Asymptotic properties of adaptive Gauss-Hermite based estimators in latent variable models.

Latent variable models have been widely applied 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 arise since analytical solutions do not exist. A recent applied numerical technique is the Adaptive Gauss-Hermite (AGH) that provides a good approximation of the function to be inte- grated, and it is also computational feasible in presence of many latent variables and/or random effects. In this paper, we analyze the asymptotic behavior of the AGH-based estimators used to perform inference in generalized linear latent variable models.