Between-and within-cluster covariate effects and model misspecification in the analysis of clustered data

We consider the analysis of clustered data using linear mixed effects models and generalized estimating equations, where covariates can be decomposed into betweenand within-cluster components. Under the false assumption of equal betweenand within-cluster covariate effects, we simultaneously study the asymptotic behavior of the estimators for regression coefficients, intra-cluster correlation and residual error variance. This provides a more complete assessment of the effect of such model misspecification than is currently available in the literature. We then apply the results to gain insights into the effects of confounding and measurement error. Key findings include the structure of bias when both cohort and period effect confounding are present, quantification of the attenuation effect of measurement error, effects of measurement error of some covariates on the estimation of coefficients of error-free covariates, and consistent estimation in the presence of measurement error. The results are extended to allow different cluster sizes, and three longitudinal data sets are used for illustrative purposes.