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Testing for IIA with the Hausman-McFadden Test

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  • Vijverberg, Wim P.

    () (CUNY Graduate Center)

Abstract

The Independence of Irrelevant Alternatives assumption inherent in multinomial logit models is most frequently tested with a Hausman-McFadden test. As is confirmed by many findings in the literature, this test sometimes produces negative outcomes, in contradiction of its asymptotic χ² distribution. This problem is caused by the use of an improper variance matrix and may lead to an invalid statistical inference even when the test value is positive. With a correct specification of the variance, the sampling distribution for small samples is indeed close to a χ² distribution.

Suggested Citation

  • Vijverberg, Wim P., 2011. "Testing for IIA with the Hausman-McFadden Test," IZA Discussion Papers 5826, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp5826
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    References listed on IDEAS

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    1. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    2. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 112-134.
    3. Simon Cheng & J. Scott Long, 2007. "Testing for IIA in the Multinomial Logit Model," Sociological Methods & Research, , vol. 35(4), pages 583-600, May.
    4. Zheng, Xu, 2008. "Testing for discrete choice models," Economics Letters, Elsevier, vol. 98(2), pages 176-184, February.
    5. Small, Kenneth A., 1994. "Approximate generalized extreme value models of discrete choice," Journal of Econometrics, Elsevier, vol. 62(2), pages 351-382, June.
    6. McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
    7. Small, Kenneth A & Hsiao, Cheng, 1985. "Multinomial Logit Specification Tests," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-627, October.
    8. Fry, Tim R. L. & Harris, Mark N., 1996. "A Monte Carlo study of tests for the independence of irrelevant alternatives property," Transportation Research Part B: Methodological, Elsevier, vol. 30(1), pages 19-30, February.
    9. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    10. Wim P. M. Vijverberg, 1993. "Educational Investments and Returns for Women and Men in Côte d'Ivoire," Journal of Human Resources, University of Wisconsin Press, vol. 28(4), pages 933-974.
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    Cited by:

    1. Zhelyazkova, N., 2014. "Discovering and explaining work-family strategies of parents in Luxembourg," MERIT Working Papers 022, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    2. Lewis, Justin S., 2016. "Maritime piracy confrontations across the globe: Can crew action shape the outcomes?," Marine Policy, Elsevier, vol. 64(C), pages 116-122.

    More about this item

    Keywords

    multinomial logit; IIA assumption; Hausman-McFadden test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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