Behavioral Foundations of Spatial Interaction Models

Abstract

This chapter gives an overviewof the content of the book. The book deals with a new approach to logit type discrete choice probability models – for transportation networks in particular. The models are derived from a new definition of cost-minimizing behavior – the likelihood of a sample is decreasing as a function of average cost. The formal definitions are given in Chap. 4: Definition 1 (multinomial logit model) and Definition 4 (general logit model). The results for the multinomial logit model and the general logit model are obtained in Propositions 1 and 3 respectively. All logit type choice probability functions satisfy the new definition. The new definition is in Part I applied to networks with constant link costs. It is shown that the simple (multinomial) logit model exhibits cost-minimizing behavior. Furthermore cost-minimizing behavior implies the logit model. A number of standard logit models are derived – stochastic route choice model, multi-attribute discrete choice model, gravity model and the general logit model. New structured logit models, different from the standard nested logit model, are obtained. A welfare measure based on cost and a measure of freedom of choice is given. The new welfare measure is shown to be identical with composite cost. The presence of cost-minimizing behavior in an observed data set can be investigated by using the property that the likelihood is decreasing as a function of average cost. This is used in constructing a graphical test for cost-minimizing behavior. In Part II of the book the new definition of cost-minimizing behavior is extended to the case of volume dependent separable link costs. Here equilibrium is studied. Cost-minimizing behavior implies that the most probable trip patterns are user equilibria. The most probable flow patterns are approximately obtained by solving the optimization problem obtained by relaxing the integer constraints and replacing the cumulative cost function with the Beckmann integral.Models are derived for route choice, combined choice of origin, destination and route as well as combined choice of origin, destination, mode and route.