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Biostatistics 3:347-360 (2002)
© 2002 Oxford University Press

A Monte Carlo EM algorithm for generalized linear mixed models with flexible random effects distribution

Junliang Chen, Daowen Zhang* and Marie Davidian

Department of Statistics, Box 8203, North Carolina State University, Raleigh, NC 27695-8203, USA jchen2{at}stat.ncsu.edu

*To whom correspondence should be addressed

A popular way to represent clustered binary, count, or other data is via the generalized linear mixed model framework, which accommodates correlation through incorporation of random effects. A standard assumption is that the random effects follow a parametric family such as the normal distribution; however, this may be unrealistic or too restrictive to represent the data. We relax this assumption and require only that the distribution of random effects belong to a class of ‘smooth’ densities and approximate the density by the seminonparametric (SNP) approach of Gallant and Nychka (1987). This representation allows the density to be skewed, multi-modal, fat- or thin-tailed relative to the normal and includes the normal as a special case. Because an efficient algorithm to sample from an SNP density is available, we propose a Monte Carlo EM algorithm using a rejection sampling scheme to estimate the fixed parameters of the linear predictor, variance components and the SNP density. The approach is illustrated by application to a data set and via simulation.

Keywords: Correlated data; Rejection sampling; Seminonparametric density; Semiparametric mixed model


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