Latent variable models for the University process evaluation by using different integration methods

Latent variable models for categorical data represent a useful tool for a consistent assessment of the University system. However, the evaluation process is characterized by different facets and often several latent variables are required to reduce its complexity. In these cases problems related to the integration of the likelihood arise. Indeed the most used classical numerical approximation procedure, that is the Gauss Hermite (G-H) quadrature, cannot be applied since it requires several quadrature points per dimension in order to obtain accurate estimates and hence the computational effort becomes not feasible. Different alternative solutions have been proposed in literature, like the Laplace approximation and the adaptive quadrature. In this work we present a simulation study for evaluating the performance of the adaptive quadrature approximation of a latent variable model for ordinal data under different conditions of study and we compare the results with the classical and more used G-H.