Cluster-level Correlated Error Variance and the Estimation of Parameters in Linear Mixed Models

Abstract

Multilevel theory is extended primarily through the evaluation of cross-level effects, or how some between-cluster predictor explains a within-cluster outcome. Cross-level effects are often estimated using linear mixed models (LMMs). LMMs are susceptible to a bias from correlated error variance, resulting from omitted predictors and correlated error variance or common method variance. The effects of correlated error variance are well known in linear regression, but are relatively less understood in LMMs, an extension of LMM. The current study extends previous research on correlated error variance on cross-level effect LMM parameter estimation by applying a tracing rule methodology to demonstrate the mathematical structure of the bias produced by correlated error variance. The current study shows that bias is mainly produced by omitted variable-between-cluster predictor relationships paired with common method variance in the between-cluster predictor. In particular, both parameters can produce attenuation or accentuation of parameter estimates, depending on the magnitude and direction of the effects. The