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 Medjournal_title
Statistics in medicineauthors
Hu B,Palta M,Shao Jdoi
10.1002/sim.2300subject
Has Abstractpub_date
2006-04-30 00:00:00pages
1383-95issue
8eissn
0277-6715issn
1097-0258journal_volume
25pub_type
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