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Testing for Independence of Irrelevant Alternatives

Author

Listed:
  • TIM R. L. FRY

    (Monash University)

  • MARK N. HARRIS

    (University of Melbourne)

Abstract

In a recent article, Zhang and Hoffman discuss the use of discrete choice logit models in sociological research. In the present article, the authors estimate a multinomial logit model of U.K. Magistrates Courts sentencing using a data set collected by the National Association for the Care and Resettlement of Offenders (NACRO) and test the independence of irrelevant alternatives (IIA) property using six tests. Conducting the tests with the appropriate large sample critical values, the authors find that the acceptance or rejection of IIA depends both on which test and which variant of a given test is used. The authors then use simulation techniques to assess the size and power performance of the tests. The empirical example is revisited with the inferences performed using empirical critical values obtained by simulation, and the resultant inferences are compared. The results show that empirical workers should exercise caution when testing for IIA.

Suggested Citation

  • Tim R. L. Fry & Mark N. Harris, 1998. "Testing for Independence of Irrelevant Alternatives," Sociological Methods & Research, , vol. 26(3), pages 401-423, February.
    • Handle: RePEc:sae:somere:v:26:y:1998:i:3:p:401-423
    DOI: 10.1177/0049124198026003005
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    References listed on IDEAS

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    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    2. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    4. T.R.L. Fry & R.D. Brooks & Br. Comley & J. Zhang, 1993. "Economic Motivations for Limited Dependent and Qualitative Variable Models," The Economic Record, The Economic Society of Australia, vol. 69(2), pages 193-205, June.
    5. 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.
    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, vol. 30(1), pages 19-30, February.
    7. Tse, Y K, 1987. "A Diagnostic Test for the Multinomial Logit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 283-286, April.
    8. Horowitz, Joel, 1981. "Identification and diagnosis of specification errors in the multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 15(5), pages 345-360, October.
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    Cited by:

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    2. Arjun Seshadri & Johan Ugander, 2020. "Fundamental Limits of Testing the Independence of Irrelevant Alternatives in Discrete Choice," Papers 2001.07042, arXiv.org.
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    12. Curtis, John & McCoy, Daire & Aravena Novielli, Claudia, 2017. "Determinants of residential heating system choice: an analysis of Irish households," Papers WP576, Economic and Social Research Institute (ESRI).
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