IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i1d10.1007_s00180-016-0677-z.html
   My bibliography  Save this article

Integrated likelihood computation methods

Author

Listed:
  • Zhenyu Zhao

    (Northwestern University)

  • Thomas A. Severini

    (Northwestern University)

Abstract

Suppose a model has parameter $$\theta =(\psi , \lambda )$$ θ = ( ψ , λ ) , where $$\psi $$ ψ is the parameter of interest and $$\lambda $$ λ is a nuisance parameter. The integrated likelihood method eliminates $$\lambda $$ λ from the likelihood function $$L(\psi , \lambda )$$ L ( ψ , λ ) by integrating with respect to a weight function $$\pi (\lambda | \psi )$$ π ( λ | ψ ) . The resulting integrated likelihood function $$\bar{L}(\psi )$$ L ¯ ( ψ ) can be used for inference for $$\psi $$ ψ . However, the analytical form for the integrated likelihood is not always available. This paper discusses 12 different approaches to computing the integrated likelihood. Some methods were originally developed for other computation purposes and they are modified to fit in the integrated likelihood framework. Methods considered include direct numerical integration methods such as Monte Carlo integration method, importance sampling, Laplace method; marginal likelihood computation methods; and methods for computing the marginal posterior density. Simulation studies and real data example are presented to evaluate and compare these methods empirically.

Suggested Citation

  • Zhenyu Zhao & Thomas A. Severini, 2017. "Integrated likelihood computation methods," Computational Statistics, Springer, vol. 32(1), pages 281-313, March.
  • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0677-z
    DOI: 10.1007/s00180-016-0677-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0677-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00180-016-0677-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. T. A. Severini, 2010. "Likelihood ratio statistics based on an integrated likelihood," Biometrika, Biometrika Trust, vol. 97(2), pages 481-496.
    2. Charles S. Bos, 2002. "A Comparison of Marginal Likelihood Computation Methods," Tinbergen Institute Discussion Papers 02-084/4, Tinbergen Institute.
    3. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    4. Thomas A. Severini, 2007. "Integrated likelihood functions for non-Bayesian inference," Biometrika, Biometrika Trust, vol. 94(3), pages 529-542.
    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. Edgar C. Merkle & Daniel Furr & Sophia Rabe-Hesketh, 2019. "Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 802-829, September.

    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. Thomas A. Severini, 2023. "Integrated likelihood inference in multinomial distributions," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 131-142, August.
    2. Giuliana Cortese & Nicola Sartori, 2016. "Integrated likelihoods in parametric survival models for highly clustered censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 382-404, July.
    3. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    4. Ruggero Bellio & Annamaria Guolo, 2016. "Integrated Likelihood Inference in Small Sample Meta-analysis for Continuous Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 191-201, March.
    5. Zaigraev, A. & Podraza-Karakulska, A., 2014. "Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 99-106.
    6. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    7. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    8. Kakamu, Kazuhiko & Yunoue, Hideo & Kuramoto, Takashi, 2014. "Spatial patterns of flypaper effects for local expenditure by policy objective in Japan: A Bayesian approach," Economic Modelling, Elsevier, vol. 37(C), pages 500-506.
    9. Parent, Olivier & LeSage, James P., 2011. "A space-time filter for panel data models containing random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 475-490, January.
    10. Gary Bolton & Duncan Fong & Paul Mosquin, 2003. "Bayes Factors with an Application to Experimental Economics," Experimental Economics, Springer;Economic Science Association, vol. 6(3), pages 311-325, November.
    11. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate stochastic volatility with co-heteroscedasticity," CAMA Working Papers 2018-52, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Jouchi Nakajima & Yasuhiro Omori, 2007. "Leverage, Heavy-Tails and Correlated Jumps in Stochastic Volatility Models (Revised in January 2008; Published in "Computational Statistics and Data Analysis", 53-6, 2335-2353. April 2009. )," CARF F-Series CARF-F-107, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    14. repec:hum:wpaper:sfb649dp2013-028 is not listed on IDEAS
    15. Moeltner, Klaus, 2019. "Bayesian nonlinear meta regression for benefit transfer," Journal of Environmental Economics and Management, Elsevier, vol. 93(C), pages 44-62.
    16. Will Penny & Biswa Sengupta, 2016. "Annealed Importance Sampling for Neural Mass Models," PLOS Computational Biology, Public Library of Science, vol. 12(3), pages 1-25, March.
    17. Asai, Manabu, 2009. "Bayesian analysis of stochastic volatility models with mixture-of-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2579-2596.
    18. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    19. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    20. Malley, Jim & Woitek, Ulrich, 2010. "Technology shocks and aggregate fluctuations in an estimated hybrid RBC model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1214-1232, July.
    21. Schumann, Martin & Severini, Thomas A. & Tripathi, Gautam, 2021. "Integrated likelihood based inference for nonlinear panel data models with unobserved effects," Journal of Econometrics, Elsevier, vol. 223(1), pages 73-95.

    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:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0677-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.