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Obtaining reliable Likelihood Ratio tests from simulated likelihood functions

Author

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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

    as
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    11. 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. Czajkowski, Mikołaj & Budziński, Wiktor, 2019. "Simulation error in maximum likelihood estimation of discrete choice models," Journal of choice modelling, Elsevier, vol. 31(C), pages 73-85.

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    More about this item

    Keywords

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