IDEAS home Printed from https://ideas.repec.org/a/inm/ormksc/v29y2010i3p393-421.html
   My bibliography  Save this article

The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity

Author

Listed:
  • Denzil G. Fiebig

    (School of Economics, University of New South Wales, Sydney, New South Wales 2052, Australia)

  • Michael P. Keane

    (University of Technology Sydney, Sydney, New South Wales 2007; and Arizona State University, Tempe, Arizona 85287)

  • Jordan Louviere

    (School of Marketing, Centre for the Study of Choice, University of Technology Sydney, Sydney, New South Wales 2007, Australia)

  • Nada Wasi

    (School of Finance and Economics, Centre for the Study of Choice, University of Technology Sydney, Sydney, New South Wales 2007, Australia)

Abstract

The mixed or heterogeneous multinomial logit (MIXL) model has become popular in a number of fields, especially marketing, health economics, and industrial organization. In most applications of the model, the vector of consumer utility weights on product attributes is assumed to have a multivariate normal (MVN) distribution in the population. Thus, some consumers care more about some attributes than others, and the IIA property of multinomial logit (MNL) is avoided (i.e., segments of consumers will tend to switch among the subset of brands that possess their most valued attributes). The MIXL model is also appealing because it is relatively easy to estimate. Recently, however, some researchers have argued that the MVN is a poor choice for modelling taste heterogeneity. They argue that much of the heterogeneity in attribute weights is accounted for by a pure scale effect (i.e., across consumers, all attribute weights are scaled up or down in tandem). This implies that choice behaviour is simply more random for some consumers than others (i.e., holding attribute coefficients fixed, the scale of their error term is greater). This leads to a “scale heterogeneity” MNL model (S-MNL). Here, we develop a generalized multinomial logit model (G-MNL) that nests S-MNL and MIXL. By estimating the S-MNL, MIXL, and G-MNL models on 10 data sets, we provide evidence on their relative performance. We find that models that account for scale heterogeneity (i.e., G-MNL or S-MNL) are preferred to MIXL by the Bayes and consistent Akaike information criteria in all 10 data sets. Accounting for scale heterogeneity enables one to account for “extreme” consumers who exhibit nearly lexicographic preferences, as well as consumers who exhibit very “random” behaviour (in a sense we formalize below).

