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Estimating Proportion of Explained Variation for an Underlying Linear Model using Logistic Regression Analysis

 

D. Sharma and D. McGee (2008). Estimating Proportion of Explained Variation for an Underlying Linear Model using Logistic Regression Analysis. Journal of Statistical Research, Vol. 42, No. 1, pp.  59-69.

 

Abstract

Eight $ R^2 $ type statistics proposed to use in logistics regression analysis are evaluated based upon their ability to predict the proportion of explained variation $ (\rho^2) $ for an underlying linear model with latent scale continuous dependent variable. Functional relationships between these statistics are also studied. Predictive quality of these statistics depends mainly upon the proportion of success in the sample and $ \rho^2, $ the quantity to be predicted. We found $ R^2_{CS} $ (Hagle and Mitchell (1992)) to be numerically closest to the underlying $ \rho^2. $ There is a one-to-one correspondence between the likelihood based $ R^2 $ statistics, some of which have been considered independent until recently.

 

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