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Obtaining reliable Likelihood Ratio tests from simulated likelihood functions

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  • Laura Mørch Andersen

    () (Department of Food and Resource Economics, University of Copenhagen)

Abstract

It is standard practice by researchers and the default option in many statistical programs to base test statistics for mixed models on simulations using asymmetric draws (e.g. Halton draws). This paper shows that when the estimated likelihood functions depend on standard deviations of mixed parameters this practice is very likely to cause misleading test results for the number of draws usually used today. The paper shows that increasing the number of draws is a very inefficient solution strategy requiring very large numbers of draws to ensure against misleading test statistics. The paper shows that using one dimensionally antithetic draws does not solve the problem but that the problem can be solved completely by using fully antithetic draws. The paper also shows that even when fully antithetic draws are used, models testing away mixing dimensions must replicate the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood. Again this is not standard in research or statistical programs. The paper therefore recommends using fully antithetic draws replicating the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood and that this should become the default option in statistical programs.

Suggested Citation

  • Laura Mørch Andersen, 2013. "Obtaining reliable Likelihood Ratio tests from simulated likelihood functions," IFRO Working Paper 2013/1, University of Copenhagen, Department of Food and Resource Economics.
  • Handle: RePEc:foi:wpaper:2013_1
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    File URL: http://okonomi.foi.dk/workingpapers/WPpdf/WP2013/IFRO_WP_2013_1.pdf
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    References listed on IDEAS

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    1. Lorenzo Cappellari & Stephen P. Jenkins, 2006. "Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation," Stata Journal, StataCorp LP, vol. 6(2), pages 156-189, June.
    2. Laura Mørch Andersen, 2011. "Animal Welfare and Eggs – Cheap Talk or Money on the Counter?," Journal of Agricultural Economics, Wiley Blackwell, vol. 62(3), pages 565-584, September.
    3. Chiou, Lesley & Walker, Joan L., 2007. "Masking identification of discrete choice models under simulation methods," Journal of Econometrics, Elsevier, vol. 141(2), pages 683-703, December.
    4. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    5. 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.
    6. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, May.
    7. Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
    8. 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.
    9. Ben-Akiva, M. & Bolduc, D. & Bradley, M., 1993. "Estimation of Travel Choice Models with Randomly Distributed Values of Time," Papers 9303, Laval - Recherche en Energie.
    10. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
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    Cited by:

    1. Mikołaj Czajkowski & Wiktor Budziński, 2017. "Simulation error in maximum likelihood estimation of discrete choice models," Working Papers 2017-18, Faculty of Economic Sciences, University of Warsaw.

    More about this item

    Keywords

    Quasi-Monte Carlo integration; Antithetic draws; Likelihood Ratio tests; simulated likelihood; panel Mixed MultiNomial Logit; Halton draws;

    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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