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormksc:v:29:y:2010:i:3:p:393-421
    DOI: 10.1287/mksc.1090.0508
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mksc.1090.0508
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mksc.1090.0508?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Robert Bartels & Denzil Fiebig & Arthur Soest, 2006. "Consumers and experts: an econometric analysis of the demand for water heaters," Empirical Economics, Springer, vol. 31(2), pages 369-391, June.
    2. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    3. Keane, Michael & Moffitt, Robert, 1998. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 553-589, August.
    4. 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.
    5. Hanming Fang & Michael P. Keane & Dan Silverman, 2008. "Sources of Advantageous Selection: Evidence from the Medigap Insurance Market," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 303-350, April.
    6. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    7. Cameron, Trudy Ann, 1988. "A new paradigm for valuing non-market goods using referendum data: Maximum likelihood estimation by censored logistic regression," Journal of Environmental Economics and Management, Elsevier, vol. 15(3), pages 355-379, September.
    8. Garrett Sonnier & Andrew Ainslie & Thomas Otter, 2007. "Heterogeneity distributions of willingness-to-pay in choice models," Quantitative Marketing and Economics (QME), Springer, vol. 5(3), pages 313-331, 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. Harris, Katherine M. & Keane, Michael P., 1998. "A model of health plan choice:: Inferring preferences and perceptions from a combination of revealed preference and attitudinal data," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 131-157, November.
    11. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    12. Kenneth A. Small & Clifford Winston & Jia Yan, 2005. "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability," Econometrica, Econometric Society, vol. 73(4), pages 1367-1382, July.
    13. W. Michael Hanemann, 1984. "Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(3), pages 332-341.
    14. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
    15. Hall, Jane & Fiebig, Denzil G. & King, Madeleine T. & Hossain, Ishrat & Louviere, Jordan J., 2006. "What influences participation in genetic carrier testing?: Results from a discrete choice experiment," Journal of Health Economics, Elsevier, vol. 25(3), pages 520-537, May.
    16. Cameron, Trudy Ann & Poe, Gregory L. & Ethier, Robert G. & Schulze, William D., 2002. "Alternative Non-market Value-Elicitation Methods: Are the Underlying Preferences the Same?," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 391-425, November.
    17. Elrod, Terry & Keane, Michael, 1995. "A Factor-Analytic Probit Model for Representing the Market Structure in Panel Data," MPRA Paper 52434, University Library of Munich, Germany.
    18. Allenby, Greg M. & Rossi, Peter E., 1998. "Marketing models of consumer heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 57-78, November.
    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. Michael P. Keane & Nada Wasi, 2013. "The Structure of Consumer Taste Heterogeneity in Revealed vs. Stated Preference Data," Economics Papers 2013-W10, Economics Group, Nuffield College, University of Oxford.
    2. Keane, Michael P. & Wasi, Nada, 2016. "How to model consumer heterogeneity? Lessons from three case studies on SP and RP data," Research in Economics, Elsevier, vol. 70(2), pages 197-231.
    3. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, September.
    4. Michael P. Keane, 2013. "Panel data discrete choice models of consumer demand," Economics Papers 2013-W08, Economics Group, Nuffield College, University of Oxford.
    5. Keane, Michael & Ketcham, Jonathan & Kuminoff, Nicolai & Neal, Timothy, 2021. "Evaluating consumers’ choices of Medicare Part D plans: A study in behavioral welfare economics," Journal of Econometrics, Elsevier, vol. 222(1), pages 107-140.
    6. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
    7. Siikamaki, Juha & Layton, David F., 2007. "Discrete choice survey experiments: A comparison using flexible methods," Journal of Environmental Economics and Management, Elsevier, vol. 53(1), pages 122-139, January.
    8. Victoria Prowse, 2012. "Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 411-431, April.
    9. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    10. Vij, Akshay & Krueger, Rico, 2017. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 76-101.
    11. Balcombe, Kelvin & Chalak, Ali & Fraser, Iain, 2009. "Model selection for the mixed logit with Bayesian estimation," Journal of Environmental Economics and Management, Elsevier, vol. 57(2), pages 226-237, March.
    12. Robert J. Johnston & Kevin J. Boyle & Wiktor (Vic) Adamowicz & Jeff Bennett & Roy Brouwer & Trudy Ann Cameron & W. Michael Hanemann & Nick Hanley & Mandy Ryan & Riccardo Scarpa & Roger Tourangeau & Ch, 2017. "Contemporary Guidance for Stated Preference Studies," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 4(2), pages 319-405.
    13. Arne Hole & Julie Kolstad, 2012. "Mixed logit estimation of willingness to pay distributions: a comparison of models in preference and WTP space using data from a health-related choice experiment," Empirical Economics, Springer, vol. 42(2), pages 445-469, April.
    14. Arouna, Aminou & Adegbola, Patrice Y. & Raphael, Babatunde & Diagne, Aliou, 2015. "Contract farming preferences by smallholder rice producers in Africa: a stated choice model using mixed logic," 2015 Conference, August 9-14, 2015, Milan, Italy 210957, International Association of Agricultural Economists.
    15. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    16. Fiebig, Denzil G. & Haas, Marion & Hossain, Ishrat & Street, Deborah J. & Viney, Rosalie, 2009. "Decisions about Pap tests: What influences women and providers?," Social Science & Medicine, Elsevier, vol. 68(10), pages 1766-1774, May.
    17. Richard T. Carson, 2011. "Contingent Valuation," Books, Edward Elgar Publishing, number 2489.
    18. Jose Blandon & Spencer Henson & Towhidul Islam, 2009. "Marketing preferences of small-scale farmers in the context of new agrifood systems: a stated choice model," Agribusiness, John Wiley & Sons, Ltd., vol. 25(2), pages 251-267.
    19. Gebreegziabher, Z. & Mekonnen, A. & Beyene, A.D. & Hagos, F., 2018. "Valuation of access to irrigation water in rural Ethiopia: application of choice experiment and contingent valuation methods," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277168, International Association of Agricultural Economists.

    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:inm:ormksc:v:29:y:2010:i:3:p:393-421. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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: Matthew Walls (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.