Fitting multivariate normal finite mixtures subject to structural equation modeling

This paper is about fitting multivariate normal mixture distributions subject to structural equation modeling. The general model comprises common factor and structural regression models. The introduction of covariance and mean structure models reduces the number of parameters to be estimated in fitting the mixture and enables one to investigate a variety of substantive hypotheses concerning the differences between the components in the mixture. Within the general model,individual parameters can be subjected to equality, nonlinear and simple bounds constraints. Confidence intervals are based on the inverse of the Hessian and on the likelihood profile. Several illustrations are given and results of a simulation study concerning the confidence intervals are reported.