Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

Abstract

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the L ν-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider a Bayesian semiparametric approach for estimation and model comparison in the context of structural equation models with fixed covariates. A finite dimensional Dirichlet process is used to model the crucial latent variables, and a blocked Gibbs sampler is implemented for estimation. Empirical performance of the L ν-measure is evaluated through a simulation study. Results obtained indicate that the L ν-measure, which additionally requires very minor computational effort, gives satisfactory performance. Moreover, the methodologies are demonstrated through an example with a real data set on kidney disease. Finally, the application of the L ν-measure to Bayesian semiparametric nonlinear structural equation models is outlined.