A type of restricted maximum likelihood estimator of variance components in generalised linear mixed models

Jiangang (Jason) Liao, Stuart R. Lipsitz

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)401-409
Number of pages9
JournalBiometrika
Volume89
Issue number2
DOIs
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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