A New Measure of Coefficient of Determination for Regression Models

• Activity Number: 431
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Chun Li*+
• Companies: Vanderbilt University
• Keywords: coefficient of determination ; goodness of fit ; regression models

Abstract

Coefficient of determination is a measure of the goodness of fit for a model. Best known as $R^2$ for continuous outcomes, its extensions to other outcome types often are less appealing. We propose a new coefficient of determination as a correlation between observed values and fitted distributions, taking into account the variation in the latter. It is intuitive, easy to interpret, and is identical to $R^2$ for ordinary least squares, thus giving $R^2$ a new interpretation as a correlation. We present the measure for continuous (both ordinary and weighted least squares), count, binary, ordinal, and time-to-event outcomes, describe its properties, and compare it with existing definitions of coefficient of determination.