Predictive performance of the binary logit model in unbalanced samples

In a binary logit analysis with unequal sample frequencies of the two outcomes the less frequent outcome always has tower estimated prediction probabilities than the other outcome. This effect is unavoidable, and its extent varies inversely with the fit of the model, as given by a new measure that follows naturally from the argument. Unbalanced samples with a poor fit are typical for survey analyses in the social sciences and epidemiology, and there the difference in prediction probabilities is most acute. It affects two common diagnostics: the within-sample 'percentage correctly predicted' and the identification of outliers. Partial remedies are suggested.