Testing for IIA with the Hausman-McFadden Test
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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- Hausman, Jerry & McFadden, Daniel, 1984.
"Specification Tests for the Multinomial Logit Model,"
Econometric Society, vol. 52(5), pages 1219-1240, September.
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- McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
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Oxford Bulletin of Economics and Statistics,
Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
- Jurgen A Doornik & Henrik Hansen, "undated". "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford.
- Simon Cheng & J. Scott Long, 2007. "Testing for IIA in the Multinomial Logit Model," Sociological Methods & Research, , vol. 35(4), pages 583-600, May.
- 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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