Recent Developments in Approximated-Likelihood Inference Methods for Latent Variable Models

Abstract

In this paper we describe some developments on likelihood-based inference for latent variable models (LVMs). The latent variable approach is wide and frequently used in social sciences with the aim of knowing more about some unobservable features, such as attitudes, beliefs or abilities. The definition of LVMs is broad, and a unique definition is not possible. However, all LVMs can be considered powerful tools to take into account the dependence within complex data structure that cannot be fully explained through the observed variables. Nevertheless, despite this flexibility, they could cause some inferential problems, mainly when some independence assumptions are relaxed. A full maximum likelihood approach, although it is the most efficient estimation method statistically, is not always the most efficient computationally. In this paper we provide an overview on some existing approaches developed to solve difficult computational problems, focusing on some particular classes of LVMs. We summarize and compare the main features of three estimation methods: composite likelihood, Monte Carlo likelihood and variational approach. It is not possible to conclude which is the best estimation method; it mainly depends on the data structure (and consequently on the latent variable model used). Thus, we outline some practical guidelines that could help the reader to choose the best estimation method for the latent variable model involved.