Effect of regression to the mean in the presence of within‐subject variability

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Abstract
Regression to the mean arises often in statistical applications where the units chosen for study relate to some observed characteristic in the extreme of its distribution. Gardner and Heady attribute the effect of regression to the mean to measurement errors. They assume the modelYi = U + ei, where U is a fixed within-subject component and ei is the random measurement error. They suggest several replicate measurements to reduce the regression effect under the assumption that the measurement errors ei are independent within subjects. While measurement errors play an important role in regression to the mean, one should not overlook within-subject variation. In this paper, we consider a model to estimate the regression effect in the presence of correlated within-subject effects as well as independent measurement errors.