Maximum Likelihood Estimation and ModelComparison for Mixtures of Structural EquationModels with Ignorable Missing Data

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