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Obtaining reliable Likelihood Ratio tests from simulated likelihood functions

  • Laura Mørch Andersen

    ()

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

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.

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File URL: http://okonomi.foi.dk/workingpapers/WPpdf/WP2013/IFRO_WP_2013_1.pdf
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Paper provided by University of Copenhagen, Department of Food and Resource Economics in its series IFRO Working Paper with number 2013/1.

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Length: 29 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:foi:wpaper:2013_1
Contact details of provider: Web page: http://www.ifro.ku.dk/english/
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  1. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt3tb6j874, University of California Transportation Center.
  2. Lorenzo Cappellari & Stephen P. Jenkins, 2006. "Calculation of Multivariate Normal Probabilities by Simulation, with Applications to Maximum Simulated Likelihood Estimation," Discussion Papers of DIW Berlin 584, DIW Berlin, German Institute for Economic Research.
  3. repec:ese:iserwp:2006-16 is not listed on IDEAS
  4. 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.
  5. 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.
  6. 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, 09.
  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. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, March.
  9. 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.
  10. 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.
  11. 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.
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