Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01x346d4172
 Title: A Useful Interpretation of R-Squared in Binary Choice Models (Or, Have We Dismissed the Good Old R-Squared; Prematurely) Authors: Gronau, Reuben Keywords: binary variablequalitative choicearithmetic mean Issue Date: 1-Feb-1998 Series/Report no.: Working Papers (Princeton University. Industrial Relations Section) ; 397 Abstract: The discreditation of the Linear Probability Model (LPM) has led to the dismissal of the standard $$R^{2}$$ as a measure of goodness-of-ﬁt in binary choice models. It is argued that as a descriptive tool the standard $$R^{2}$$ is still superior to the measures currently in use. In the LPM model $$R^{2}$$ has a simple interpretation: it equals the difference between the average predicted probability in the two groups. It also measures the fraction of the explained part of the variance (SSR) due to the difference between the conditional means (SSB). Given $$R^{2}$$ and the sample proportion $$P$$ one can calculate the conditional means, $$\bar{P}_{0}$$ and $$\bar{P}_{1}$$. This interpretation still holds for non-linear cases when $$R$$ is computed as the regression coefﬁcient of the predicted value on the dependent binary variable: However, even if other deﬁnitions of $$R^{2}$$ are used in this case (e. g., the share of the variance explained by the regression, or the correlation coefficient between true and predicted values), the measure is very close to $$\bar{P}_{1} - \bar{P}_{0}$$. URI: http://arks.princeton.edu/ark:/88435/dsp01x346d4172 Appears in Collections: IRS Working Papers