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Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood

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  • Peter Haan

    (DIW Berlin)

  • Arne Uhlendorff

    (DIW Berlin)

Abstract

In this paper, we suggest a Stata routine for multinomial logit mod- els with unobserved heterogeneity using maximum simulated likelihood based on Halton sequences. The purpose of this paper is twofold. First, we describe the technical implementation of the estimation routine and discuss its properties. Further, we compare our estimation routine with the Stata program gllamm, which solves integration by using Gauss-Hermite quadrature or 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. Adaptive quadrature leads to more stable results relative to the other integration methods. However, simulation is more time efficient. We find that maximum simulated like- lihood leads to estimation results with reasonable accuracy in roughly half the time required when using adaptive quadrature. Copyright 2006 by StataCorp LP.

Suggested Citation

  • Peter Haan & Arne Uhlendorff, 2006. "Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 6(2), pages 229-245, June.
    • Handle: RePEc:tsj:stataj:v:6:y:2006:i:2:p:229-245
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    References listed on IDEAS

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    1. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, March.
    2. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "GLLAMM Manual," U.C. Berkeley Division of Biostatistics Working Paper Series 1160, Berkeley Electronic Press.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    4. 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.
    5. Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, March.
    6. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, September.
    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. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
    9. 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.
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    11. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 3(3), pages 278-294, September.
    12. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
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