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

TL;DR

This paper introduces the Dimension Reduction Method (DRM), a computational technique for approximate likelihood inference in generalized linear latent variable models, enabling feasible analysis of complex models with high-dimensional integrals.

Contribution

The paper proposes DRM, a novel dimension reduction approach that improves computational feasibility and maintains desirable asymptotic properties for latent variable models.

Findings

DRM reduces computational complexity of likelihood estimation.

DRM outperforms traditional quadrature methods in high-dimensional settings.

The method retains asymptotic properties of estimators.

Abstract

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved analytically. We propose a computational approach, referred to as Dimension Reduction Method (DRM), that consists of 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 compared with other existing approximation procedures in terms of both computational feasibility of the method and asymptotic properties of the resulting estimators.