Latent variable structural equation modeling with categorical data

Abstract

Structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous, ordered polytomous, and continuous indicators of latent variables. Special emphasis is placed on categorical variables. Models in psychometrics, econometrics and biometrics are interrelated via a general model due to Muthén. Limited information least squares estimators and full information estimation are discussed. An example is estimated with a model for a four-wave longitudinal data set, where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure.