Technical aspects of Muthén's liscomp approach to estimation of latent variable relations with a comprehensive measurement model

Abstract

Muthen (1984) formulated a general model and estimation procedure for structural equation modeling with a mixture of dichotomous, ordered categorical, and continuous measures of latent variables. A general three-stage procedure was developed to obtain estimates, standard errors, and a chi-square measure of fit for a given structural model. While the last step uses generalized least-squares estimation to fit a structural model, the first two steps involve the computation of the statistics used in this model fitting. A key component in the procedure was the development of a GLS weight matrix corresponding to the asymptotic covariance matrix of the sample statistics computed in the first two stages. This paper extends the description of the asymptotics involved and shows how the Muthen formulas can be derived. The emphasis is placed on showing the asymptotic normality of the estimates obtained in the first and second stage and the validity of the weight matrix used in the GLS estimation of the third stage.