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Maximum simulated likelihood and expectation-maximization methods to estimate random coefficients logit with panel data

Lookup NU author(s): Professor Elisabetta Cherchi


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The random coefficients Logit model allows a more realistic representation of agents’ behavior. However, the estimation of such model may involve simulation, which may become impractical when the number of random coefficients is large, because of what is known as the curse of dimensionality. In this article, we compare the traditional Maximum Simulated Likelihood (MSL) method with the alternative Expectation-Maximization (EM) method that does not require simulation. Previous literature had shown that, for cross-sectional data, MSL outperforms the EM method in terms of ability to recover the true parameters and estimation time, and that EM has more difficulties in recovering the true scale of the coefficients. In this article, we extend the analysis from cross-sectional data to the less volatile case of panel data to explore the impact in the relative performance of the methods of having several realizations of the random coefficients. Using a series of Monte Carlo experiments, we found evidence suggesting four main conclusions. (1) Efficiency increases when the true variance-covariance matrix becomes diagonal. (2) EM is more robust to curse of dimensionality both in terms of efficiency and estimation time. (3) EM does not recover the true scale neither with cross-sectional nor with panel data. (4) EM systematically attains more efficient estimators than the MSL method. This implies that, if the purpose of the estimation is only to determine the ratios of the model parameters (e.g. the value of time), the EM should be preferred. For all other cases, MSL should be used.

Publication metadata

Author(s): Cherchi E, Guevara CA

Publication type: Article

Publication status: Published

Journal: Transportation Research Record

Year: 2012

Volume: 2302

Issue: 1

Pages: 65-73

Print publication date: 01/01/2012

Online publication date: 01/01/2012

ISSN (print): 0361-1981

ISSN (electronic): 2169-4052

Publisher: Sage Publications, Inc.


DOI: 10.3141/2302-07


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