Robustness of the linear mixed model to misspecified error distribution

A simulation study is performed to investigate the robustness of the maximum likelihood estimator of fixed effects from a linear mixed model when the error distribution is misspecified. Inference for the fixed effects under the assumption of independent normally distributed errors with constant variance is shown to be robust when the errors are either non-gaussian or heteroscedastic, except when the error variance depends on a covariate included in the model with interaction with time. Inference is impaired when the errors are correlated. In the latter case, the model including a random slope in addition to the random intercept is more robust than the random intercept model. The use of Cholesky residuals and conditional residuals to evaluate the fit of a linear mixed model is also discussed.