Simulation Based Estimation for Generalized Latent Linear Variables Models

Generalized Linear Latent Variables Models (GLLVM) constitute a broad class of models that offer a general framework for modeling relationships between manifest and latent variables, as the manifest variables can follow any distribution of the exponential family (e.g, binomial, multinomial or normal). However, the estimation of such models is quite difficult due to the complexity of the associated log-likelihood function which contains integrals without closed form expression, except in the normal case. We propose a method based on indirect inference (Gourieroux, Monfort, and Renault 1993) which starts from an easy to compute estimator that is then corrected for bias.