A Monte Carlo study of structural equation models for finite mixtures

Empirical applications of structural equation modeling (SEM) typically rest on the assumption that the analysed sample is homogenous with respect to the underlying structural model or that homogenous subsamples have been formed based on a priori knowledge. However, researchers often are ignorant about the true causes of heterogeneity and thus risk to produce misleading results. Using a sequential procedure of cluster analysis in combination with multi-group SEM has been shown to be inappropriate to solve the problem of unobserved heterogeneity. Recently, two encouraging approaches have been developed in this regard: (1) Finite mixtures of structural equation models and (2) hierarchical Bayesian estimation. In this paper, we focus exclusively on the MECOSA approach to finite normal mixtures subject to conditional mean and covariance structures. Since not much is known about the performance of MECOSA, which is both a specific odel and a software, we present the results of an extensive Monte Carlo simulation. It was found that MECOSA performed best where homogenous groups were present in the data in equal proportions and in conjunction with rather large differences in parameters across the groups. MECOSA performed worse when the proportions were unequal and parameters were relatively close together across groups. Of the three estimation methods available in MECOSA the two-stage minimum distance estimation (MDE) in general performed worse than the alternative EM algorithms (EM and EMG). This effect was especially pronounced under conditions of close parameters and unequal group proportions. Above that, for these conditions the modified likelihood ratio test turned out to be inappropriate in the three groups case.