Generalized linear latent variable models with flexible distributions

Abstract

We consider first a semi-nonparametric specification for the density of latent variables in Generalized Linear Latent Variable Models (GLLVM). This specification is flexible enough to allow for an asymmetric, multi-modal, heavy or light tailed smooth density. The degree of flexibility required by many applications can be achieved through this semi-nonparametric specification with a finite number of parameters. Even with this additional flexibility, we obtain an explicit expression of the likelihood for conditionally normal manifest variables. We show that the estimated density of latent variables capture the true one with good accuracy. In the second part we consider a spatial generalized linear latent variable model with and without assumption of normality on latent variables. The Laplace approximation is applicable when latent variables are multivariate normal. Otherwise the assumption of marginal normality is relaxed in favor of a mixture of normals. The pairwise likelihood estimators are explored by simulations.