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Biometrika 2001 88(4):973-985; doi:10.1093/biomet/88.4.973
© 2001 by Biometrika Trust
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Misspecified maximum likelihood estimates and generalised linear mixed models

Patrick J.Heagerty1 and Brenda F.Kurland1

1 Department of Biostatistics, University of Washington, Seattle, Washington 98195, U.S.Aheagerty{at}u.washington.edukurland{at}u.washington.edu

We investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model. Specifically, we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects. We compare the impact of model violation for two parameterisations of the regression model.Substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects. A marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification.

Key Words: Marginal model; Quasilikelihood; Random effects; Variance estimation

Received December 1999. Revised May 2001


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