IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v14y2020i4d10.1007_s11634-020-00400-z.html
   My bibliography  Save this article

The ultrametric correlation matrix for modelling hierarchical latent concepts

Author

Listed:
  • Carlo Cavicchia

    (University of Rome La Sapienza)

  • Maurizio Vichi

    (University of Rome La Sapienza)

  • Giorgia Zaccaria

    (University of Rome La Sapienza)

Abstract

Many relevant multidimensional phenomena are defined by nested latent concepts, which can be represented by a tree-structure supposing a hierarchical relationship among manifest variables. The root of the tree is a general concept which includes more specific ones. The aim of the paper is to reconstruct an observed data correlation matrix of manifest variables through an ultrametric correlation matrix which is able to pinpoint the hierarchical nature of the phenomenon under study. With this scope, we introduce a novel model which detects consistent latent concepts and their relationships starting from the observed correlation matrix.

Suggested Citation

  • Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2020. "The ultrametric correlation matrix for modelling hierarchical latent concepts," 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. 14(4), pages 837-853, December.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:4:d:10.1007_s11634-020-00400-z
    DOI: 10.1007/s11634-020-00400-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-020-00400-z
    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/s11634-020-00400-z?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. Yiu-Fai Yung & David Thissen & Lori McLeod, 1999. "On the relationship between the higher-order factor model and the hierarchical factor model," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 113-128, June.
    2. Karl Holzinger & Frances Swineford, 1937. "The Bi-factor method," Psychometrika, Springer;The Psychometric Society, vol. 2(1), pages 41-54, March.
    3. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    4. Harold Bechtoldt, 1961. "An empirical study of the factor analysis stability hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 26(4), pages 405-432, December.
    5. John Schmid & John Leiman, 1957. "The development of hierarchical factor solutions," Psychometrika, Springer;The Psychometric Society, vol. 22(1), pages 53-61, March.
    6. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    7. Robert Jennrich & Peter Bentler, 2011. "Exploratory Bi-Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 537-549, October.
    8. Robert Wherry, 1959. "Hierarchical factor solutions without rotation," Psychometrika, Springer;The Psychometric Society, vol. 24(1), pages 45-51, March.
    9. Matthijs Warrens, 2015. "Some Relationships Between Cronbach’s Alpha and the Spearman-Brown Formula," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 127-137, April.
    10. Robert Jennrich & Peter Bentler, 2012. "Exploratory Bi-factor Analysis: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 442-454, July.
    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. 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.
    2. 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.

    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. Carlo Cavicchia & Maurizio Vichi, 2022. "Second-Order Disjoint Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 289-309, March.
    2. Niels G. Waller, 2018. "Direct Schmid–Leiman Transformations and Rank-Deficient Loadings Matrices," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 858-870, December.
    3. 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.
    4. Michela Gnaldi, 2017. "A multidimensional IRT approach for dimensionality assessment of standardised students’ tests in mathematics," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1167-1182, May.
    5. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2022. "Gaussian mixture model with an extended ultrametric covariance structure," 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. 16(2), pages 399-427, June.
    6. 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.
    7. Robert Jennrich & Peter Bentler, 2012. "Exploratory Bi-factor Analysis: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 442-454, July.
    8. Li Cai, 2015. "Lord–Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 535-559, June.
    9. Robert Jennrich & Peter Bentler, 2011. "Exploratory Bi-Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 537-549, October.
    10. Matthijs J. Warrens, 2021. "Kappa coefficients for dichotomous-nominal classifications," 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. 15(1), pages 193-208, March.
    11. Kan, Kees-Jan & van der Maas, Han L.J. & Levine, Stephen Z., 2019. "Extending psychometric network analysis: Empirical evidence against g in favor of mutualism?," Intelligence, Elsevier, vol. 73(C), pages 52-62.
    12. Jeanne A. Teresi & Katja Ocepek-Welikson & John A. Toner & Marjorie Kleinman & Mildred Ramirez & Joseph P. Eimicke & Barry J. Gurland & Albert Siu, 2017. "Methodological Issues in Measuring Subjective Well-Being and Quality-of-Life: Applications to Assessment of Affect in Older, Chronically and Cognitively Impaired, Ethnically Diverse Groups Using the F," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 12(2), pages 251-288, June.
    13. David J. Hessen, 2017. "Lower Bounds to the Reliabilities of Factor Score Estimators," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 648-659, September.
    14. P. Bentler, 1986. "Structural modeling and psychometrika: An historical perspective on growth and achievements," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 35-51, March.
    15. Harold Bechtoldt, 1961. "An empirical study of the factor analysis stability hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 26(4), pages 405-432, December.
    16. Charley Xia & Sarah J. Pickett & David C. M. Liewald & Alexander Weiss & Gavin Hudson & W. David Hill, 2023. "The contributions of mitochondrial and nuclear mitochondrial genetic variation to neuroticism," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    17. Torbjørn Torsheim & Franco Cavallo & Kate Ann Levin & Christina Schnohr & Joanna Mazur & Birgit Niclasen & Candace Currie, 2016. "Psychometric Validation of the Revised Family Affluence Scale: a Latent Variable Approach," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 9(3), pages 771-784, September.
    18. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2018. "CFA Models with a General Factor and Multiple Sets of Secondary Factors," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 785-808, December.
    19. Frank Rijmen & Minjeong Jeon & Matthias von Davier & Sophia Rabe-Hesketh, 2014. "A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 235-256, August.
    20. Sayed H. Kadhem & Aristidis K. Nikoloulopoulos, 2023. "Bi-factor and Second-Order Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 132-157, March.

    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:14:y:2020:i:4:d:10.1007_s11634-020-00400-z. 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.