Coefficients of determination for multiple logistic regression analysis

Coefficients of determination for continuous predicted values (R-2 analogs) in logistic regression are examined for their conceptual and mathematical similarity to the familiar R-2 statistic from ordinary least squares regression, and compared to coefficients of determination for discrete predicted values (indexes of predictive efficiency). An example motivated by substantive concerns and using empirical data from a national household probability sample is presented to illustrate the behavior of the different coefficients of determination in the evaluation of models including dependent variables with different base rates-that is, different proportions of cases or observations with positive outcomes. One R-2 analog appears to be preferable to the others both in terms of conceptual similarity to the ordinary least squares coefficient of determination, and in terms of its relative independence from the base rate. In addition, base rate should also be considered when selecting an index of predictive efficiency. As expected, the conclusions based on R-2 analogs are not necessarily consistent with conclusions based on predictive efficiency, with respect to which of several outcomes is better predicted by a given model.