Maximum Likelihood Estimation of Destination Choice Models with Constrained Attractions

• Published in: Transportation research record Vol. 2677; no. 5; pp. 760 - 776
• Main Author: Gibb, John
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.05.2023
• Subjects: planning and analysis; destination choice models
• ISSN: 0361-1981; 2169-4052
• DOI: 10.1177/03611981221136136

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 Cramér-Rao bounds. Experiments demonstrate its computational tractability and performance, and compare its estimations with those of unconstrained and other methods.