Some Considerations about Mode Choice Model

This paper discusses the representability of discrete logit-type models including multinomial logit and nested logit model from a mathematical approach. It is shown that the logit-type models can be reconstructed from mathematical approximation theory with sigmoidal functions widely used in Neural Network modeling without the basic assumptions such as IIA and iid, and the distribution (or density) function of the unobserved portion of utility. This explains mathematically why logit-type models can approximate the choice probability function to some accuracy. It is hoped that this may suggest the way to improve the accuracy in model specification for logit type models. 2