Maximum likelihood estimation and model comparison for mixtures of structural equation models with ignorable missing data

The objective of this paper is to develop the maximum likelihood approach for analyzing a finite mixture of structural equation models with missing data that are missing at random. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates. A well-known statistic in model comparison, namely the Bayesian Information Criterion (BIC), is used for model comparison. With the presence of missing data, the computation of the observed-data likelihood function value involved in the BIC is not straightforward. A procedure based on path sampling is developed to compute this function value. It is shown by means of simulation studies that ignoring the incomplete data with missing entries gives less accurate ML estimates. An illustrative real example is also presented.