A Partial Coefficient of Determination for Generalized Linear Models

• Activity Number: 50
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: ENAR
• Author(s): Sundar Natarajan*+ and Stuart R. Lipsitz
• Companies: NYU School of Medicine and the VA New York Harbor Healthcare System and Medical University of South Carolina
• Keywords: generalized linear models ; partial correlation

Abstract

In a regression setting, the partial coefficient of determination is used as a measure of "standardized" partial association between an outcome and a covariate given all other covariates. In ordinary least squares linear regression with y as the response, the estimated partial coefficient of determination between y and x_K is the difference in the coefficient of determination for a regression model with covariates [x_1,...,x_{K-1},x_K] and a regression model with covariates [x_1,...,x_{K-1}]. For generalized linear models (GLM), no definition of partial coefficients of determination can be found in the literature. Zheng and Agresti (2000) propose a coefficient of determination for GLM, which is the squared correlation between the observed and fitted outcomes. Analogous to linear regression, we propose a partial coefficient of determination between y and x_K, which is the difference in the coefficients of determination for GLM with and without x_K. The bootstrap will be used to obtain confidence intervals for this new partial coefficient. To illustrate the method, we use a study evaluating racial differences in control of risk factors in diabetes.