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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.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 5826.

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Length: 52 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:iza:izadps:dp5826

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Keywords: multinomial logit; IIA assumption; Hausman-McFadden test;

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  1. 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, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
  2. Small, Kenneth A., 1994. "Approximate generalized extreme value models of discrete choice," Journal of Econometrics, Elsevier, Elsevier, vol. 62(2), pages 351-382, June.
  3. McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, Elsevier, vol. 34(1-2), pages 63-82.
  4. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1251-71, November.
  5. Zheng, Xu, 2008. "Testing for discrete choice models," Economics Letters, Elsevier, Elsevier, vol. 98(2), pages 176-184, February.
  6. 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, Elsevier, vol. 30(1), pages 19-30, February.
  7. D. McFadden & J. Hausman, 1981. "Specification Tests for the Multinominal Logit Model," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 292, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. 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.
  9. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-27, October.
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