IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp281-297.html
   My bibliography  Save this article

Mode jumping MCMC for Bayesian variable selection in GLMM

Author

Listed:
  • Hubin, Aliaksandr
  • Storvik, Geir

Abstract

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.

Suggested Citation

  • Hubin, Aliaksandr & Storvik, Geir, 2018. "Mode jumping MCMC for Bayesian variable selection in GLMM," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 281-297.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:281-297
    DOI: 10.1016/j.csda.2018.05.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731830135X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.05.020?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. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    2. Al-Awadhi, Fahimah & Hurn, Merrilee & Jennison, Christopher, 2004. "Improving the acceptance rate of reversible jump MCMC proposals," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 189-198, August.
    3. repec:dau:papers:123456789/7305 is not listed on IDEAS
    4. repec:dau:papers:123456789/5724 is not listed on IDEAS
    5. A. Doucet & M. K. Pitt & G. Deligiannidis & R. Kohn, 2015. "Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator," Biometrika, Biometrika Trust, vol. 102(2), pages 295-313.
    6. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    7. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    8. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    9. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    10. Bivand, Roger & Gómez-Rubio, Virgilio & Rue, Håvard, 2015. "Spatial Data Analysis with R-INLA with Some Extensions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i20).
    11. 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.
    12. Frommlet Florian & Ljubic Ivana & Arnardóttir Helga Björk & Bogdan Malgorzata, 2012. "QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-26, May.
    13. Nial Friel & Jason Wyse, 2012. "Estimating the evidence – a review," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 288-308, August.
    14. Qifan Song & Faming Liang, 2015. "A split-and-merge Bayesian variable selection approach for ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(5), pages 947-972, November.
    15. Geir Storvik, 2011. "On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 342-358, June.
    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. Messner, Wolfgang, 2023. "The contingency impact of culture on health security capacities for pandemic preparedness: A moderated Bayesian inference analysis," Journal of International Management, Elsevier, vol. 29(5).
    2. Bettina Grün & Paul Hofmarcher, 2021. "Identifying groups of determinants in Bayesian model averaging using Dirichlet process clustering," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1018-1045, 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. 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.
    2. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    3. Darren J. Mayne & Geoffrey G. Morgan & Bin B. Jalaludin & Adrian E. Bauman, 2018. "Does Walkability Contribute to Geographic Variation in Psychosocial Distress? A Spatial Analysis of 91,142 Members of the 45 and Up Study in Sydney, Australia," IJERPH, MDPI, vol. 15(2), pages 1-24, February.
    4. Bhattacharya, Arnab & Wilson, Simon P., 2018. "Sequential Bayesian inference for static parameters in dynamic state space models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 187-203.
    5. White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
    6. Alzahrani, Naif & Neal, Peter & Spencer, Simon E.F. & McKinley, Trevelyan J. & Touloupou, Panayiota, 2018. "Model selection for time series of count data," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 33-44.
    7. Virgilio Gómez-Rubio & Roger S. Bivand & Håvard Rue, 2021. "Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    8. Li, Dan & Clements, Adam & Drovandi, Christopher, 2021. "Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 22-46.
    9. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    10. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.
    11. I. Gede Nyoman Mindra Jaya & Henk Folmer, 2020. "Bayesian spatiotemporal mapping of relative dengue disease risk in Bandung, Indonesia," Journal of Geographical Systems, Springer, vol. 22(1), pages 105-142, January.
    12. Chien-Chou Chen & Guo-Jun Lo & Ta-Chien Chan, 2022. "Spatial Analysis on Supply and Demand of Adult Surgical Masks in Taipei Metropolitan Areas in the Early Phase of the COVID-19 Pandemic," IJERPH, MDPI, vol. 19(11), pages 1-12, May.
    13. Ruiz-Cárdenas, Ramiro & Krainski, Elias T. & Rue, Håvard, 2012. "Direct fitting of dynamic models using integrated nested Laplace approximations — INLA," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1808-1828.
    14. Arnaud Dufays, 2014. "On the conjugacy of off-line and on-line Sequential Monte Carlo Samplers," Working Paper Research 263, National Bank of Belgium.
    15. Sheyla Rodrigues Cassy & Samuel Manda & Filipe Marques & Maria do Rosário Oliveira Martins, 2022. "Accounting for Sampling Weights in the Analysis of Spatial Distributions of Disease Using Health Survey Data, with an Application to Mapping Child Health in Malawi and Mozambique," IJERPH, MDPI, vol. 19(10), pages 1-15, May.
    16. Axel Finke & Ruth King & Alexandros Beskos & Petros Dellaportas, 2019. "Efficient Sequential Monte Carlo Algorithms for Integrated Population Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 204-224, June.
    17. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    18. Perrakis, Konstantinos & Ntzoufras, Ioannis & Tsionas, Efthymios G., 2014. "On the use of marginal posteriors in marginal likelihood estimation via importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 54-69.
    19. Ajay Jasra & Kody Law & Carina Suciu, 2020. "Advanced Multilevel Monte Carlo Methods," International Statistical Review, International Statistical Institute, vol. 88(3), pages 548-579, December.
    20. Zongyuan Xia & Bo Tang & Long Qin & Huiguo Zhang & Xijian Hu, 2023. "Spatially Dependent Bayesian Modeling of Geostatistics Data and Its Application for Tuberculosis (TB) in China," Mathematics, MDPI, vol. 11(19), pages 1-15, October.

    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:eee:csdana:v:127:y:2018:i:c:p:281-297. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.