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Standard and Shuffled Halton Sequences in a Mixed Logit Model

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  • Alexander Staus

    (Institute for Agricultural Policy and Agricultural Markets, University of Hohenheim)

Abstract

Modeling consumer choice in different areas has lead to an increase use of discrete choice models. Probit or Multinomial Logit Models are often the base of further empirical research of consumer choice. In some of these models the equations to solve have no closed-form expression. They include multi-dimensional integrals which can not be solved analytically. Simulation methods have been developed to approximate a solution for these integrals. This paper describes the Standard Halton sequence and a modification of it, the Shuffled Halton sequence. Both are simulation methods which can reduce computational effort compared to a random sequence. We compare the simulation methods in their coverage of the multi-dimensional area and in their estimation results using data of consumer choice on grocery store formats.

Suggested Citation

  • Alexander Staus, 2008. "Standard and Shuffled Halton Sequences in a Mixed Logit Model," Hohenheimer Agrarökonomische Arbeitsberichte 17, University of Hohenheim, Institute for Agricultural Policy and Agricultural Markets.
    • Handle: RePEc:hoh:hoh420:17
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    References listed on IDEAS

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    1. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    2. 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.
    3. Train, Kenneth, 2000. "Halton Sequences for Mixed Logit," Department of Economics, Working Paper Series qt6zs694tp, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    5. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
    6. Arne Risa Hole, 2007. "Fitting mixed logit models by using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 7(3), pages 388-401, September.
    7. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
    8. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    9. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
    10. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
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    More about this item

    Keywords

    simulation; mixed logit; halton sequence;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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