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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    5. 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.
    6. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. Zhang, Siliang & Chen, Yunxiao, 2024. "A note on Ising network analysis with missing data," LSE Research Online Documents on Economics 123984, London School of Economics and Political Science, LSE Library.
    2. 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.

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