IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2211.00671.html
   My bibliography  Save this paper

Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis

Author

Listed:
  • Darjus Hosszejni
  • Sylvia Fruhwirth-Schnatter

Abstract

Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we present a counting rule on the number of nonzero factor loadings that is sufficient for achieving generic uniqueness of the variance decomposition in the factor representation. This is formalized in the framework of sparse matrix spaces and some classical elements from graph and network theory. Furthermore, we provide a computationally efficient tool for verifying the counting rule. Our methodology is illustrated for real data in the context of post-processing posterior draws in Bayesian sparse factor analysis.

Suggested Citation

  • Darjus Hosszejni & Sylvia Fruhwirth-Schnatter, 2022. "Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis," Papers 2211.00671, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2211.00671
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2211.00671
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:bfi:wpaper:2014-014 is not listed on IDEAS
    2. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    3. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    4. James Dunn, 1973. "A note on a sufficiency condition for uniqueness of a restricted factor matrix," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 141-143, March.
    5. Kaufmann, Sylvia & Schumacher, Christian, 2019. "Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification," Journal of Econometrics, Elsevier, vol. 210(1), pages 116-134.
    6. Benjamin Williams, 2020. "Identification of the linear factor model," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 92-109, January.
    7. Sirio Legramanti & Daniele Durante & David B Dunson, 2020. "Bayesian cumulative shrinkage for infinite factorizations," Biometrika, Biometrika Trust, vol. 107(3), pages 745-752.
    8. A. Bhattacharya & D. B. Dunson, 2011. "Sparse Bayesian infinite factor models," Biometrika, Biometrika Trust, vol. 98(2), pages 291-306.
    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. Sylvia Fruhwirth-Schnatter & Darjus Hosszejni & Hedibert Freitas Lopes, 2023. "When it counts -- Econometric identification of the basic factor model based on GLT structures," Papers 2301.06354, arXiv.org.
    2. Sylvia Fruhwirth-Schnatter, 2023. "Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis," Papers 2303.00473, arXiv.org.

    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. Sylvia Fruhwirth-Schnatter & Darjus Hosszejni & Hedibert Freitas Lopes, 2023. "When it counts -- Econometric identification of the basic factor model based on GLT structures," Papers 2301.06354, arXiv.org.
    2. Sylvia Fruhwirth-Schnatter, 2023. "Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis," Papers 2303.00473, arXiv.org.
    3. Simon Beyeler & Sylvia Kaufmann, 2021. "Reduced‐form factor augmented VAR—Exploiting sparsity to include meaningful factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 989-1012, November.
    4. Florian Huber & Gary Koop, 2023. "Subspace shrinkage in conjugate Bayesian vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 556-576, June.
    5. 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.
    6. Kaufmann, Sylvia & Schumacher, Christian, 2019. "Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification," Journal of Econometrics, Elsevier, vol. 210(1), pages 116-134.
    7. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    8. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    9. Roberta De Vito & Ruggero Bellio & Lorenzo Trippa & Giovanni Parmigiani, 2019. "Multi‐study factor analysis," Biometrics, The International Biometric Society, vol. 75(1), pages 337-346, March.
    10. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    11. Daewon Yang & Taeryon Choi & Eric Lavigne & Yeonseung Chung, 2022. "Non‐parametric Bayesian covariate‐dependent multivariate functional clustering: An application to time‐series data for multiple air pollutants," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1521-1542, November.
    12. Hauber, Philipp & Schumacher, Christian, 2021. "Precision-based sampling with missing observations: A factor model application," Discussion Papers 11/2021, Deutsche Bundesbank.
    13. Sung, Bongjung & Lee, Jaeyong, 2023. "Covariance structure estimation with Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    14. Simon Freyaldenhoven, 2020. "Identification Through Sparsity in Factor Models," Working Papers 20-25, Federal Reserve Bank of Philadelphia.
    15. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," PSE Working Papers halshs-03626503, HAL.
    16. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    17. Veronika Ročková & Edward I. George, 2016. "Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1608-1622, October.
    18. Daniel R. Kowal & Antonio Canale, 2021. "Semiparametric Functional Factor Models with Bayesian Rank Selection," Papers 2108.02151, arXiv.org, revised May 2022.
    19. Leung, Dennis & Drton, Mathias, 2016. "Order-invariant prior specification in Bayesian factor analysis," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 60-66.
    20. Mohsen Maleki & Darren Wraith, 2019. "Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework," Computational Statistics, Springer, vol. 34(3), pages 1039-1053, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2211.00671. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.