In a binary logit analysis with unequal sample frequencies of the twooutcomes the less frequent outcome always has lower estimatedprediction probabilities than the other one. This effect is unavoidable,and its extent varies inversely with the fit of the model, as given by anew measure that...

The discrete outcome of a probability model is recordedas Y(i)=1 while otherwise Y(i)=0. y is the vector of observedoutcomes, p the corresponding probabilities, p^a consistent estimate of p, and residuals are defined ase = y - p^. Under quite general conditions, theasymptotic properties of p^...