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Easy and flexible mixture distributions

Author

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  • Fosgerau, Mogens
  • Mabit, Stefan

Abstract

We propose a method to generate flexible mixture distributions that are useful for estimating models such as the mixed logit model using simulation. The method is easy to implement, yet it can approximate essentially any mixture distribution. We test it with good results in a simulation study and on real data.

Suggested Citation

  • Fosgerau, Mogens & Mabit, Stefan, 2013. "Easy and flexible mixture distributions," MPRA Paper 46078, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:46078
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    References listed on IDEAS

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    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    3. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    4. Fosgerau, Mogens & Nielsen, Søren Feodor, 2010. "Deconvoluting Preferences And Errors: A Model For Binomial Panel Data," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1846-1854, December.
    5. Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441 Elsevier.
    6. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    7. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
    8. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
    9. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    10. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    11. Bierens, Herman J., 2008. "Semi-Nonparametric Interval-Censored Mixed Proportional Hazard Models: Identification And Consistency Results," Econometric Theory, Cambridge University Press, vol. 24(03), pages 749-794, June.
    12. Headrick, Todd C., 2002. "Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 685-711, October.
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    Citations

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    Cited by:

    1. repec:eee:transb:v:106:y:2017:i:c:p:76-101 is not listed on IDEAS
    2. Mabit, Stefan L., 2014. "Vehicle type choice under the influence of a tax reform and rising fuel prices," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 32-42.
    3. Fosgerau, Mogens & Börjesson, Maria, 2015. "Manipulating a stated choice experiment," Journal of choice modelling, Elsevier, vol. 16(C), pages 43-49.
    4. Riccardo Scarpa & Cristiano Franceschinis & Mara Thiene, 2017. "A Monte Carlo Evaluation of the Logit-Mixed Logit under Asymmetry and Multimodality," Working Papers in Economics 17/23, University of Waikato.
    5. Hess, Stephane & Daly, Andrew & Dekker, Thijs & Cabral, Manuel Ojeda & Batley, Richard, 2017. "A framework for capturing heterogeneity, heteroskedasticity, non-linearity, reference dependence and design artefacts in value of time research," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 126-149.
    6. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    7. 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.
    8. Jan (J.) Rouwendal, 2017. "Specification Tests for The Multinomial Logit Model Revisited: The Role of Alternative-Specific Constants," Tinbergen Institute Discussion Papers 17-068/VIII, Tinbergen Institute, revised 29 Jan 2018.

    More about this item

    Keywords

    Mixture distributions; mixed logit; simulation; maximum simulated likelihood;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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