A GENERAL STRUCTURAL EQUATION MODEL WITH D ICHOTOMOUS, ORDERED CATEGORICAL, AND CONTINUOUS LATENT VARIABLE INDICATORS

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in additi n to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed vari-able types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multi-variate probit regressions. Key words: polychoric correlations, probit regressions, generalized least-squares, weight matrix. 1