7. Mixture Structural Equation Models

  1. Xin-Yuan Song and
  2. Sik-Yum Lee

Published Online: 18 JUL 2012

DOI: 10.1002/9781118358887.ch7

Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences

Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences

How to Cite

Song, X.-Y. and Lee, S.-Y. (2012) Mixture Structural Equation Models, in Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118358887.ch7

Author Information

  1. Department of Statistics, The Chinese University of Hong Kong

Publication History

  1. Published Online: 18 JUL 2012
  2. Published Print: 24 AUG 2012

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470669525

Online ISBN: 9781118358887

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Keywords:

  • Bayesian estimation;
  • finite mixture SEMs;
  • modified mixture SEM

Summary

This chapter focuses on heterogeneous data which involve independent observations that come from one of the K populations with different distributions, and no information is available on which of the K populations an individual observation belongs to. The chapter discusses the Bayesian methodologies for analyzing heterogeneous data through these models. It presents a general finite mixture structural equation models (SEM), in which the probabilities of component memberships are unknown and estimated together with other parameters. The chapter introduces a modified mixture SEM which extends the previous mixture SEMs in three respects. First, a multinomial logit model with covariates is incorporated to predict the unknown component membership. Second, a nonlinear structural equation is introduced in each component to capture the component-specific nonlinear effects of explanatory latent variables and covariates on outcome latent variables. Third, nonignorable missing data are considered for both responses and covariates.

Controlled Vocabulary Terms

Bayes estimator; Bayesian information criterion; mixture distribution; mixture model