McCulloch, C.E. (1994) Maximum Likelihood Variance Components Estimation for Binary Data. Journal of the American Statistical Association, 89, 330-335.
http://dx.doi.org/10.1080/01621459.1994.10476474

has been cited by the following article:

• 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.