TITLE:
Quasi-Monte Carlo Estimation in Generalized Linear Mixed Model with Correlated Random Effects
AUTHORS:
Yin Chen, Yu Fei, Jianxin Pan
KEYWORDS:
Generalized Linear Mixed Models, Correlated Random Effects, Quasi-Monte Carlo, Mean-Covariance Modelling, High-Dimensional Integrals, Newton-Raphson Method
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.10,
October
12,
2015
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.