Separation of individual-level and cluster-level covariate effects in regression analysis of correlated data

The focus of this paper is regression analysis of clustered data. Although the presence of intracluster correlation (the tendency for items within a cluster to respond alike) is typically viewed as an obstacle to good inference, the complex structure of clustered data offers significant analytic advantages over independent data. One key advantage is the ability to separate effects at the individual (or item-specific) level and the group (or cluster-specific) level. We review different approaches for the separation of individual-level and cluster-level effects on response, their appropriate interpretation and give recommendations for model fitting based on the intent of the data analyst. Unlike many earlier papers on this topic, we place particular emphasis on the interpretation of the cluster-level covariate effect. The main ideas of the paper are highlighted in an analysis of the relationship between birth weight and IQ using sibling data from a large birth cohort study.