A Multinomial Probit Model with Choquet Integral and Attribute Cut-offs

TL;DR

This paper introduces a novel multinomial probit model using the Choquet Integral to improve interpretability and flexibility in discrete choice analysis, incorporating attribute cut-offs for semi-compensatory behavior, validated through simulations and an application to mobility preferences.

Contribution

It develops a new MNP-CI model with attribute cut-offs, enhancing interpretability, capturing attribute interactions, and providing policy-relevant insights in choice modeling.

Findings

The MNP-CI model captures attribute interactions effectively.

It maintains monotonicity and interpretability in utility specification.

Empirical application reveals insights into mobility preferences.

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 modelling 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 modeller to approximately mimic the semi-compensatory behaviour 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.