Numerical integration in logistic-normal models

When estimating logistic-normal models, the integral appearing in the marginal likelihood is analytically intractable, so that numerical methods such as GaussHermite quadrature (GH) are needed. When the dimensionality increases, the number of quadrature points becomes too high. A possible solution can be found among the Quasi-Monte Carlo (QMC) methods, because these techniques yield quite good approximations for high dimensional integrals with a much lower number of points, chosen for their optimal location. In this paper a comparison will be made between three integration methods: GH, QMC, and full Monte Carlo integration (MC).