Integrating a Pareto-Distributed Scale into the Mixed Logit Model: A Mathematical Concept

Author:

Ohdoko Taro1ORCID,Komatsu Satoru2ORCID

Affiliation:

1. Department of Economics on Sustainability, Faculty of Economics, Dokkyo University, 1-1, Gakuen-cho, Soka-shi 340-0042, Saitama, Japan

2. Graduate School of Global Humanities and Social Sciences, Nagasaki University, 1-14, Bunkyo-machi, Nagasaki-shi 852-8521, Nagasaki, Japan

Abstract

A generalized multinomial logit (G-MNL) model is proposed to alleviate the four challenges inherent to the conditional logit model, including (1) simultaneous unidentifiability, (2) the immediacy of decision-making, (3) the homogeneity of preferences in unobservable variables, and (4) the independence of irrelevant alternatives. However, the G-MNL model has some restrictions that are caused by the assumed logit scale of the lognormal distribution used in the G-MNL model. We propose a mixed logit with integrated Pareto-distributed scale (MIXL-iPS) model to address the restriction of the G-MNL model by introducing a logit scale in accordance with the Pareto distribution type I with an expected value of 1. We have clarified the mathematical properties and examined the distributional properties of the novel MIXL-iPS model. The results suggest that the MIXL-iPS model is a model in which the instability in the estimation of the G-MNL model is modified. Moreover, the apparent preference parameter was confirmed to have a skewed distribution in general in the MIXL-iPS model. In addition, we confirm that in the MIXL-iPS model, bounded rationality is reasonably well represented, as many individuals have below-average choice consistency.

Funder

JSPS KAKENHI

Japanese Science and Technology Agency

Japanese International Cooperation Agency

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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