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Estimation of Multinomial Logit Models with Unobserved Heterogeneity Using Maximum Simulated Likelihood

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  • Peter Haan
  • Arne Uhlendorff

Abstract

In this paper we suggest a Stata routine for multinomial logit models with unobserved heterogeneity using maximum simulated likelihood based on Halton sequences. The purpose of this paper is twofold: First, we provide a description of the technical implementation of the estimation routine and discuss its properties. Further, we compare our estimation routine to the Stata program gllamm which solves integration using Gauss Hermite quadrature or Bayesian adaptive quadrature. For the analysis we draw on multilevel data about schooling. Our empirical findings show that the estimation techniques lead to approximately the same estimation results. The advantage of simulation over Gauss Hermite quadrature is a marked reduction in computational time for integrals with higher dimensions. Bayesian quadrature, however, leads to very stable results with only a few quadrature points, thus the computational advantage of Halton based simulation vanishes in our example with one and two dimensional integrals.

Suggested Citation

  • Peter Haan & Arne Uhlendorff, 2006. "Estimation of Multinomial Logit Models with Unobserved Heterogeneity Using Maximum Simulated Likelihood," Discussion Papers of DIW Berlin 573, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp573
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    References listed on IDEAS

    as
    1. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    2. repec:tsj:spbook:mimus is not listed on IDEAS
    3. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    5. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, March.
    6. Arne Uhlendorff, 2006. "From No Pay to Low Pay and Back Again?: A Multi-State Model of Low Pay Dynamics," Discussion Papers of DIW Berlin 648, DIW Berlin, German Institute for Economic Research.
    7. Peter Haan, 2005. "State Dependence and Female Labor Supply in Germany: The Extensive and the Intensive Margin," Discussion Papers of DIW Berlin 538, DIW Berlin, German Institute for Economic Research.
    8. Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, March.
    9. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
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    12. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 3(3), pages 278-294, September.
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    Keywords

    multinomial logit model; panel data; unobserved heterogeneity; maximum simulated likelihood; Halton sequences;
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