IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v11y2017i3d10.1007_s11634-016-0263-9.html
   My bibliography  Save this article

Disjoint factor analysis with cross-loadings

Author

Listed:
  • Maurizio Vichi

    (Sapienza University of Rome)

Abstract

Disjoint factor analysis (DFA) is a new latent factor model that we propose here to identify factors that relate to disjoint subsets of variables, thus simplifying the loading matrix structure. Similarly to exploratory factor analysis (EFA), the DFA does not hypothesize prior information on the number of factors and on the relevant relations between variables and factors. In DFA the population variance–covariance structure is hypothesized block diagonal after the proper permutation of variables and estimated by Maximum Likelihood, using an Coordinate Descent type algorithm. Inference on parameters on the number of factors and to confirm the hypothesized simple structure are provided. Properties such as scale equivariance, uniqueness, optimal simplification of loadings are satisfied by DFA. Relevant cross-loadings are also estimated in case they are detected from the best DFA solution. DFA has also the option to constrain a variable to load on a pre-specified factor so that the researcher can assume, a priori, some relations between variables and loadings. A simulation study shows performances of DFA and an application to optimally identify the dimensions of well-being is used to illustrate characteristics of the new methodology. A final discussion concludes the paper.

Suggested Citation

  • Maurizio Vichi, 2017. "Disjoint factor analysis with cross-loadings," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 563-591, September.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0263-9
    DOI: 10.1007/s11634-016-0263-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-016-0263-9
    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/s11634-016-0263-9?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. Richard Sherin, 1966. "A matrix formulation of Kaiser's varimax criterion," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 535-538, December.
    2. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    3. Shen, Haipeng & Huang, Jianhua Z., 2008. "Sparse principal component analysis via regularized low rank matrix approximation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1015-1034, July.
    4. Masaya Ito & Satomi Nakajima & Daisuke Fujisawa & Mitsunori Miyashita & Yoshiharu Kim & M Katherine Shear & Angela Ghesquiere & Melanie M Wall, 2012. "Brief Measure for Screening Complicated Grief: Reliability and Discriminant Validity," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-6, February.
    5. Armstrong, J. Scott & Soelberg, Peer, 1968. "On the interpretation of factor analysis," MPRA Paper 81665, University Library of Munich, Germany.
    6. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    7. Jos Berge, 1984. "A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least-squares sense," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 347-358, September.
    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. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2023. "Hierarchical disjoint principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 537-574, September.
    2. Naoto Yamashita, 2023. "Principal component analysis constrained by layered simple structures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 347-367, June.
    3. Carlo Cavicchia & Maurizio Vichi, 2022. "Second-Order Disjoint Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 289-309, March.
    4. Cavicchia, Carlo & Sarnacchiaro, Pasquale & Vichi, Maurizio, 2021. "A composite indicator for the waste management in the EU via Hierarchical Disjoint Non-Negative Factor Analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    5. Carlo Cavicchia & Maurizio Vichi, 2021. "Statistical Model-Based Composite Indicators for Tracking Coherent Policy Conclusions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 449-479, August.
    6. Adelaide Freitas & Eloísa Macedo & Maurizio Vichi, 2021. "An empirical comparison of two approaches for CDPCA in high-dimensional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1007-1031, 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 Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    2. 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.
    3. Jin, Shaobo & Moustaki, Irini & Yang-Wallentin, Fan, 2018. "Approximated penalized maximum likelihood for exploratory factor analysis: an orthogonal case," LSE Research Online Documents on Economics 88118, London School of Economics and Political Science, LSE Library.
    4. Jos Berge, 1995. "Suppressing permutations or rigid planar rotations: A remedy against nonoptimal varimax rotations," Psychometrika, Springer;The Psychometric Society, vol. 60(3), pages 437-446, September.
    5. Shaobo Jin & Irini Moustaki & Fan Yang-Wallentin, 2018. "Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 628-649, September.
    6. Robert Jennrich, 2001. "A simple general procedure for orthogonal rotation," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 289-306, June.
    7. Nerea González-García & Ana Belén Nieto-Librero & Purificación Galindo-Villardón, 2023. "CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 5-19, March.
    8. Yoshio Takane & Kwanghee Jung & Heungsun Hwang, 2010. "An acceleration method for Ten Berge et al.’s algorithm for orthogonal INDSCAL," Computational Statistics, Springer, vol. 25(3), pages 409-428, September.
    9. Roman A. Jandarov & Lianne A. Sheppard & Paul D. Sampson & Adam A. Szpiro, 2017. "A novel principal component analysis for spatially misaligned multivariate air pollution data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 3-28, January.
    10. Rosember Guerra-Urzola & Katrijn Van Deun & Juan C. Vera & Klaas Sijtsma, 2021. "A Guide for Sparse PCA: Model Comparison and Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 893-919, December.
    11. Marie Chavent & Vanessa Kuentz-Simonet & Jérôme Saracco, 2012. "Orthogonal rotation in PCAMIX," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(2), pages 131-146, July.
    12. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," PSE Working Papers halshs-03626503, HAL.
    13. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    14. Guerra Urzola, Rosember & Van Deun, Katrijn & Vera, J. C. & Sijtsma, K., 2021. "A guide for sparse PCA : Model comparison and applications," Other publications TiSEM 4d35b931-7f49-444b-b92f-a, Tilburg University, School of Economics and Management.
    15. Seong-Yun Hong & Seonggook Moon & Sang-Hyun Chi & Yoon-Jae Cho & Jeon-Young Kang, 2022. "Local Sparse Principal Component Analysis for Exploring the Spatial Distribution of Social Infrastructure," Land, MDPI, vol. 11(11), pages 1-16, November.
    16. Mitzi Cubilla-Montilla & Ana Belén Nieto-Librero & M. Purificación Galindo-Villardón & Carlos A. Torres-Cubilla, 2021. "Sparse HJ Biplot: A New Methodology via Elastic Net," Mathematics, MDPI, vol. 9(11), pages 1-15, June.
    17. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    18. Fernando Castelló-Sirvent & Pablo Pinazo-Dallenbach, 2021. "Corruption Shock in Mexico: fsQCA Analysis of Entrepreneurial Intention in University Students," Mathematics, MDPI, vol. 9(14), pages 1-31, July.
    19. Matkovskyy, Roman, 2013. "To the Problem of Financial Safety Estimation: the Index of Financial Safety of Turkey," MPRA Paper 47673, University Library of Munich, Germany.
    20. Jha, Raghbendra & Murthy, K. V. Bhanu, 2003. "An inverse global environmental Kuznets curve," Journal of Comparative Economics, Elsevier, vol. 31(2), pages 352-368, June.

    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:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0263-9. 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.