Approximate likelihood inference in latent variable models for categorical data.

Latent variable models represent a useful tool for the analysis of complex data characterized by the fact that the constructs of interest are not directly observable. One problem related to these models is that the integrals involved in the maximization of the likelihood function cannot be solved analytically. In this paper we propose a new approach for approximating integrals in latent variable models for binary data. Based on a fundamental theorem by Xu and Rahman (2004a), it consists of reducing the dimen- sionality of the integrals involved in the computations.