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Predictive accuracy and explained variation
Author(s) -
Schemper Michael
Publication year - 2003
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1486
Subject(s) - covariate , statistics , regression , variation (astronomy) , econometrics , regression analysis , polytomous rasch model , computer science , mathematics , psychometrics , item response theory , physics , astrophysics
Measures of the predictive accuracy of regression models quantify the extent to which covariates determine an individual outcome. Explained variation measures the relative gains in predictive accuracy when prediction based on covariates replaces unconditional prediction. A unified concept of predictive accuracy and explained variation based on the absolute prediction error is presented for models with continuous, binary, polytomous and survival outcomes. The measures are given both in a model‐based formulation and in a formulation directly contrasting observed and expected outcomes. Various aspects of application are demonstrated by examples from three forms of regression models. It is emphasized that the likely degree of absolute or relative predictive accuracy often is low even if there are highly significant and relatively strong covariates. Copyright © 2003 John Wiley & Sons, Ltd.