Approximate likelihood inference in generalized linear latent variable models based on integral dimension reduction

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problemrelated to the estimation of these models is that the integrals involved in the likelihood function cannot be solved analytically. We propose a new approach, referred to as Dimension Reduction Method (DRM), that consists in a dimension reduction of the multidimensional integral that makes the computation feasible in situations in which the quadrature-based methods are not applicable. We discuss the advantages of DRM comparedwith other existing approximation procedures in terms of both computational feasibility as well as asymptotic properties of the resulting estimators