On the overspecification of multinomial and nested logit models due to alternative specific constants

Discrete choice models as demand forecasting techniques have been used for transportation applications for more than thirty years. The multinomial and nested logit models are probably the most widely applied in this context. Alternative specific constants, although playing an important role in these models, have received very little attention in theoretical studies. In this paper, we try to fill this gap by providing an analysis of the overspecification caused by alternative specific constants to the log-likelihood function of multinomial and nested logit models. The theoretical results lead directly to a particular strategy of alternative specific constant specification, called here the orthogonal strategy. The analysis of the relationship between any two arbitrary strategies and the derivation of an interesting geometrical property of the orthogonal strategy provide a motivation to prefer the latter.