Effect of regression to the mean in multivariate distributions

Estimating treatment effects in the presence of regression to the mean is a problem arising in truncated distributions that is being recognized with increasing interest in recent literature. As noted in a previous communication by the authors (1991), any extraneous source of variability such as within-subject variability and measurement errors can contribute to the magnitude of regression toward the mean. The main focus of this paper is consideration of a model for estimating treatment effects when truncation and regression to the mean occur on more than one random variable. This situation occurs often in investigations where subjects are selected for study because measurements on two characteristics of interest both exceed specified values.