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...

In a discrete model, the predicted probabilities of a particular eventcan be matched to the observed (0, I) outcomes and this will give riseto a measure of fit for that event. Previous results for the binomialmodel are applied to multinomial models. In these models the measureof fit will vary...

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^...

A bank employs logistic regression with state-dependent sample selection to identify loans thatmay go wrong. Inspection shows that the logit model is inappropriate. A bounded logit model witha ceiling of (far) less than 1 fits the data much better.