, Volume 60, Issue 4, pp 489-503

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

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Muthén (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 Muthén 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.

The research of the first author was supported by grant AA 08651-01 from NIAAA for the project “Psychometric Advances for Alcohol and Depression Studies” and grant 40859 from the National Institute for Mental Health. The research of the second author was partially supported by the Spanish DGICYT grants PB91-0814 and PB93-0403.