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

Author

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  • Taro Ohdoko

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

  • Satoru Komatsu

    (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.

Suggested Citation

  • Taro Ohdoko & Satoru Komatsu, 2023. "Integrating a Pareto-Distributed Scale into the Mixed Logit Model: A Mathematical Concept," Mathematics, MDPI, vol. 11(23), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4727-:d:1285320
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