Quasi-Monte Carlo Estimation in Generalized Linear Mixed Model with Correlated Random Effects

Yin Chen¹, Yu Fei², Jianxin Pan^3*

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.

DOI: 10.4236/oalib.1102002                

Abstract

Parameter estimation by maximizing the marginal likelihood function in generalized linear mixed models (GLMMs) is highly challenging because it may involve analytically intractable high-dimensional integrals. In this paper, we propose to use Quasi-Monte Carlo (QMC) approximation through implementing Newton-Raphson algorithm to address the estimation issue in GLMMs. The random effects release to be correlated and joint mean-covariance modelling is considered. We demonstrate the usefulness of the proposed QMC-based method in approximating high-dimensional integrals and estimating the parameters in GLMMs through simulation studies. For illustration, the proposed method is used to analyze the infamous salamander mating binary data, of which the marginalized likelihood involves six 20-dimensional integrals that are analytically intractable, showing that it works well in practices.

Keywords

Generalized Linear Mixed Models, Correlated Random Effects, Quasi-Monte Carlo, Mean-Covariance Modelling, High-Dimensional Integrals, Newton-Raphson Method

Conflicts of Interest

The authors declare no conflicts of interest.

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