Bayesian model selection for structural equation models for myopia data

Structural equation models (SEMs) are extensively used in behavioral, social, and psychological research to model relationships between latent variables and observations. However, most models include redundant variables that are not important to relationships within the model. This study uses a Bayesian model selection procedure with mixture priors for SEMs to determine variables that have a meaningful relationship. The posterior probabilities for all possible models are calculated through the MCMC algorithm and the model with the largest probability is selected. The predictors of non-zero fixed-effect coefficients and/or non-zero random-effect variance components in the MCMC procedure are determined without the need for complex model selection criteria. The proposed methodologies are illustrated in a simulation and applied to a multidimensional longitudinal myopia data set in which the dimensionality of the parameter space is reduced and a more parsimonious model is selected.