Abstract

Abstract This chapter deals with models which combine ordinary regression and within-cluster correlation. The development closely parallels the combination of linear regression and ANOVA into the analysis of covariance (ANCOVA). Our focus is on settings with large numbers of clusters, or clusters being a random sample from a population, and so parsimonious description of (adjusted) between-cluster differences is a relevant issue. The principal difference between ANCOVA and our approach is in the role of the levels of the factor (clusters). In ANCOVA the effects associated with each cluster are unknown constants (they are fixed), in the random-effects approach, which we refer to as random-effects analysis of covariance, they are random.

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