Maximum Likelihood Estimation of Destination Choice Models with Constrained Attractions

Attraction constraints are common and often appropriate for destination choice models, including, but not limited to, doubly constrained gravity distribution models. Estimation of their parameters by discrete-choice methods, however, seldom accounts for the constraints, despite bias known from their omission. For multinomial logit destination choice, this paper first formulates the parameter estimation for maximum likelihood of a set of observations, subject to exogenous attraction constraints on the model's application to a population. Second, this formulation is extended for attraction constraints being linear combinations of size variables with coefficients to be estimated. Both the utility and size parameter estimations are distinct from the well-known formulation for unconstrained estimation, because of the contribution of the constraining shadow-price utilities to the likelihood gradients. Gradients and the Hessian are identified, along with adaptations of them for Newton-Raphson parameter updates and Cramer-Rao bounds. Experiments demonstrate its computational tractability and performance, and compare its estimations with those of unconstrained and other methods.