Entropy models with entropy constraints on aggregated events

Most spatial models deal with a number of objects, such as segments of demand, as well as supply choices including houses, jobs, transport modes or routes, etc. A choice of or by any of these objects represents a probabilistic event (decision step). The problem is to determine the joint probability density for the collection of events. In this paper, the joint probability function is estimated using an extended entropy model, constrained by additional information on the entropy of aggregated events. The resulting models are compared with existing formulations, based either on entropy maximization or on utility maximization. It is also shown that models which are used for predicting demand can be generalized to allow for the dependence of demand on supply, allowing for nonhomogeneous zonal supply and supply - demand imbalances.