Misspecified maximum likelihood estimates and generalised linear mixed models

We investigate the impact of model violations on the estimate of a regressi on coefficient in a generalised linear mixed model. Specifically, we evalua te the asymptotic relative bias that results from incorrect assumptions reg arding the random effects. We compare the impact of model violation for two parameterisations of the regression model. Substantial bias in the conditi onally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depend s on measured covariates or there are autoregressive random effects. A marg inally specified regression structure that is estimated using maximum likel ihood is much less susceptible to bias resulting from random effects model misspecification.