Discrete choice theory, information theory and the multinomial logit and gravity models

The strong "similarity" between "information minimizing" and "utility maximizing" models of spatial interaction has been known for some time (see Anas 1975, Williams, 1977), but the extent of this "similarity" has been underestimated. This paper proves that the two approaches are identical in that the multinomial logit model can be derived and identically estimated by either method. It is also proved that the doubly-constrained gravity model derived by Wilson (1967) is identical to a multinomial logit model of joint origin-destination choice, consistent with stochastic utility maximization. It follows that behaviorally valid "gravity models" can be estimated from disaggregated data on individual choices. In closure, "behavioral demand modeling", which follows McFadden (1973), and "entropy-maximizing modeling", which follows Wilson (1967), should be seen as two equivalent views of the same problem. The behavioral content of models estimated by either approach is entirely determined by the model specification and data aggregation beliefs of the analysts, and not by any inherent structural property of the models themselves.