A doubly-differentiable bounded choice model: formulation and application to three large-scale case studies

Abstract

Most choice models assign non-zero probabilities to all alternatives. However, decision-makers may not consider many alternatives due to their high cost. The Bounded Choice Model (BCM) accounts for this by assigning zero probabilities to alternatives with costs exceeding some bound, thus determining a subset of alternatives individuals consider using a consistent criterion with the choice from this consideration set. The BCM is, however, non-differentiable, which prevents calculating parameter estimates’ standard errors.

In this paper, we develop a doubly differentiable BCM, the C 2 BCM. Likelihood derivatives and Hessian matrices of the C 2 BCM are derived analytically, enabling the calculation of the model estimates’ covariance matrix and elasticities. The C 2 BCM is estimated and benchmarked with the Multinomial Logit and BCM in large-scale mode choice and route choice case studies. The C 2 BCM provides a richer interpretation and analysis than the MNL and BCM while providing the best fit in both datasets.