Generalized linear la tent variable models with flexible distribution of latent variables

We consider 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 of GLLVM can be achieved through the semi-nonparametric specification with a finite number of parameters estimated by maximum likelihood. We show by simulations that the estimated latent variables density capture the true one with good degree of accuracy. Thus, a flexible distribution of latent variables is a powerful tool for exploring the adequacy of the GLLVM for real data. This flexibility brings new insights into the behavior of latent variables.