Title: Approximate likelihood inference via dimension reduction in latent variable models for categorical data
Authors: Silvia Cagnone - University of Bologna (Italy) [presenting]
Silvia Bianconcini - University of Bologna (Italy)
Dimitris Rizopoulos - Erasmus University Rotterdam (Netherlands)
Abstract: Latent variable models represent a useful tool in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In these cases, problems related to the integration of the likelihood function of the model can arise since analytical solutions do not exist. Usually, numerical quadrature-based methods like Gauss-Hermite or adaptive Gauss-Hermite are used to overcome this problem. They work quite well in several situations, but become unfeasible in presence of many latent variables and/or random effects. We propose a new 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 as well as asymptotic properties of the resulting estimators. Applications to real data are also illustrated.