The effect of misspecifying the random effects distribution in linear mixed models for longitudinal data

Abstract

Abstract Maximum likelihood estimators for fixed effects and variance components in linear mixed models, obtained under the assumption of normally distributed random effects, are shown to be consistent and asymptotically normally distributed, even when the random-effects distribution is not normal. However, a sandwich-type correction to the inverse Fisher information matrix is then needed in order to get the correct asymptotic covariance matrix. Extensive simulations show that the so-obtained corrected standard errors are clearly superior to the naive uncorrected ones, especially for the parameters in the random-effects covariance matrix, even in moderate samples.