods are highlighted.

Conclusions:

• Bayesian estimation with weakly informative priors offers advantages for structural equation modeling in sport and exercise psychology.
• The Bayesian approach can provide better model fit than maximum likelihood.
• Potential benefits and limitations of the Bayesian method are discussed.