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A Generalized Additive Model for Discrete-Choice Data

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  • Abe, Makoto

Abstract

The usual assumption of a linear-in-parameters utility function in a multinomial logit model is relaxed by a sum of one-dimensional nonparametric functions of the explanatory variables. The model generalizes the logistic regression of the generalized additive model for a binary response to a qualitative variable that can assume more than two values. Simulation studies show that the proposed method can recover underlying nonlinearity in utility of various shapes. The model is applied to consumer panel data collected by bar-code scanners from two product categories, and the marketing implications are sought.

Suggested Citation

  • Abe, Makoto, 1999. "A Generalized Additive Model for Discrete-Choice Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 271-284, July.
    • Handle: RePEc:bes:jnlbes:v:17:y:1999:i:3:p:271-84
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    Citations

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    Cited by:

    1. Sung, Ming-Chien & McDonald, David C.J. & Johnson, Johnnie E.V., 2016. "Probabilistic forecasting with discrete choice models: Evaluating predictions with pseudo-coefficients of determination," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1021-1030.
    2. De Bock, Koen W. & Coussement, Kristof & Van den Poel, Dirk, 2010. "Ensemble classification based on generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1535-1546, June.
    3. Steven Scott, 2011. "Data augmentation, frequentist estimation, and the Bayesian analysis of multinomial logit models," Statistical Papers, Springer, vol. 52(1), pages 87-109, February.
    4. Daisuke Fukuda & Tetsuo Yai, 2010. "Semiparametric specification of the utility function in a travel mode choice model," Transportation, Springer, vol. 37(2), pages 221-238, March.
    5. Hruschka, Harald & Fettes, Werner & Probst, Markus, 2004. "An empirical comparison of the validity of a neural net based multinomial logit choice model to alternative model specifications," European Journal of Operational Research, Elsevier, vol. 159(1), pages 166-180, November.
    6. Silvia Ferrini & Carlo Fezzi, 2012. "Generalized Additive Models for Nonmarket Valuation via Revealed or Stated Preference Methods," Land Economics, University of Wisconsin Press, vol. 88(4), pages 782-802.
    7. Schulz, Rainer & Watson, Verity & Wersing, Martin, 2023. "Teleworking and housing demand," Regional Science and Urban Economics, Elsevier, vol. 101(C).
    8. Roland Langrock & Nils-Bastian Heidenreich & Stefan Sperlich, 2014. "Kernel-based semiparametric multinomial logit modelling of political party preferences," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 435-449, August.
    9. Riccardo Scarpa & Cristiano Franceschinis & Mara Thiene, 2017. "A Monte Carlo Evaluation of the Logit-Mixed Logit under Asymmetry and Multimodality," Working Papers in Economics 17/23, University of Waikato.
    10. Abe, Makoto & Boztuæg, Yasemin & Hildebrandt, Lutz, 2000. "Investigation of the stochastic utility maximization process of consumer brand choice by semiparametric modeling," SFB 373 Discussion Papers 2000,84, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Guhl, Daniel & Baumgartner, Bernhard & Kneib, Thomas & Steiner, Winfried J., 2018. "Estimating time-varying parameters in brand choice models: A semiparametric approach," International Journal of Research in Marketing, Elsevier, vol. 35(3), pages 394-414.
    12. Bansal, Prateek & Daziano, Ricardo A. & Sunder, Naveen, 2019. "Arriving at a decision: A semi-parametric approach to institutional birth choice in India," Journal of choice modelling, Elsevier, vol. 31(C), pages 86-103.
    13. Sumanta Adhya & Tathagata Banerjee & Gaurangadeb Chattopadhyay, 2012. "Inference on finite population categorical response: nonparametric regression-based predictive approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 69-98, January.
    14. Bernhard Baumgartner & Daniel Guhl & Thomas Kneib & Winfried J. Steiner, 2018. "Flexible estimation of time-varying effects for frequently purchased retail goods: a modeling approach based on household panel data," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 837-873, October.
    15. Huang, J u-Chin & Nychka, Douglas W., 2000. "A nonparametric multiple choice method within the random utility framework," Journal of Econometrics, Elsevier, vol. 97(2), pages 207-225, August.
    16. Makoto Abe & Yasemin Boztug & Lutz Hildebrandt, 2004. "Investigating the competitive assumption of Multinomial Logit models of brand choice by nonparametric modeling," Computational Statistics, Springer, vol. 19(4), pages 635-657, December.
    17. Harald Hruschka, 2007. "Using a heterogeneous multinomial probit model with a neural net extension to model brand choice," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(2), pages 113-127.
    18. Sifringer, Brian & Lurkin, Virginie & Alahi, Alexandre, 2020. "Enhancing discrete choice models with representation learning," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 236-261.
    19. Elrod, Terry & Johnson, Richard D. & White, Joan, 2004. "A new integrated model of noncompensatory and compensatory decision strategies," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 1-19, September.
    20. Baumgartner, Bernhard & Hruschka, Harald, 2005. "Allocation of catalogs to collective customers based on semiparametric response models," European Journal of Operational Research, Elsevier, vol. 162(3), pages 839-849, May.
    21. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.

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