IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4727-d1285320.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4727/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4727/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Grebitus Carola & Roosen Jutta & Seitz Carolin Claudia, 2015. "Visual Attention and Choice: A Behavioral Economics Perspective on Food Decisions," Journal of Agricultural & Food Industrial Organization, De Gruyter, vol. 13(1), pages 73-81, January.
    2. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    3. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    4. Hess, Stephane & Train, Kenneth, 2017. "Correlation and scale in mixed logit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 1-8.
    5. DeShazo, J. R. & Fermo, German, 2002. "Designing Choice Sets for Stated Preference Methods: The Effects of Complexity on Choice Consistency," Journal of Environmental Economics and Management, Elsevier, vol. 44(1), pages 123-143, July.
    6. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    7. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    8. Hensher,David A. & Rose,John M. & Greene,William H., 2015. "Applied Choice Analysis," Cambridge Books, Cambridge University Press, number 9781107465923, September.
    9. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    10. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    11. Uggeldahl, Kennet & Jacobsen, Catrine & Lundhede, Thomas Hedemark & Olsen, Søren Bøye, 2016. "Choice certainty in Discrete Choice Experiments: Will eye tracking provide useful measures?," Journal of choice modelling, Elsevier, vol. 20(C), pages 35-48.
    12. Denzil G. Fiebig & Michael P. Keane & Jordan Louviere & Nada Wasi, 2010. "The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity," Marketing Science, INFORMS, vol. 29(3), pages 393-421, 05-06.
    13. A. Dallas, 1976. "Characterizing the pareto and power distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 491-497, December.
    14. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
    15. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
    16. Ruckdeschel, Peter & Kohl, Matthias, 2014. "General Purpose Convolution Algorithm in S4 Classes by Means of FFT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i04).
    17. Andrew Daly & Stephane Hess & Kenneth Train, 2012. "Assuring finite moments for willingness to pay in random coefficient models," Transportation, Springer, vol. 39(1), pages 19-31, January.
    18. William Greene & David Hensher, 2010. "Does scale heterogeneity across individuals matter? An empirical assessment of alternative logit models," Transportation, Springer, vol. 37(3), pages 413-428, May.
    19. Mariel, Petr & Artabe, Alaitz, 2020. "Interpreting correlated random parameters in choice experiments," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    20. Ryan Webb, 2019. "The (Neural) Dynamics of Stochastic Choice," Management Science, INFORMS, vol. 65(1), pages 230-255, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    2. Kassie, Girma T. & Zeleke, Fresenbet & Birhanu, Mulugeta Y. & Scarpa, Riccardo, 2020. "Reminder Nudge, Attribute Nonattendance, and Willingness to Pay in a Discrete Choice Experiment," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304208, Agricultural and Applied Economics Association.
    3. Ge, Ge & Godager, Geir, 2021. "Predicting strategic medical choices: An application of a quantal response equilibrium choice model," Journal of choice modelling, Elsevier, vol. 39(C).
    4. Ahtiainen, Heini & Tienhaara, Annika & Pouta, Eija & Czajkowski, Mikolaj, 2017. "Role of information in the valuation of unfamiliar goods – the case of genetic resources in agriculture," 2017 International Congress, August 28-September 1, 2017, Parma, Italy 261423, European Association of Agricultural Economists.
    5. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    6. Mariel, Petr & Meyerhoff, Jürgen, 2018. "A More Flexible Model or Simply More Effort? On the Use of Correlated Random Parameters in Applied Choice Studies," Ecological Economics, Elsevier, vol. 154(C), pages 419-429.
    7. Hess, Stephane & Train, Kenneth, 2017. "Correlation and scale in mixed logit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 1-8.
    8. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    9. Carson, Richard T. & Czajkowski, Mikołaj, 2019. "A new baseline model for estimating willingness to pay from discrete choice models," Journal of Environmental Economics and Management, Elsevier, vol. 95(C), pages 57-61.
    10. Kettlewell, Nathan & Walker, Matthew J. & Yoo, Hong Il, 2024. "Alternative Models of Preference Heterogeneity for Elicited Choice Probabilities," IZA Discussion Papers 16821, Institute of Labor Economics (IZA).
    11. Alves, Maria Odete & Valente, Airton Saboya Jr, 2006. "Comunicação Rural Entre Três Atores Nas Áreas De Concentração De Fruteiras No Nordeste Brasileiro:," 44th Congress, July 23-27, 2006, Fortaleza, Ceará, Brazil 148515, Sociedade Brasileira de Economia, Administracao e Sociologia Rural (SOBER).
    12. Kaambwa, Billingsley & Lancsar, Emily & McCaffrey, Nicola & Chen, Gang & Gill, Liz & Cameron, Ian D. & Crotty, Maria & Ratcliffe, Julie, 2015. "Investigating consumers' and informal carers' views and preferences for consumer directed care: A discrete choice experiment," Social Science & Medicine, Elsevier, vol. 140(C), pages 81-94.
    13. Hoyos, David, 2010. "The state of the art of environmental valuation with discrete choice experiments," Ecological Economics, Elsevier, vol. 69(8), pages 1595-1603, June.
    14. West, Grant H. & Snell, Heather & Kovacs, Kent & Nayga, Rodolfo M., 2020. "Estimation of the preferences for the intertemporal services from groundwater," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304220, Agricultural and Applied Economics Association.
    15. Shr, Yau-Huo & Ready, Richard C. & Orland, Brian & Echols, Stuart, 2017. "Do Visual Representations Influence Survey Responses? Evidence from a Choice Experiment on Landscape Attributes of Green Infrastructure," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258397, Agricultural and Applied Economics Association.
    16. Maaya, Leonard & Meulders, Michel & Vandebroek, Martina, 2021. "Joint analysis of preferences and drop out data in discrete choice experiments," Journal of choice modelling, Elsevier, vol. 41(C).
    17. Rocha, Luiz Eduardo Vasconcelos & Santos, Gilnei Costa & Bastos, Patricia de Melo Abrita, 2006. "Evolução Da Distribuição Da Renda E Da Pobreza Das Famílias Ocupadas E Residentes No Meio Rural Do Estado De Minas Gerais, De 1981 A 2003," 44th Congress, July 23-27, 2006, Fortaleza, Ceará, Brazil 148649, Sociedade Brasileira de Economia, Administracao e Sociologia Rural (SOBER).
    18. Mariel, Petr & Artabe, Alaitz, 2020. "Interpreting correlated random parameters in choice experiments," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    19. John C. Whitehead & Daniel K. Lew, 2020. "Estimating recreation benefits through joint estimation of revealed and stated preference discrete choice data," Empirical Economics, Springer, vol. 58(4), pages 2009-2029, April.
    20. Leite, Sheila Cristina Ferreira & De Figueiredo, Margarida Garcia, 2006. "Fluxos De Algodão Em Pluma Para Exportação No Estado Da Bahia: Uma Aplicação De Programação Linear," 44th Congress, July 23-27, 2006, Fortaleza, Ceará, Brazil 149116, Sociedade Brasileira de Economia, Administracao e Sociologia Rural (SOBER).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4727-:d:1285320. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.