Properties of R(2) statistics for logistic regression.

Abstract:

:Various R(2) statistics have been proposed for logistic regression to quantify the extent to which the binary response can be predicted by a given logistic regression model and covariates. We study the asymptotic properties of three popular variance-based R(2) statistics. We find that two variance-based R(2) statistics, the sum of squares and the squared Pearson correlation, have identical asymptotic distribution whereas the third one, Gini's concentration measure, has a different asymptotic behaviour and may overstate the predictivity of the model and covariates when the model is mis-specified. Our result not only provides a theoretical basis for the findings in previous empirical and numerical work, but also leads to asymptotic confidence intervals. Statistical variability can then be taken into account when assessing the predictive value of a logistic regression model.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Hu B,Palta M,Shao J

doi

10.1002/sim.2300

subject

Has Abstract

pub_date

2006-04-30 00:00:00

pages

1383-95

issue

8

eissn

0277-6715

issn

1097-0258

journal_volume

25

pub_type

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