Pseudo-$R^2$ statistics under complex sampling
Methodology
2017-01-27 v1
Abstract
Model summaries based on the ratio of fitted and null likelihoods have been proposed for generalised linear models, reducing to the familiar coefficient of determination in the Gaussian model with identity link. In this note I show how to define the Cox--Snell and Nagelkerke summaries under arbitrary probability sampling designs, giving a design-consistent estimator of the population model summary. I also show that for logistic regression models under case--control sampling the usual Cox--Snell and Nagelkerke are not design-consistent, but are systematically larger than would be obtained with a cross-sectional or cohort sample, even in settings where the weighted and unweighted logistic regression estimators are similar or identical.
Cite
@article{arxiv.1701.07745,
title = {Pseudo-$R^2$ statistics under complex sampling},
author = {Thomas Lumley},
journal= {arXiv preprint arXiv:1701.07745},
year = {2017}
}