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Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects
School of Insurance, University of International Business and Economics, Beijing, China
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China
School of Mathematics, University of Manchester, Manchester, UK
- 1 School of Insurance, University of International Business and Economics, Beijing, China
- 2 School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China
- 3 School of Mathematics, University of Manchester, Manchester, UK
Open Journal of Statistics·Volume 05 (2015)·Pages 568–584·Published 13 October 2015·DOI10.4236/ojs.2015.56059
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Abstract
Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.
KeywordsGeneralized Linear Mixed ModelsMultivariate t DistributionMultivariate Mixture Normal DistributionQuasi-Monte CarloNewton-RaphsonJoint Modelling of Mean and Covariance
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