Limited Information Estimation and Testing of Discretized Multivariate Normal Structural Models

(WP03/03 Clave pdf) We consider the estimation of multivariate normal structural models that have been discretized according to a set of thresholds. A popular estimation procedure for this restricted multinomial model consists in the following three stage estimator: First, estimate by maximum likelihood the thresholds for each variable separately from the univariate marginals of the contingency table. Then, estimate by maximum likelihood each of the polychoric correlations separately from the bivariate marginals of the contingency table given the estimated thresholds. Finally, if restrictions are imposed on the thresholds and polychoric correlations.