IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v87y2022i1d10.1007_s11336-022-09848-8.html
   My bibliography  Save this article

Objective Bayesian Edge Screening and Structure Selection for Ising Networks

Author

Listed:
  • M. Marsman

    (University of Amsterdam, Psychological Methods)

  • K. Huth

    (University of Amsterdam, Psychological Methods
    Centre for Urban Mental Health)

  • L. J. Waldorp

    (University of Amsterdam, Psychological Methods)

  • I. Ntzoufras

    (Athens University of Economics and Business)

Abstract

The Ising model is one of the most widely analyzed graphical models in network psychometrics. However, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our methods build on a continuous spike-and-slab approach. We show that our methods consistently select the correct structure and provide a new objective method to set the spike-and-slab hyperparameters. To circumvent the exploration of the complete structure space, which is too large in practical situations, we propose a novel approach that first screens for promising edges and then only explore the space instantiated by these edges. We apply our proposed methods to estimate the network of depression and alcohol use disorder symptoms from symptom scores of over 26,000 subjects.

Suggested Citation

  • M. Marsman & K. Huth & L. J. Waldorp & I. Ntzoufras, 2022. "Objective Bayesian Edge Screening and Structure Selection for Ising Networks," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 47-82, March.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:1:d:10.1007_s11336-022-09848-8
    DOI: 10.1007/s11336-022-09848-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-022-09848-8
    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/s11336-022-09848-8?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. Epskamp, Sacha & Cramer, Angélique O.J. & Waldorp, Lourens J. & Schmittmann, Verena D. & Borsboom, Denny, 2012. "qgraph: Network Visualizations of Relationships in Psychometric Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i04).
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Veronika Ročková & Edward I. George, 2014. "EMVS: The EM Approach to Bayesian Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 828-846, June.
    4. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    5. Sacha Epskamp & Joost Kruis & Maarten Marsman, 2017. "Estimating psychopathological networks: Be careful what you wish for," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-13, June.
    6. Angélique O J Cramer & Claudia D van Borkulo & Erik J Giltay & Han L J van der Maas & Kenneth S Kendler & Marten Scheffer & Denny Borsboom, 2016. "Major Depression as a Complex Dynamic System," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-20, December.
    7. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    8. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    9. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    10. Veronika Ročková & Edward I. George, 2018. "The Spike-and-Slab LASSO," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 431-444, January.
    11. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    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. Maarten Marsman & Mijke Rhemtulla, 2022. "Guest Editors’ Introduction to The Special Issue “Network Psychometrics in Action”: Methodological Innovations Inspired by Empirical Problems," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 1-11, March.

    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. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    2. Gonzalo García-Donato & María Eugenia Castellanos & Alicia Quirós, 2021. "Bayesian Variable Selection with Applications in Health Sciences," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    3. Nadja Bodner & Laura Bringmann & Francis Tuerlinckx & Peter Jonge & Eva Ceulemans, 2022. "ConNEcT: A Novel Network Approach for Investigating the Co-occurrence of Binary Psychopathological Symptoms Over Time," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 107-132, March.
    4. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    6. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    7. Maarten Marsman & Mijke Rhemtulla, 2022. "Guest Editors’ Introduction to The Special Issue “Network Psychometrics in Action”: Methodological Innovations Inspired by Empirical Problems," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 1-11, March.
    8. Zhang, Chun-Xia & Xu, Shuang & Zhang, Jiang-She, 2019. "A novel variational Bayesian method for variable selection in logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 1-19.
    9. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    10. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    11. Denny Borsboom, 2022. "Possible Futures for Network Psychometrics," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 253-265, March.
    12. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    13. Zhou, Jianhua & Zhang, Lulu & Gong, Xue, 2023. "Longitudinal network relations between symptoms of problematic internet game use and internalizing and externalizing problems among Chinese early adolescents," Social Science & Medicine, Elsevier, vol. 333(C).
    14. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon T. Willard, 2020. "Global-Local Mixtures: A Unifying Framework," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 426-447, August.
    15. Dufays, Arnaud & Rombouts, Jeroen V.K., 2020. "Relevant parameter changes in structural break models," Journal of Econometrics, Elsevier, vol. 217(1), pages 46-78.
    16. Ovielt Baltodano L'opez & Roberto Casarin, 2022. "A Dynamic Stochastic Block Model for Multi-Layer Networks," Papers 2209.09354, arXiv.org.
    17. Ruggieri, Eric & Lawrence, Charles E., 2012. "On efficient calculations for Bayesian variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1319-1332.
    18. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    19. Juliana Ribeiro Francelino Sampaio & Suely Arruda Vidal & Paulo Savio Angeiras de Goes & Paulo Felipe R. Bandeira & José Eulálio Cabral Filho, 2021. "Sociodemographic, Behavioral and Oral Health Factors in Maternal and Child Health: An Interventional and Associative Study from the Network Perspective," IJERPH, MDPI, vol. 18(8), pages 1-13, April.
    20. Agota Fodor & Vincent Segura & Marie Denis & Samuel Neuenschwander & Alexandre Fournier-Level & Philippe Chatelet & Félix Abdel Aziz Homa & Thierry Lacombe & Patrice This & Loic Le Cunff, 2014. "Genome-Wide Prediction Methods in Highly Diverse and Heterozygous Species: Proof-of-Concept through Simulation in Grapevine," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-14, November.

    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:psycho:v:87:y:2022:i:1:d:10.1007_s11336-022-09848-8. 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.