Goodness-of-Fit Measures for Probit and Logit

Some regression analysts find the R2 statistic to be of little utility. Others use it extensively while evaluating model performance. One of the shortcomings of probit and logit analyses is the lack of an analog to the Ordinary Least Squares (OLS) R2 statistic. To aid in the evaluation of model performance, several pseudo-R2s have been proposed. Dichotomizing a continuous interval-level variable results in distortions due to a loss of information. We do not know, however, the degree to which these distortions affect the pseudo-R2s vis-a-vis the OLS R2 that is based on the underlying continuous dependent variable. In this study we use simulation techniques to compare four common pseudo-R2s for probit and logit with the R2 that would be obtained under OLS regression. After making a correction to one of the measures, two of them perform quite well, comparing favorably with the OLS R2. The choice between them may be simply a matter of availability and ease of use.