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Identification of parameters in normal error component logit-mixture (NECLM) models

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Author Info

  • Joan L. Walker

    (Department of Geography and Environment, Boston University, Boston, Massachusetts, USA)

  • Moshe Ben-Akiva

    (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA)

  • Denis Bolduc

    (Département d'économique, Université Laval, Laval, Canada)

Abstract

Although the basic structure of logit-mixture models is well understood, important identification and normalization issues often get overlooked. This paper addresses issues related to the identification of parameters in logit-mixture models containing normally distributed error components associated with alternatives or nests of alternatives (normal error component logit mixture, or NECLM, models). NECLM models include special cases such as unrestricted, fixed covariance matrices; alternative-specific variances; nesting and cross-nesting structures; and some applications to panel data. A general framework is presented for determining which parameters are identified as well as what normalization to impose when specifying NECLM models. It is generally necessary to specify and estimate NECLM models at the levels, or structural, form. This precludes working with utility differences, which would otherwise greatly simplify the identification and normalization process. Our results show that identification is not always intuitive; for example, normalization issues present in logit-mixture models are not present in analogous probit models. To identify and properly normalize the NECLM, we introduce the 'equality condition', an addition to the standard order and rank conditions. The identifying conditions are worked through for a number of special cases, and our findings are demonstrated with empirical examples using both synthetic and real data. Copyright © 2007 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.971
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 22 (2007)
Issue (Month): 6 ()
Pages: 1095-1125

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Handle: RePEc:jae:japmet:v:22:y:2007:i:6:p:1095-1125

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References

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Citations

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Cited by:
  1. Bolduc, Denis & Khalaf, Lynda & Yélou, Clément, 2010. "Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models," Journal of Econometrics, Elsevier, vol. 157(2), pages 317-327, August.
  2. Pierpaolo De Blasi & Lancelot F. James & John W. Lau, 2007. "Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models," ICER Working Papers - Applied Mathematics Series 15-2007, ICER - International Centre for Economic Research.
  3. Joan Walker & Jieping Li, 2007. "Latent lifestyle preferences and household location decisions," Journal of Geographical Systems, Springer, vol. 9(1), pages 77-101, April.
  4. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
  5. Guevara, C. Angelo & Ben-Akiva, Moshe E., 2013. "Sampling of alternatives in Logit Mixture models," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 185-198.
  6. Yongjie Ji & Joseph A. Herriges & Catherine L. Kling, 2013. "Modeling Recreation Demand when the Access Point is Unknown," Center for Agricultural and Rural Development (CARD) Publications 13-wp540, Center for Agricultural and Rural Development (CARD) at Iowa State University.
  7. Batarce, Marco & Ivaldi, Marc, 2011. "Travel Demand Model with Heterogeneous Users and Endogenous Congestion: An application to optimal pricing of bus services," CEPR Discussion Papers 8416, C.E.P.R. Discussion Papers.
  8. Zenetti, German, 2010. "A Note on 'Bayesian analysis of the random coefficient model using aggregate data', an alternative approach," MPRA Paper 26449, University Library of Munich, Germany.
  9. de Lapparent, M., & Axhausen , K.W. & Frei, A., 2013. "Long distance mode choice and distributions of values of travel time savings in three European countries," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 53, pages 7.
  10. Laura Mørch Andersen, 2013. "Obtaining reliable Likelihood Ratio tests from simulated likelihood functions," IFRO Working Paper 2013/1, University of Copenhagen, Department of Food and Resource Economics.
  11. Bekhor, Shlomo & Prato, Carlo Giacomo, 2009. "Methodological transferability in route choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 422-437, May.
  12. Batarce, Marco & Ivaldi, Marc, 2010. "Travel Demand Model with Heterogeneous Users and Endogenous Congestion: An application to optimal pricing of bus services," TSE Working Papers 10-226, Toulouse School of Economics (TSE), revised Apr 2011.
  13. Chiou, Lesley & Walker, Joan L., 2007. "Masking identification of discrete choice models under simulation methods," Journal of Econometrics, Elsevier, vol. 141(2), pages 683-703, December.

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