2002/08/01 by Alfred DeMaris, ALFRED DeMARIS · 144 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Econometrics #Economics #Estimator #Forecasting Techniques and Applications #Linear regression #Logistic regression #Mathematics #Ordinary least squares #Regression analysis #Statistics #Variance (accounting)
paper · doi:10.1177/0049124102031001002
published in Sociological Methods & Research 31(1), 27-74 (SAGE Publishing)
openalex publication_date 2002/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
R² is widely relied on in linear regression to index a model's discriminatory power. Many counterparts have been proposed for use in logistic regression, but no single measure is consistently used. Two potential criterion values are relevant: the explained variance in the latent scale underlying the binary indicator of event occurrence and the explained risk of the event itself. In this study, Monte Carlo methods were used to examine the performance, with respect to fixed theoretical levels of explained variance and explained risk, of eight R² analogues. The McKelvey-Zavoina measure appears to be best at estimating explained variance and either the sample-estimated explained risk or the ordinary least squares R² to be best at indexing explained risk. Other measures appear to be poor choices, primarily because asymptotic trends suggest they may be inconsistent estimators of the relevant criterion.