IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0106136.html
   My bibliography  Save this article

Obtaining Reliable Likelihood Ratio Tests from Simulated Likelihood Functions

Author

Listed:
  • Laura Mørch Andersen

Abstract

Mixed models: Models allowing for continuous heterogeneity by assuming that value of one or more parameters follow a specified distribution have become increasingly popular. This is known as ‘mixing’ parameters, and 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). Problem 1: Inconsistent LR tests due to asymmetric 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 illustrates 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 main conclusion of this paper is that the problem can be solved completely by using fully antithetic draws, and that using one dimensionally antithetic draws is not enough to solve the problem. Problem 2: Maintaining the correct dimensions when reducing the mixing distribution:: A second point of the paper is that even when fully antithetic draws are used, models reducing the dimension of the mixing distribution 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. JEL classification: C15; C25.

Suggested Citation

  • Laura Mørch Andersen, 2014. "Obtaining Reliable Likelihood Ratio Tests from Simulated Likelihood Functions," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-12, October.
    • Handle: RePEc:plo:pone00:0106136
    DOI: 10.1371/journal.pone.0106136
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0106136
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0106136&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0106136?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    3. 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.
    4. Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
    5. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    6. 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.
    7. Jae Bong Chang & Jayson L. Lusk, 2011. "Mixed logit models: accuracy and software choice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 167-172, January/F.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zijlstra, Toon & Goos, Peter & Verhetsel, Ann, 2019. "A mixture-amount stated preference study on the mobility budget," Transportation Research Part A: Policy and Practice, Elsevier, vol. 126(C), pages 230-246.
    2. 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.
    3. Becker, Felix & Danaf, Mazen & Song, Xiang & Atasoy, Bilge & Ben-Akiva, Moshe, 2018. "Bayesian estimator for Logit Mixtures with inter- and intra-consumer heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 1-17.
    4. Czajkowski, Mikołaj & Barczak, Anna & Budziński, Wiktor & Giergiczny, Marek & Hanley, Nick, 2016. "Preference and WTP stability for public forest management," Forest Policy and Economics, Elsevier, vol. 71(C), pages 11-22.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. William Greene, 2001. "Fixed and Random Effects in Nonlinear Models," Working Papers 01-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    3. Bernard Fortin & Nicolas Jacquemet & Bruce Shearer, 2008. "Policy Analysis in Health-Services Market: Accounting for Quality and Quantity," Annals of Economics and Statistics, GENES, issue 91-92, pages 293-319.
    4. Timothy J. Richards & Paul M. Patterson & Abebayehu Tegene, 2007. "Obesity And Nutrient Consumption: A Rational Addiction?," Contemporary Economic Policy, Western Economic Association International, vol. 25(3), pages 309-324, July.
    5. Joan L. Walker & Moshe Ben-Akiva, 2011. "Advances in Discrete Choice: Mixture Models," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 8, Edward Elgar Publishing.
    6. Helveston, John Paul & Feit, Elea McDonnell & Michalek, Jeremy J., 2018. "Pooling stated and revealed preference data in the presence of RP endogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 70-89.
    7. Bliemer, Michiel C.J. & Rose, John M., 2010. "Construction of experimental designs for mixed logit models allowing for correlation across choice observations," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 720-734, July.
    8. Walker, Joan & Ben-Akiva, Moshe, 2002. "Generalized random utility model," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 303-343, July.
    9. Yoshifumi Konishi & Sho Kuroda & Shunsuke Managi, 2024. "Income-based or Place-based? Carbon Dividends under Spatial Distribution of Automobile Demand," Keio-IES Discussion Paper Series 2024-019, Institute for Economics Studies, Keio University.
    10. Victoria Prowse, 2012. "Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 411-431, April.
    11. 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.
    12. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    13. Sándor, Z. & Franses, Ph.H.B.F., 2004. "Experimental investigation of consumer price evaluations," Econometric Institute Research Papers EI 2004-12, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Hess, Stephane & Rose, John M., 2009. "Allowing for intra-respondent variations in coefficients estimated on repeated choice data," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 708-719, July.
    15. Kalouptsidis, N. & Psaraki, V., 2010. "Approximations of choice probabilities in mixed logit models," European Journal of Operational Research, Elsevier, vol. 200(2), pages 529-535, January.
    16. Helveston, John Paul & Liu, Yimin & Feit, Elea McDonnell & Fuchs, Erica & Klampfl, Erica & Michalek, Jeremy J., 2015. "Will subsidies drive electric vehicle adoption? Measuring consumer preferences in the U.S. and China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 73(C), pages 96-112.
    17. Algers, S. & Bergstrom, P. & Dahlberg, M. & Dillen, J.L., 1998. "Mixed Logit Estimation of the Value of Travel Time," Papers 1998:15, Uppsala - Working Paper Series.
    18. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    19. Amine Ouazad & Romain Rancière, 2019. "City Equilibrium With Borrowing Constraints: Structural Estimation And General Equilibrium Effects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(2), pages 721-749, May.
    20. Jayarajan, Dinakar & Siddarth, S. & Silva-Risso, Jorge, 2018. "Cannibalization vs. competition: An empirical study of the impact of product durability on automobile demand," International Journal of Research in Marketing, Elsevier, vol. 35(4), pages 641-660.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0106136. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.