  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. In such models, problems related to the integration of the
likelihood function can arise since analytical solutions do not exist.
Numerical approximations, like the widely used Gauss Hermite (GH) quadrature,
are generally applied to solve these problems. However, GH becomes unfeasible
as the number of latent variables increases. Thus, alternative solutions have
to be found. In this paper, we propose an extended version of the Laplace
method for approximating the integrals, known as fully exponential Laplace
approximation. It is computational feasible also in presence of many latent
variables, and it is more accurate than the classical Laplace method.
