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Covariance, identification, and finite-sample performance of the MSL and Bayes estimators of a logit model with latent attributes

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  • Ricardo Daziano
  • Denis Bolduc

Abstract

In this paper we discuss the specification, covariance structure, estimation, identification, and point-estimate analysis of a logit model with endogenous latent attributes that avoids problems of inconsistency. We show first that the total error term induced by the stochastic latent attributes is heteroskedastic and nonindependent. In addition, we show that the exact identification conditions support the two-stage analysis found in much current work. Second, we set up a Monte Carlo experiment where we compare the finite-sample performance of the point estimates of two alternative methods of estimation, namely frequentist full information maximum simulated likelihood and Bayesian Metropolis Hastings-within-Gibbs sampling. The Monte Carlo study represents a virtual case of travel mode choice. Even though the two estimation methods we analyze are based on different philosophies, both the frequentist and Bayesian methods provide estimators that are asymptotically equivalent. Our results show that both estimators are feasible and offer comparable results with a large enough sample size. However, the Bayesian point estimates outperform maximum likelihood in terms of accuracy, statistical significance, and efficiency when the sample size is low. Copyright Springer Science+Business Media, LLC. 2013

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  • Ricardo Daziano & Denis Bolduc, 2013. "Covariance, identification, and finite-sample performance of the MSL and Bayes estimators of a logit model with latent attributes," Transportation, Springer, vol. 40(3), pages 647-670, May.
    • Handle: RePEc:kap:transp:v:40:y:2013:i:3:p:647-670
    DOI: 10.1007/s11116-012-9434-5
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    Cited by:

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    2. Akshay Vij & Joan L. Walker, 2014. "Hybrid choice models: the identification problem," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 22, pages 519-564, Edward Elgar Publishing.
    3. Bouscasse, H., 2018. "Integrated choice and latent variable models: A literature review on mode choice," Working Papers 2018-07, Grenoble Applied Economics Laboratory (GAEL).
    4. Xuemei Fu & Zhicai Juan, 2017. "Estimation of multinomial probit-kernel integrated choice and latent variable model: comparison on one sequential and two simultaneous approaches," Transportation, Springer, vol. 44(1), pages 91-116, January.
    5. Schmid, Basil & Axhausen, Kay W., 2019. "In-store or online shopping of search and experience goods: A hybrid choice approach," Journal of choice modelling, Elsevier, vol. 31(C), pages 156-180.
    6. Daziano, Ricardo A. & Chiew, Esther, 2012. "Electric vehicles rising from the dead: Data needs for forecasting consumer response toward sustainable energy sources in personal transportation," Energy Policy, Elsevier, vol. 51(C), pages 876-894.
    7. Marcel Paulssen & Dirk Temme & Akshay Vij & Joan Walker, 2014. "Values, attitudes and travel behavior: a hierarchical latent variable mixed logit model of travel mode choice," Transportation, Springer, vol. 41(4), pages 873-888, July.
    8. Chae, Dasol & Jung, Jaeyoung & Sohn, Keemin, 2018. "Facilitating an expectation-maximization (EM) algorithm to solve an integrated choice and latent variable (ICLV) model with fully correlated latent variables," Journal of choice modelling, Elsevier, vol. 26(C), pages 64-79.
    9. Daziano, Ricardo A., 2015. "Inference on mode preferences, vehicle purchases, and the energy paradox using a Bayesian structural choice model," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 1-26.
    10. Hélène Bouscasse, 2018. "Integrated choice and latent variable models: A literature review on mode choice," Working Papers hal-01795630, HAL.
    11. Rose, John M. & Hensher, David A., 2018. "User satisfaction with taxi and limousine services in the Melbourne metropolitan area," Journal of Transport Geography, Elsevier, vol. 70(C), pages 234-245.

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