A Bayesian analysis of finite mixtures in the LISREL model

In this paper, we propose a Bayesian framework for estimating finite mixtures of the LISREL model. The basic idea in our analysis is to augment the observed data of the manifest variables with the latent variables and the allocation variables. The Gibbs sampler is implemented to obtain the Bayesian solution. Other associated statistical inferences, such as the direct estimation of the latent variables, establishment of a goodness-of-fit assessment for a posited model, Bayesian classification, residual and outlier analyses, are discussed. The methodology is illustrated with a simulation study and a real example.This research was supported by a Hong Kong UGC Earmarked grant CUHK 4026/97H. The authors are indebted to the Editor, the Associate Editor, and three anonymous reviewers for constructive comments in improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.