Local Influence Analysis for Mixture of Structural Equation Models

Abstract

Finite mixture of structural equation models is very useful to analyze data from heterogeneous populations. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influential aspects on the maximum likelihood estimation of a finite mixture of structural equation models. A Monte Carlo EM algorithm which treats both latent variables and allocation variables as hypothetical missing data is implemented. The local influence measures are developed on the basis of a Q-displacement function at the E-step of the algorithm. The diagnostic measures are based on the conformal normal curvature that can be computed easily. Building blocks of the diagnostic measures are derived, and they are evaluated via observations simulated by the Gibbs sampler from the appropriate conditional distributions. A number of interesting and novel perturbations are considered. The methodology is illustrated with a real example.