Unbiased Estimation of Destination Choice Models with Attraction Constraints

Availability, capacity or attraction constraints are common in the application of destination choice models, especially for work and school location choice models. These constraints can also be important to include in models of non-home-based trips to improve consistency with tours. Following traditional terminology of gravity models, these models are typically referred to as “doubly constrained.” However, while common in application, shadow prices (Lagrangian or similar penalty terms) which enforce the attraction constraints are rarely included in parameter estimation. It is known that this can lead to biased parameter estimates, but this is commonly ignored. This paper presents an empirical study of destination choice models developed for Iowa, using a genetic algorithm to develop parameter estimates with and without shadow prices to determine the significance of parameter bias in a practical application. The study shows that most parameters were biased by the omission of constraints in estimation, that this can lead to erroneous conclusion about the statistical significance of various parameters and that the model with constraints does fit the observed data significantly better than the unconstrained model. This both confirms the model with constraints is the proper specification and that omitting these constraints in estimation does lead to practical problems and significant specification bias.