11. Structural Equation Models with Mixed Continuous and Unordered Categorical Variables

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

Published Online: 18 JUL 2012

DOI: 10.1002/9781118358887.ch11

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) Structural Equation Models with Mixed Continuous and Unordered Categorical Variables, 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.ch11

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:

  • confirmatory factor analysis (CFA) model;
  • Dirichlet process (DP);
  • mixed continuous;
  • structural equation models (SEMs);
  • unordered categorical variables

Summary

This chapter discusses structural equation models (SEMs) with mixed continuous and multinomial variables to analyze the interrelationships among phenotype and genotype latent variables. The SEM is composed of two components. The first component is a confirmatory factor analysis (CFA) model in which the mean vector and the factor loading matrix are defined for modeling the multinomial variables. The second component is a regression type structural equation, which regresses outcome latent variables on the linear and nonlinear terms of explanatory latent variables. The chapter discusses semiparametric SEMs without the normal assumption on the explanatory latent variables. It develops a nonlinear SEM with mixed continuous and unordered categorical variables to study the interrelationships of the latent variables formed by those observed variables. The chapter introduces Bayesian semiparametric approach for analyzing SEMs with mixed continuous and unordered categorical variables, with the explanatory latent variables being modeled through an appropriate truncated Dirichlet process (DP).

Controlled Vocabulary Terms

confirmatory factor analysis; Dirichlet process