Generating a Percent Reduction in Error (PRE) Statistic using Stata

A common measure of model fit for logit and probit is the Percent Reduction in Error (PRE) statistic (Hagle and Mitchell 1992):



where, PCP = percent correctly predicted and PMC = percent in modal category of the dependent variable. The logic behind this statistic is intuitively pleasing as it compares the percentage of cases the independent variables predicted correctly to the percentage of cases that would have been correctly predicted if the researcher adopted a naïve model that only used the central tendency of the dependent variable to make predictions.

Stata does not include this measure in its standard output of logit and probit results, nor does it include a table that overlays predicted values of the dependent variable with observed values of the dependent variable from which this statistic could be calculated. To remedy this, I have programmed the command -pred-, which generates such a table and displays the percent correctly predicted, percent modal category, and percent reduction in error statistics.


References

Hagle, Timoth M. and Glen E. Mitchell, II. 1992. "Goodness-of–Fit Measures for Probit and Logit." American Journal of Political Science, 36(3): 762-84.