Diagnostics in some Discrete Choice Models

Discrete choice models form a class of models widely used in econometrics for modelling the individual choice from a finite set of alternatives. The most widely used model is the multinomial logit model, implicitly assuming independence of irrelevant alternatives. A generalization is the nested multinomial logit model, relaxing this strong assurnp tion. Viewing both models as nonlinear regression models a set of diagnostics is derived. This includes a hat matrix, measures of leverage, influence and residuals and an approximation to the parameters for case deletion. In an example for the multinomid logit model a good performance of these diagnostics is observed and the parameter approximation by the proposed formula is better than a one step Newton-Raphson procedure. In an example for the nested logit model a constructed outlier with high influence is revealed by the measures of leverage and residual, but the parameter approximation is insufficient.