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Biometrika 2002 89(2):401-409; doi:10.1093/biomet/89.2.401
© 2002 by Biometrika Trust
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A type of restricted maximum likelihood estimator of variance components in generalised linear mixed models

J.G. Liao1 and Stuart R.Lipsitz2

1 Division of Biometrics, University of Medicine and Dentistry of New Jersey, 335 George Street, Suite 2200, New Brunswick, New Jersey 08903, U.S.A.jg_liao@yahoo.com 2 Department of Biometry and Epidemiology, Medical University of South Carolina, 135 Rutledge Avenue, Suite 1148, Charleston, South Carolina 29425, U.S.A. lipsitzs@musc.edu

The maximum likelihood estimator of the variance components in a linear model can be biased downwards.Restricted maximum likelihood (REML) corrects this problem by using the likelihood of a set of residual contrasts and is generally considered superior. However, this original restricted maximum likelihood definition does not directly extend beyond linear models. We propose a REML-type estimator for generalised linear mixed models by correcting the bias in the profile score function of the variance components. The proposed estimator has the same consistency properties as the maximum likelihood estimator if the number of parameters in the mean and variance components models remains fixed. However, the estimator of the variance components has a smaller finite sample bias. A simulation study with a logistic mixed model shows that the proposed estimator is effective in correcting the downward bias in the maximum likelihood estimator.

Key Words: Bias correction; EM algorithm; Logistic mixed model

Received July 2000. Revised September 2001


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