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


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.

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Chen, Y. , Fei, Y. and Pan, J. (2015) Quasi-Monte Carlo Estimation in Generalized Linear Mixed Model with Correlated Random Effects. Open Access Library Journal, 2, 1-16. doi: 10.4236/oalib.1102002.

Conflicts of Interest

The authors declare no conflicts of interest.


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