A multinomial probit model with Choquet integral and attribute cut-offs. (April 2022) - Dubey, Subodh; Cats, Oded; Hoogendoorn, Serge; Bansal, Prateek
Highlights: Specified indirect utility in multinomial probit model using Choquet integral (CI). Modeled semi-compensatory choice behavior by specifying attribute cut-offs. Estimated the proposed model using a constrained maximum likelihood estimator. Validated statistical properties of the estimator in a Monte Carlo study. Showed advantages of the model in understanding New Yorkers' travel mode choices. Abstract: Several non-linear functions and machine learning methods have been developed for flexible specification of the systematic utility in discrete choice models. However, they lack interpretability, do not ensure monotonicity conditions, and restrict substitution patterns. We address the first two challenges by modeling the systematic utility using the Choquet Integral (CI) function and the last one by embedding CI into the multinomial probit (MNP) choice probability kernel. We also extend the MNP-CI model to account for attribute cut-offs that enable a modeler to approximately mimic the semi-compensatory behavior using the traditional choice experiment data. The MNP-CI model is estimated using a constrained maximum likelihood approach, and its statistical properties are validated through a comprehensive Monte Carlo study. The CI-based choice model is empirically advantageous as it captures interaction effects while maintaining monotonicity. It also provides information on the complementarity between pairs of attributes coupled with their importance ranking as a by-product of the estimation. These insights could potentially assist policymakers in making policies to improve the preference level for an alternative. These advantages of the MNP-CI model with attribute cut-offs are illustrated in an empirical application to understand New Yorkers' preferences towards mobility-on-demand services.