Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Monte Carlo Statistical Methods
Monte Carlo Statistical Methods
Restricted likelihood inference for generalized linear mixed models
Statistics and Computing
Modeling the random effects covariance matrix for generalized linear mixed models
Computational Statistics & Data Analysis
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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.