Misspecified maximum likelihood estimates and generalised linear mixed models

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.