Robust Analysis of Generalized Linear Mixed Models

Abstract

The method of maximum likelihood (ML) is widely used for analyzing generalized linear mixed models (GLMM's). A full maximum likelihood analysis requires numerical integration techniques for calculation of the log-likelihood, and to avoid the computational problems involving irreducibly high-dimensional integrals, several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log-likelihood function. Although these likelihood algorithms are useful for fitting the GLMM's efficiently under strict model assumptions, they can be highly influenced by the presence of unusual data points. In this article, the author develops a technique for finding robust maximum likelihood (RML) estimates of the model parameters in GLMM's, which appears to be useful in downweighting the influential data points when estimating the parameters. The asymptotic properties of the robust estimators are investigated under some regularity conditions. Small simulations are carried out to study the behavior of the robust estimates in the presence of outliers, and these estimates are also compared to the ordinary classical estimates. To avoid the computational problems involving high-dimensional integrals, the author proposes a robust Monte Carlo Newton–Raphson (RMCNR) algorithm for fitting GLMM's. The proposed robust method is illustrated in an analysis of data from a clinical experiment described in a biometrical journal.

KEY WORDS :

• Generalized linear models
• Metropolis algorithm
• Mixed models
• Newton-Raphson algorithm
• Robust estimation