Likelihood Inference in Latent Variable Models for ordinal data based on different approximation methods

Latent variable models for ordinal data 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. One of the most used classical numerical approximat on is the Gauss Hermite (GH) quadrature. With this approximation the accuracy of estimates is strictly related to the number of quadrature points as well as to the sample size. In presence of many latent variables, the GH cannot be applied since it requires several quadrature points per dimension in order to obtain quite accurate estimates, and, hence, the computational effort becomes not feasible.We propose alternative solutions in order to overcome the main drawbacks of this approach