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A Monte Carlo study of tests for the independence of irrelevant alternatives property

  • Fry, Tim R. L.
  • Harris, Mark N.

A plethora of tests for the Independence of Irrelevant Alternatives (IIA) property of Logit models of discrete choice behavior has been proposed in the literature. These tests are based upon asymptotic arguments and little is known about their size and power properties in finite samples. This paper uses a Monte Carlo simulation study to investigate the size and power properties of six tests for IIA in the multinomial Logit model. Our results show that the majority of tests based upon partitioning the choice set appear to have very poor size and power properties in small samples. Tests for IIA based upon the DOGIT model, similarly have poor size properties, but in some circumstances do have reasonable power properties.

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Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 30 (1996)
Issue (Month): 1 (February)
Pages: 19-30

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Handle: RePEc:eee:transb:v:30:y:1996:i:1:p:19-30
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  1. Gaundry, Marc J. I. & Dagenais, Marcel G., 1979. "The dogit model," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 105-111, June.
  2. Tse, Y K, 1989. "A Proportional Random Utility Approach to Qualitative Response Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 61-65, January.
  3. Tse, Y K, 1987. "A Diagnostic Test for the Multinomial Logit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 283-86, April.
  4. Gaudry, Marc J. I. & Wills, Michael J., 1979. "Testing the dogit model with aggregate time-series and cross-sectional travel data," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 155-166, June.
  5. D. McFadden & J. Hausman, 1981. "Specification Tests for the Multinominal Logit Model," Working papers 292, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Swait, Joffre & Ben-Akiva, Moshe, 1987. "Incorporating random constraints in discrete models of choice set generation," Transportation Research Part B: Methodological, Elsevier, vol. 21(2), pages 91-102, April.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, March.
  8. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  9. Marc J. I. Gaudry, 1980. "Dogit and Logit Models of Travel Mode Choice in Montreal," Canadian Journal of Economics, Canadian Economics Association, vol. 13(2), pages 268-79, May.
  10. Fry, T R L, et al, 1993. "Economic Motivations for Limited Dependent and Qualitative Variable Models," The Economic Record, The Economic Society of Australia, vol. 69(205), pages 193-205, June.
  11. Swait, Joffre & Ben-Akiva, Moshe, 1987. "Empirical test of a constrained choice discrete model: Mode choice in São Paulo, Brazil," Transportation Research Part B: Methodological, Elsevier, vol. 21(2), pages 103-115, April.
  12. 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 619-27, October.
  13. Bordley, Robert F., 1990. "The dogit model is applicable even without perfectly captive buyers," Transportation Research Part B: Methodological, Elsevier, vol. 24(4), pages 315-323, August.
  14. 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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