Efficient Laplacian and Adaptive Gaussian Quadrature Algorithms for Multilevel Generalized Linear Mixed Models

Abstract

Mixed-effects models have become a popular approach for the analysis of grouped data that arise in many areas as diverse as clinical trials, epidemiology, and sociology. Examples of grouped data include longitudinal data, repeated measures, and multilevel data. In the case of linear mixed-effects (LME) models, the likelihood function can be expressed in closed form, with efficient computational algorithms having been proposed for maximum likelihood and restricted maximum likelihood estimation. For nonlinear mixed-effects (NLME) models and generalized linear mixed models (GLMMs), however, the likelihood function does not have a closed form. Different likelihood approximations, with varying degrees of accuracy and computational complexity, have been proposed for these models. This article describes algorithms for one such approximation, the adaptive Gaussian quadrature (AGQ), for GLMMs which scale up efficiently to multilevel models with arbitrary number of levels. The proposed algorithms greatly reduce the computational complexity and the memory usage for approximating the multilevel GLMM likelihood, when compared to a direct application of a single-level AGQ approximation algorithm to the multilevel case. The accuracy of the associated estimates is evaluated and compared to that of estimates obtained from other approximations via simulation studies.

Interviewer Effects on a Network-Size Filter Question

“…for the xtlogit and AGQ with the multicoefficient extension from Pinheiro and Bates (1995) and the multilevel extension from Pinheiro and Chao (2006) for xtmelogit (cf. StataCorp 2011).…”

Expansive Phenotypic Landscape of Botrytis cinerea Shows Differential Contribution of Genetic Diversity and Plasticity

“…The LSMean of each trait within a treatment and associated for each fixed and random effect was calculated using the 'doBy' package in R, which calls upon the 'nlme' package allowing for the use of adaptive Gaussian quadrature to minimize the effects of deviations from normality and the calculation of variances using REML (Pinheiro and Chao 2006). The LSMean of each trait was used for further downstream statistical analyses.…”

Network Quantitative Trait Loci Mapping of Circadian Clock Outputs Identifies Metabolic Pathway-to-Clock Linkages in Arabidopsis

“…Period estimates with an RAE >0.6 were excluded from downstream analyses. A linear model was fit to the circadian period data from three separate trials to determine if the mutants were significantly different than Col-0; the nlme package (Pinheiro and Chao, 2006) in R (R Development Core Team, 2008) was used for this analysis.…”