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Estimating Nonlinear Parameters in the Multinomial Logit Model

Author

Listed:
  • Peter S. Fader

    (University of Pennsylvania)

  • James M. Lattin

    (Stanford University)

  • John D. C. Little

    (Massachusetts Institute of Technology)

Abstract

Multinomial logit models, especially those calibrated on scanner data, often use explanatory variables that are nonlinear functions of the parameters to be estimated. A common example is the smoothing constant in an exponentially weighted brand loyalty variable. Such parameters cannot be estimated directly using commercially available logit packages. We provide a simple iterative method for estimating nonlinear parameters at the same time as the usual linear coefficients. The procedure uses standard multinomial logit software and, in experience to date, converges rapidly. We prove that, under suitable conditions, the resulting parameter values are maximum likelihood estimates and show how to calculate asymptotic standard errors from normal computer output. Three applications illustrate the method in practice.

Suggested Citation

  • Peter S. Fader & James M. Lattin & John D. C. Little, 1992. "Estimating Nonlinear Parameters in the Multinomial Logit Model," Marketing Science, INFORMS, vol. 11(4), pages 372-385.
    • Handle: RePEc:inm:ormksc:v:11:y:1992:i:4:p:372-385
    DOI: 10.1287/mksc.11.4.372
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    Citations

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    Cited by:

    1. Jürgen Strohhecker & Michael Hamann & Jörn-Henrik Thun, 2016. "Loading and sequencing heuristics for job scheduling on two unrelated parallel machines with long, sequence-dependent set-up times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(22), pages 6747-6767, November.
    2. Roozbeh Irani-Kermani & Edward C. Jaenicke & Ardalan Mirshani, 2023. "Accommodating heterogeneity in brand loyalty estimation: application to the U.S. beer retail market," Journal of Marketing Analytics, Palgrave Macmillan, vol. 11(4), pages 820-835, December.
    3. Bernhard Baumgartner & Harald Hruschka, 2002. "Ein Discrete Choice-Modell zur Erklärung von Markentreue auf Grundlage von Theorien des Lernens und der wahrgenommenen Unsicherheit," Schmalenbach Journal of Business Research, Springer, vol. 54(4), pages 299-316, June.
    4. Boztuğ, Yasemin & Hildebrandt, Lutz, 1998. "Nicht- und semiparametrische Markenwahlmodelle im Marketing," SFB 373 Discussion Papers 1998,99, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Ngobo, Paul-Valentin & Legohérel, Patrick & Guéguen, Nicolas, 2010. "A cross-category investigation into the effects of nine-ending pricing on brand choice," Journal of Retailing and Consumer Services, Elsevier, vol. 17(5), pages 374-385.
    6. Irani-Kermani, Roozbeh & Jaenicke, Edward C., 2017. "Accommodating Heterogeneity in Brand Loyalty Estimation: Application to the U.S. Beer Retail," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258203, Agricultural and Applied Economics Association.
    7. Little, John D. C. & Anderson, Eric T., 1994. "A product choice model with marketing, filtering and purchase feedback," Working papers 3670-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Praveen K. Kopalle & Aradhna Krishna & João L. Assunção, 1999. "The role of market expansion on equilibrium bundling strategies," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 20(7), pages 365-377.
    9. Pierre Volle, 2001. "The Short-Term Effect of Store-Level Promotions on Store Choice and the Moderating Role of Individual Variables," Post-Print halshs-00164831, HAL.
    10. David R. Bell & James M. Lattin, 2000. "Looking for Loss Aversion in Scanner Panel Data: The Confounding Effect of Price Response Heterogeneity," Marketing Science, INFORMS, vol. 19(2), pages 185-200, May.
    11. J. Miguel Villas-Boas & Russell S. Winer, 1999. "Endogeneity in Brand Choice Models," Management Science, INFORMS, vol. 45(10), pages 1324-1338, October.
    12. Chen, Bo & Saghaian, Sayed, 2017. "Does Consumers’ Preference for Organic Foods Affect Their Store Format Choices?," 2017 Annual Meeting, February 4-7, 2017, Mobile, Alabama 252827, Southern Agricultural Economics Association.
    13. Moon, Sangkil & Voss, Glenn, 2009. "How do price range shoppers differ from reference price point shoppers?," Journal of Business Research, Elsevier, vol. 62(1), pages 31-38, January.
    14. Sergio Brasini & Marzia Freo & Giorgio Tassinari, 2005. "The effects of marketing activities on fast moving consumer good purchases : the case of yoghurt Italian market," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
    15. Byun, Kyung-Ah (Kay) & Duhan, Dale F. & Dass, Mayukh, 2020. "The preservation of loyalty halo effects: An investigation of the post-product-recall behavior of loyal customers," Journal of Business Research, Elsevier, vol. 116(C), pages 163-175.
    16. Volle, Pierre, 2001. "The short-term effect of store-level promotions on store choice, and the moderating role of individual variables," Journal of Business Research, Elsevier, vol. 53(2), pages 63-73, August.
    17. Praveen K. Kopalle & Carl F. Mela & Lawrence Marsh, 1999. "The Dynamic Effect of Discounting on Sales: Empirical Analysis and Normative Pricing Implications," Marketing Science, INFORMS, vol. 18(3), pages 317-332.
    18. Irani-Kermani, Roozbeh & Jaenicke, Edward C., 2018. "Generalizing Variety Seeking Measurement from Brand Space to Product Attribute Space," 2018 Annual Meeting, August 5-7, Washington, D.C. 273818, Agricultural and Applied Economics Association.

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