Model Selection in Structural Equation Models With Continuous and Polytomous Data

Recently, analysis of structural equation models with polytomous and continuous variables has received a lot of attention. However, contributions to the selection of good models are limited. The main objective of this article is to investigate the maximum likelihood estimation of unknown parameters in a general LISREL-type model with mixed polytomous and continuous data and propose a model selection procedure for obtaining good models for the underlying substantive theory. The maximum likelihood estimate is obtained by a Monte Carlo Expectation Maximization algorithm, in which the E step is evaluated via the Gibbs sampler and the M step is completed via the method of conditional maximization. The convergence of the Monte Carlo Expectation Maximization algorithm is monitored by the bridge sampling. A model selection procedure based on Bayes factor and Occam’s window search strategy is proposed. The effectiveness of the procedure in accounting for the model uncertainty and in picking good models is discussed. The proposed methodology is illustrated with a real example.