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

  • Peter Haan
  • Arne Uhlendorff

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.

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Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 573.

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Length: 16 p.
Date of creation: 2006
Date of revision:
Handle: RePEc:diw:diwwpp:dp573
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  1. 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.
  2. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," United Kingdom Stata Users' Group Meetings 2003 10, Stata Users Group.
  3. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
  4. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2.
  5. 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.
  6. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
  7. repec:tsj:spbook:mimus is not listed on IDEAS
  8. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, November.
  9. Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, November.
  10. 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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