Evaluating Pseudo-R2's for binary probit models

Many applied researchers of limited dependent variable models found it disadvantageous that a widely accepted Pseudo-R2 does not exist for this type of estimation. The paper provides guidance for researchers in choosing a Pseudo-R2 in the binary probit case. The starting point is that R2 is best understood in the ordinary least squares (OLS) case with continuous data, which is chosen as the reference situation. It is considered which Pseudo-R2 is best able to mimic the OLS-R2. The results are surprisingly clear: a measure suggested by McKelvey-Zavoina performs the best under our criterion. However, in the more likely case of low Pseudo-R2's, a normalization of a measure proposed by Aldrich-Nelson which we suggest is almost as good as the McKelvey-Zavoina, and is in general easier to calculate. We also show that if the underlying R2 is predicted using cubic regressions given the Pseudo-R2, all measures perform much better.