A two-stage estimation of structural equation models with continuous and polytomous variables

This paper develops a computationally efficient procedure for analysis of structural equation models with continuous and polytomous variables. A partition maximum likelihood approach is used to obtain the first stage estimates of the thresholds and the polyserial and polychoric correlations in the underlying correlation matrix. Then, based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, a generalized least squares approach is employed to estimate the structural parameters in the correlation structure. Asymptotic properties of the estimators are derived. Some simulation studies are conducted to study the empirical behaviours and robustness of the procedure, and compare it with some existing methods.