Numerical integration in logistic-normal models

Marginal maximum likelihood estimation is commonly used to estimate logistic-normal models. In this approach, the contribution of random effects to the likelihood is represented as an intractable integral over their distribution. Thus, numerical methods such as Gauss–Hermite quadrature (GH) are needed. However, as the dimensionality increases, the number of quadrature points becomes rapidly 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. A comparison between three integration methods for logistic-normal models: GH, QMC, and full Monte Carlo integration (MC) is presented. It turns out that, under certain conditions, the QMC and MC method perform better than the GH in terms of accuracy and computing time.