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The Logit Model And Response-Based Samples

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  • XIE, Y.
  • MANSKI, C.F.

Abstract

It is well-known that, under the logit model for binary response, the random sampling and response-based sampling maximum likelihood estimators coincide for all parameters except the intercept. Citing this coincidence, many researchers have assumed the logit model and analyzed data from response-based samples as if those data were obtained by random sampling. We argue that this practice should be avoided unless the researcher really believes the logit specification. One preferable alternative is the weighted maximum likelihood estimator of Manski and Lerman (1977). Random sampling maximum likelihood analysis does not have a natural interpretation when the true response function is not logit. Weighted maximum likelihood analysis estimates a constrained best predictor of the binary response and so remains interpretable.
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Suggested Citation

  • Xie, Y. & Manski, C.F., 1988. "The Logit Model And Response-Based Samples," Working papers 8811, Wisconsin Madison - Social Systems.
    • Handle: RePEc:att:wimass:8811
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    References listed on IDEAS

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    1. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    2. Manski, Charles F. & Thompson, T. Scott, 1989. "Estimation of best predictors of binary response," Journal of Econometrics, Elsevier, vol. 40(1), pages 97-123, January.
    3. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, vol. 31(1), pages 31-40, February.
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    1. Xie, Xian-Jin & Pendergast, Jane & Clarke, William, 2008. "Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2703-2713, January.
    2. Maalouf, Maher & Trafalis, Theodore B., 2011. "Robust weighted kernel logistic regression in imbalanced and rare events data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 168-183, January.
    3. Sung Jae Jun & Sokbae Lee, 2024. "Causal Inference Under Outcome-Based Sampling with Monotonicity Assumptions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 998-1009, July.
    4. Matthew Roskruge & Jacques Poot & Laura King, 2016. "Social capital, entrepreneurship and living standards: differences between migrants and the native born," Chapters, in: Hans Westlund & Johan P. Larsson (ed.), Handbook of Social Capital and Regional Development, chapter 9, pages 221-254, Edward Elgar Publishing.
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    6. Tao Xu, 2022. "The Effect of Health Change on Long-Term Settlement Intentions of International Immigrants in New Destination Countries: Evidence from Yiwu City in China," IJERPH, MDPI, vol. 19(13), pages 1-18, June.
    7. J. S. Cramer, 2004. "Scoring bank loans that may go wrong: a case study," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 365-380, August.
    8. Yossi Perelman & Meir Yaish & Benjamin Bental, 2019. "The price of religiosity: Enticing young Haredi men into secular academic studies," Rationality and Society, , vol. 31(2), pages 129-151, May.
    9. Kroneberg, Clemens & Stocké, Volker & Yaish, Meir, 2006. "Norms or rationality? : The rescue of jews, electoral participation, and educational decisions," Papers 06-09, Sonderforschungsbreich 504.
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    11. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    12. Pamela Giustinelli, 2016. "Group Decision Making With Uncertain Outcomes: Unpacking Child–Parent Choice Of The High School Track," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(2), pages 573-602, May.
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    14. Duarte Trigueiros, 2019. "Improving the effectiveness of predictors in accounting-based models," Journal of Applied Accounting Research, Emerald Group Publishing Limited, vol. 20(2), pages 207-226, June.
    15. Tran Thu & Moritaka Masahiro & Liu Ran & Fukuda Susumu, 2018. "Information effect on consumer adoption for a new beef brand in the Vietnamese market: prior knowledge, appealing the brand distinction, differentiation and similarity," Management & Marketing, Sciendo, vol. 13(3), pages 1014-1034, September.
    16. Sung Jae Jun & Sokbae (Simon) Lee, 2020. "Causal inference in case-control studies," CeMMAP working papers CWP19/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Vairetti, Carla & Gennaro, Franco & Maldonado, Sebastián, 2024. "Propensity score oversampling and matching for uplift modeling," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1058-1069.
    18. Alastair Scott & Chris Wild, 2002. "On the robustness of weighted methods for fitting models to case–control data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 207-219, May.
    19. Jensen, Paul H. & Palangkaraya, Alfons & Webster, Elizabeth, 2015. "Trust and the market for technology," Research Policy, Elsevier, vol. 44(2), pages 340-356.
    20. Clemens Kroneberg & Meir Yaish & Volker Stocké, 2010. "Norms and Rationality in Electoral Participation and in the Rescue of Jews in WWII," Rationality and Society, , vol. 22(1), pages 3-36, February.
    21. Ahmed, M.S. & Attouch, M.K. & Dabo-Niang, S., 2018. "Binary functional linear models under choice-based sampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 134-152.
    22. Christopher Paul & William Mason & Daniel McCaffrey & Sarah Fox, 2008. "A cautionary case study of approaches to the treatment of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 351-372, July.
    23. Stock, Ruth Maria & von Hippel, Eric & Gillert, Nils Lennart, 2016. "Impacts of personality traits on consumer innovation success," Research Policy, Elsevier, vol. 45(4), pages 757-769.
    24. Jian Chen & Jin Xiang & Tyler T. Yang, 2018. "Re-Default Risk of Modified Mortgages," International Real Estate Review, Global Social Science Institute, vol. 21(1), pages 1-40.
    25. Federico Varese & Meir Yaish, 2000. "The Importance Of Being Asked," Rationality and Society, , vol. 12(3), pages 307-334, August.

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