A Monte Carlo EM Algorithm for Generalized Linear Mixed Models with Flexible Random Effects Distribution
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2001-11-07
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Abstract
A popular way to model correlated binary, count, or other data arising inclinical trials and epidemiological studies of cancer and other diseases is byusing generalized linear mixed models (GLMMs), which acknowledge correlationthrough incorporation of random effects. A standard model assumption is thatthe random effects follow a parametric family such as the normal distribution.However, this may be unrealistic or too restrictive to represent the data,raising concern over the validity of inferences both on fixed and random effects if it is violated.Here we use the seminonparametric (SNP) approach (Davidian and Gallant 1992,1993) to model the random effects, which relaxes the normality assumption andjust requires that the distribution of random effects belong to a class of`"smooth'' densities given by Gallant and Nychka (1987). This representation allows the density of random effects to be very flexible, including densitiesthat are skewed, multi--modal, fat-- or thin--tailed relative to the normal, andthe normal as a special case. We also provide a reparameterization of this representation to avoid numerical instability in estimating the polynomialcoefficients. Because an efficient algorithm to sample from a SNP density is available, wepropose a Monte Carlo expectation maximization (MCEM) algorithm using arejection sampling scheme (Booth and Hobert, 1999) to estimate the fixedparameters of the linear predictor, variance components and the SNP density. Astrategy of choosing the degree of flexibility required for the SNP density isalso proposed. We illustrate the methods by application to two data sets fromthe Framingham and Six Cities Studies, and present simulations demonstratingperformance of the approach.
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Degree
PhD
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Statistics
