Title

A Useful Interpretation of R2; in Binary Choice Models (Or, Have We Dismissed the Good Old R2; Prematurely)

Author(s)

Reuben Gronau Reuben Gronau (Princeton University)

Abstract

The discreditation of the Linear Probability Model (LPM) has led to the dismissal of the standard R2 as a measure of goodness-of-fit in binary choice models. It is argued that as a descriptive tool the standard R2 is still superior to the measures currently in use. In the LPM model R2 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 R2 and the sample proportion P one can calculate the conditional means, P0 and P1. 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 R2 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 P1-P0 .

Creation Date

1998-02

Section URL ID

IRS

Paper Number

397

URL

https://dataspace.princeton.edu/bitstream/88435/dsp01x346d4172/1/397.pdf

File Function

Jel

F17

Keyword(s)

binary variable, qualitative choice, arithmetic mean

Suppress

false

Series

1