Testing for IIA with the Hausman-Mcfadden Test

(2011) - Wim Vijverberg

Journal: SSRN Electronic Journal
Link:: https://www.ssrn.com/abstract=1882845
DOI:: 10.2139/ssrn.1882845
Links::
Tags:: #paper #Methods #IrrelevantAlternatives #Hausman-Mcfadden #MLogit
Cite Key:: [@vijverbergTestingIIAHausmanMcfadden2011]

Abstract

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 χ 2 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 χ 2 distribution.

Notes

“The Independence of Irrelevant Alternatives assumption inherent in multinomial logit models is most frequently tested with a Hausman-McFadden test.” (Vijverberg, 2011, p. 0)

“Multinomial logit models are valid under the Independence of Irrelevant Alternatives (IIA) assumption that states that characteristics of one particular choice alternative do not impact the relative probabilities of choosing other alternatives.” (Vijverberg, 2011, p. 1)

“One test was devised by Hausman and McFadden (1984) as a variation of the Hausman (1978) test. It relies on the insight that (i ) under IIA, the parameters of the choice among a subset of alternatives may be estimated with a multinomial logit model on just this subset or on the full set, though the former is less efficient than the latter, and (ii ) if IIA is not true, the parameter estimates of the full set are inconsistent, whereas those of the subset are consistent provided that the subset is properly selected.” (Vijverberg, 2011, p. 1)

“The frequent occurrence of these negative values has unappreciated consequences. In this paper, I contend that ̃ H is a test statistic with poor properties that, compounded by errors in inference that are due to its common implementation, has put a significant body of empirical research at risk. However, a better version of the HM test is readily available.” (Vijverberg, 2011, p. 2)

“The simulation and analytical results presented in this paper provide convincing evidence that the distribution of the traditional implementation of the HM test through ̃ H deviates greatly from the asymptotic χ2 distribution” (Vijverberg, 2011, p. 28)