Structural Equation Models with Mixed Continuous and Unordered Categorical Variables
Xinyuan Song, Sik‐Yum Lee · Wiley series in probability and statistics · 2012
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