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Statistica Sinica 16(2006), 847-860





PSEUDO- $\mbox{\boldmath $R^2$}$ IN LOGISTIC REGRESSION MODEL


Bo Hu, Jun Shao and Mari Palta


University of Wisconsin-Madison


Abstract: Logistic regression with binary and multinomial outcomes is commonly used, and researchers have long searched for an interpretable measure of the strength of a particular logistic model. This article describes the large sample properties of some pseudo-$R^2$ statistics for assessing the predictive strength of the logistic regression model. We present theoretical results regarding the convergence and asymptotic normality of pseudo-$R^2$s. Simulation results and an example are also presented. The behavior of the pseudo-$R^2$s is investigated numerically across a range of conditions to aid in practical interpretation.



Key words and phrases: Entropy, logistic regression, pseudo-$R^2$

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