Johnson W D, George V T
Department of Biometry and Genetics, Louisiana State University Medical Center, New Orleans 70112-1393.
Stat Med. 1991 Aug;10(8):1295-302. doi: 10.1002/sim.4780100812.
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 model Yi = 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.
均值回归在统计应用中经常出现，其中选择用于研究的单位与分布极端情况下的某些观测特征相关。加德纳和希迪将均值回归的影响归因于测量误差。他们假设模型Yi = U + ei，其中U是受试者内部的固定成分，ei是随机测量误差。他们建议进行多次重复测量，以在测量误差ei在受试者内部相互独立的假设下减少回归效应。虽然测量误差在均值回归中起着重要作用，但不应忽视受试者内部的变异。在本文中，我们考虑一个模型，用于在存在相关的受试者内部效应以及独立测量误差的情况下估计回归效应。
