Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects

Yin Chen; Yu Fei; Jianxin Pan

doi:10.4236/ojs.2015.56059

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OJS> Vol.5 No.6, October 2015

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Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects

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DOI: 10.4236/ojs.2015.56059 2,244 Downloads 2,923 Views Citations

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Yin Chen¹, Yu Fei², Jianxin Pan^3*

Affiliation(s)

¹School of Insurance, University of International Business and Economics, Beijing, China.
²School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China.
³School of Mathematics, University of Manchester, Manchester, UK.

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.

KEYWORDS

Generalized Linear Mixed Models, Multivariate t Distribution, Multivariate Mixture Normal Distribution, Quasi-Monte Carlo, Newton-Raphson, Joint Modelling of Mean and Covariance

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Chen, Y. , Fei, Y. and Pan, J. (2015) Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects. Open Journal of Statistics, 5, 568-584. doi: 10.4236/ojs.2015.56059.

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