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Robust estimation in generalized linear mixed models
Author(s) -
Yau Kelvin K. W.,
Kuk Anthony Y. C.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00327
Subject(s) - generalized linear mixed model , mathematics , estimator , maximum likelihood , m estimator , generalized linear model , residual , restricted maximum likelihood , statistics , algorithm
Generalized linear mixed models (GLMMs) are widely used to analyse non‐normal response data with extra‐variation, but non‐robust estimators are still routinely used. We propose robust methods for maximum quasi‐likelihood and residual maximum quasi‐likelihood estimation to limit the influence of outlying observations in GLMMs. The estimation procedure parallels the development of robust estimation methods in linear mixed models, but with adjustments in the dependent variable and the variance component. The methods proposed are applied to three data sets and a comparison is made with the nonparametric maximum likelihood approach. When applied to a set of epileptic seizure data, the methods proposed have the desired effect of limiting the influence of outlying observations on the parameter estimates. Simulation shows that one of the residual maximum quasi‐likelihood proposals has a smaller bias than those of the other estimation methods. We further discuss the equivalence of two GLMM formulations when the response variable follows an exponential family. Their extensions to robust GLMMs and their comparative advantages in modelling are described. Some possible modifications of the robust GLMM estimation methods are given to provide further flexibility for applying the method.