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Parameter estimation in multivariate logit models with many binary choices

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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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    1. Paulo Guimarães & Octávio Figueirdo & Douglas Woodward, 2003. "A Tractable Approach to the Firm Location Decision Problem," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 201-204, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. Harald Hruschka, 2022. "Analyzing joint brand purchases by conditional restricted Boltzmann machines," Review of Managerial Science, Springer, vol. 16(4), pages 1117-1145, May.
    7. 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.
    8. Fok, D. & Paap, R., 2019. "New Misspecification Tests for Multinomial Logit Models," Econometric Institute Research Papers EI2019-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. 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.
    10. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    11. Sierminska, Eva & Oaxaca, Ronald L., 2022. "Gender differences in economics PhD field specializations with correlated choices," Labour Economics, Elsevier, vol. 79(C).
    12. 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.
    13. 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.
    14. 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.
    15. repec:ags:aaea22:335456 is not listed on IDEAS
    16. 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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