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Parameter estimation in multivariate logit models with many binary choices

Author

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  • Koen Bel
  • Dennis Fok
  • Richard Paap

Abstract

Multivariate Logit models are convenient to describe multivariate correlated binary choices as they provide closed-form likelihood functions. However, the computation time required for calculating choice probabilities increases exponentially with the number of choices, which makes maximum likelihood-based estimation infeasible when many choices are considered. To solve this, we propose three novel estimation methods: (i) stratified importance sampling, (ii) composite conditional likelihood (CCL), and (iii) generalized method of moments, which yield consistent estimates and still have similar small-sample bias to maximum likelihood. Our simulation study shows that computation times for CCL are much smaller and that its efficiency loss is small.

Suggested Citation

  • Koen Bel & Dennis Fok & Richard Paap, 2018. "Parameter estimation in multivariate logit models with many binary choices," Econometric Reviews, Taylor & Francis Journals, vol. 37(5), pages 534-550, May.
    • Handle: RePEc:taf:emetrv:v:37:y:2018:i:5:p:534-550
    DOI: 10.1080/07474938.2015.1093780
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    Cited by:

    1. Harald Hruschka, 2024. "Endogeneity of marketing variables in multicategory choice models," Journal of Business Economics, Springer, vol. 94(4), pages 639-657, May.
    2. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    3. Sumit Panja & Sayani Mukhopadhyay, 2024. "An investigation of small and marginal holder farmers’ adaptation strategies to climate variability and its determinants in coastal agriculture: evidence from east coast of India," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 29(3), pages 1-33, March.
    4. Qinan Lu & Xiaodong Du & Huanguang Qiu, 2022. "Adoption patterns and productivity impacts of agricultural mechanization services," Agricultural Economics, International Association of Agricultural Economists, vol. 53(5), pages 826-845, September.
    5. Bel, K. & Paap, R., 2014. "A Multivariate Model for Multinomial Choices," Econometric Institute Research Papers EI 2014-26, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Richards, Timothy J. & Hamilton, Stephen F. & Yonezawa, Koichi, 2018. "Retail Market Power in a Shopping Basket Model of Supermarket Competition," Journal of Retailing, Elsevier, vol. 94(3), pages 328-342.
    7. Ma, Wanglin & Zheng, Hongyun & Gong, Binlei, 2022. "Rural income growth, ethnic differences, and household cooking fuel choice: Evidence from China," Energy Economics, Elsevier, vol. 107(C).
    8. Harald Hruschka, 2022. "Analyzing joint brand purchases by conditional restricted Boltzmann machines," Review of Managerial Science, Springer, vol. 16(4), pages 1117-1145, May.
    9. Harald Hruschka, 2024. "Relevance of dynamic variables in multicategory choice models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(1), pages 109-133, March.
    10. Rodrigo Santos & Gonçalo Rodrigues Brás & Miguel Torres Preto, 2025. "Exploring Internal, Market and Institutional Dynamics That Drive Eco‐Innovation: Evidence From Portuguese Companies," Business Strategy and the Environment, Wiley Blackwell, vol. 34(8), pages 10925-10941, December.
    11. Lu, Qinan & Du, Xiaodong, 2020. "The Outsourcing Choice of Agricultural Production Tasks: Implications for Food Security - A Multiple-task Based Approach," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304333, Agricultural and Applied Economics Association.
    12. Neuhofer, Zachary T. & Lusk, Jayson L., 2023. "Impacts of Variety-Seeking, Substitution, and Demographics on Demand for Plant-Based Meat Alternatives," 2023 Annual Meeting, July 23-25, Washington D.C. 335456, Agricultural and Applied Economics Association.
    13. Fok, Dennis & Paap, Richard, 2025. "New misspecification tests for multinomial logit models," Journal of choice modelling, Elsevier, vol. 54(C).
    14. Valerie Kilders & Vincenzina Caputo & Jayson L. Lusk, 2024. "Consumer preferences for food away from home: Dine in versus delivery," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(2), pages 496-525, March.
    15. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    16. Sierminska, Eva & Oaxaca, Ronald L., 2022. "Gender differences in economics PhD field specializations with correlated choices," Labour Economics, Elsevier, vol. 79(C).
    17. Hruschka, Harald, 2025. "Multicategory choice modeling by recurrent neural nets," Journal of Retailing and Consumer Services, Elsevier, vol. 85(C).
    18. Steffen Jahn & Daniel Guhl & Ainslee Erhard, 2024. "Substitution Patterns and Price Response for Plant-Based Meat Alternatives," Rationality and Competition Discussion Paper Series 509, CRC TRR 190 Rationality and Competition.
    19. John D. Lowrey & Timothy J. Richards & Stephen F. Hamilton, 2023. "Food Donations, Retail Operations, and Retail Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 25(2), pages 792-810, March.
    20. Huong Hoang-Thi & Shah Fahad & Ashfaq Ahmad Shah & Tung Nguyen-Huu-Minh & Tuan Nguyen-Anh & Song Nguyen-Van & Nguyen To-The & Huong Nguyen-Thi-Lan, 2023. "Evaluating the farmers’ adoption behavior of water conservation in mountainous region Vietnam: extrinsic and intrinsic determinants," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 115(2), pages 1313-1330, January.
    21. Filippopoulou, Chryssanthi & Galariotis, Emilios & Spyrou, Spyros, 2020. "An early warning system for predicting systemic banking crises in the Eurozone: A logit regression approach," Journal of Economic Behavior & Organization, Elsevier, vol. 172(C), pages 344-363.
    22. Tobias Börger & Danny Campbell & Jürgen Meyerhoff & Malte Welling, 2026. "Preferences for Biodiversity-Promoting Private Garden Designs: A Basket-Based Choice Experiment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 89(1), pages 1-32, January.
    23. repec:ags:aaea22:335456 is not listed on IDEAS
    24. Caputo, Vincenzina & Lusk, Jayson L., 2022. "The Basket-Based Choice Experiment: A Method for Food Demand Policy Analysis," Food Policy, Elsevier, vol. 109(C).

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