Between- and Within-Cluster Covariate Effects in the Analysis of Clustered Data

Standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between- and within-cluster covariate effects. Implicit in these analyses is the assumption that these effects are identical. Example data show that this is frequently not the case and that analyses that ignore differential between- and within-cluster covariate effects can be misleading. Consideration of between- and within-cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods. In particular, we show that conditional likelihood methods estimate purely within-cluster covariate effects, whereas mixture model approaches estimate a weighted average of between- and within-cluster covariate effects.