Choice probabilities of random utility maximization models when the errors distribution is a polynomial copula with Gumbel marginals

ABSTRACT

The expression of the choice probabilities of RUM models in which the utility errors distribution is a polynomial copula with Gumbel marginals is derived. In particular, it is shown that the expression of the Choice Probability Generating Function can be easily obtained from the polynomial copula of the distribution. This result is particularized for two types of polynomial copulas: the multivariate Farlie–Gumbel–Morgenstern copulas and the Baker's copulas. The correlation coefficient of the errors with these copulas is also obtained. The corresponding RUM models may account for relatively large negative and positive correlation. The RUM models introduced in this work are applied to two samples of interurban trips with three alternatives: airplane, rail and car. The results of the fit show that the models presented in this work may account for the correct correlation sign between the alternative errors and yield a better fit than a nested logit model.

Keywords:

• RUM theory
• discrete choice
• closed-form choice probability
• choice probability generating function
• copula

Acknowledgments

The author gratefully thanks Daisuke Fukuda, Associate Professor at the Department of Civil and Environmental Engineering of the Tokyo Institute of Technology, for providing and allowing the use of the interurban trips samples.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research has been supported by the Research Project TRA2015-65503 of the Spanish Ministry of Economy and Competitiveness.