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

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

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Article ID: iaor20132877
Volume: 40
Issue: 3
Start Page Number: 647
End Page Number: 670
Publication Date: May 2013
Journal: Transportation
Authors: ,
Keywords: Bayesian analysis, Monte Carlo method, travel mode choice, logit
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.

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