Summarizing the predictive power of a generalized linear model

Statistics in MedicineVolume 19, Issue 13 p. 1771-1781 Research Article Summarizing the predictive power of a generalized linear model Beiyao Zheng, Corresponding Author Beiyao Zheng bzheng@wfubmc.edu Wake Forest University School of Medicine, Department of Public Health Sciences, Medical Center Boulevard, Winston-Salem, NC 27157-1051, U.S.A.Wake Forest University School of Medicine, Department of Public Health Sciences, Medical Center Boulevard, Winston-Salem, NC 27157-1051, U.S.A.Search for more papers by this authorAlan Agresti, Alan Agresti Department of Statistics, University of Florida, Gainesville, FL 32611-8545, U.S.A.Search for more papers by this author Beiyao Zheng, Corresponding Author Beiyao Zheng bzheng@wfubmc.edu Wake Forest University School of Medicine, Department of Public Health Sciences, Medical Center Boulevard, Winston-Salem, NC 27157-1051, U.S.A.Wake Forest University School of Medicine, Department of Public Health Sciences, Medical Center Boulevard, Winston-Salem, NC 27157-1051, U.S.A.Search for more papers by this authorAlan Agresti, Alan Agresti Department of Statistics, University of Florida, Gainesville, FL 32611-8545, U.S.A.Search for more papers by this author First published: 14 June 2000 https://doi.org/10.1002/1097-0258(20000715)19:13<1771::AID-SIM485>3.0.CO;2-PCitations: 185AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This paper studies summary measures of the predictive power of a generalized linear model, paying special attention to a generalization of the multiple correlation coefficient from ordinary linear regression. The population value is the correlation between the response and its conditional expectation given the predictors, and the sample value is the correlation between the observed response and the model predicted value. We compare four estimators of the measure in terms of bias, mean squared error and behaviour in the presence of overparameterization. The sample estimator and a jack-knife estimator usually behave adequately, but a cross-validation estimator has a large negative bias with large mean squared error. One can use bootstrap methods to construct confidence intervals for the population value of the correlation measure and to estimate the degree to which a model selection procedure may provide an overly optimistic measure of the actual predictive power. Copyright © 2000 John Wiley & Sons, Ltd. Citing Literature Volume19, Issue1315 July 2000Pages 1771-1781 RelatedInformation