JSM 2004 - Toronto

Abstract #301126

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Activity Number: 233
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
Sponsor: General Methodology
Abstract - #301126
Title: Regression to Where?
Author(s): Amy B. Maddox*+ and John Seaman, Jr.
Companies: Baylor University and Baylor University
Address: PO Box 97328, Waco, TX, 76798,
Keywords: regression to the mean ; regression effect ; repeated measures model
Abstract:

This research concerns the point of regression for regression effect models. There has been extensive debate in the literature about the point of regression. Galton (1886) showed that, under the assumption of normality, the regression effect was to the mean. Over 100 years later, Das and Mulder (1983) claimed, under the assumption of a normal error term, that the regression effect is to the mode. We shall show that, under the assumption of normal errors, the regression effect is to the turning point(s) of the distribution of the measurements, g. If g is symmetric unimodal then that turning point coincides with the mean and regression to the mean occurs. If g is not symmetric but unimodal, then the turning point coincides with the mode and regression to the mode occurs. If g is bimodal, then regression to the three turning points of g occurs. Under non-normal errors regression need not be to the turning point(s) of g.

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