Hypothesis Testing and Model Comparison in Two-level Structural Equation Models

One basic and important problem in two-level structural equation modeling is to find a good model for the observed sample data. This article demonstrates the use of the well-known Bayes factor in the Bayesian literature for hypothesis testing and model comparison in general two-level structural equation models. It is shown that the proposed methodology is flexible, and can be applied to situations with a wide variety of nonnested models. Moreover, some problems encountered in using existing methods for goodness-of-fit assessment of the proposed model can be alleviated. An illustrative example with some real data from an AIDS care study is presented.