IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v87y2022i1d10.1007_s11336-021-09799-6.html
   My bibliography  Save this article

Second-Order Disjoint Factor Analysis

Author

Listed:
  • Carlo Cavicchia

    (Erasmus University Rotterdam)

  • Maurizio Vichi

    (University of Rome La Sapienza)

Abstract

Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which—respect to the second-order confirmatory factor analysis—is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated with the related factor and, therefore, the associated factor loadings are constrained to be nonnegative. A cyclic block coordinate descent algorithm is proposed to maximize the likelihood. We present a simulation study that investigates the ability to get reliable factors. Furthermore, the new model is applied to identify the underlying factors of well-being showing the characteristics of the new methodology. A final discussion completes the paper.

Suggested Citation

  • Carlo Cavicchia & Maurizio Vichi, 2022. "Second-Order Disjoint Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 289-309, March.
  • Handle: RePEc:spr:psycho:v:87:y:2022:i:1:d:10.1007_s11336-021-09799-6
    DOI: 10.1007/s11336-021-09799-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09799-6
    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/s11336-021-09799-6?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. Karl Holzinger, 1944. "A simple method of factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 9(4), pages 257-262, December.
    2. 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.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Giuseppe Munda & Michela Nardo, 2009. "Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1513-1523.
    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. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    7. 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.
    8. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Sparsest factor analysis for clustering variables: a matrix decomposition approach," 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. 12(3), pages 559-585, September.
    9. Raymond Cattell, 1947. "Confirmation and clarification of primary personality factors," Psychometrika, Springer;The Psychometric Society, vol. 12(3), pages 197-220, September.
    10. Salvatore Greco & Alessio Ishizaka & Menelaos Tasiou & Gianpiero Torrisi, 2019. "On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 61-94, January.
    11. Robert Wherry, 1959. "Hierarchical factor solutions without rotation," Psychometrika, Springer;The Psychometric Society, vol. 24(1), pages 45-51, March.
    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. Chi Yuan Chen, 2023. "Are Professors Satisfied With Their Jobs? The Factors That Influence Professors’ Job Satisfaction," SAGE Open, , vol. 13(3), pages 21582440231, July.
    2. Mariaelena Bottazzi Schenone & Elena Grimaccia & Maurizio Vichi, 2024. "Structural equation models for simultaneous modeling of air pollutants," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    3. Carlo Cavicchia & Pasquale Sarnacchiaro, 2024. "A new hierarchical composite indicator model for ranking the top 20 European football teams," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4033-4051, October.

    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 & 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.
    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.
    3. 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.
    4. 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.
    5. Matheus Pereira Libório & Oseias da Silva Martinuci & Sandro Laudares & Renata de Mello Lyrio & Alexei Manso Correa Machado & Patrícia Bernardes & Petr Ekel, 2020. "Measuring Intra-Urban Inequality with Structural Equation Modeling: A Theory-Grounded Indicator," Sustainability, MDPI, vol. 12(20), pages 1-18, October.
    6. 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.
    7. 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.
    8. 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.
    9. Milica Maricic & Jose A. Egea & Veljko Jeremic, 2019. "A Hybrid Enhanced Scatter Search—Composite I-Distance Indicator (eSS-CIDI) Optimization Approach for Determining Weights Within Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 497-537, July.
    10. Patrícia Bernardes & Petr Iakovlevitch Ekel & Sérgio Fernando Loureiro Rezende & Joel Gomes Pereira Júnior & Angélica Cidália Gouveia Santos & Maurício Andrade Rodrigues Costa & Rafael Lopes Carvalhai, 2022. "Cost of doing business index in Latin America," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(4), pages 2233-2252, August.
    11. Marek Walesiak & Grażyna Dehnel, 2023. "A Measurement of Social Cohesion in Poland’s NUTS2 Regions in the Period 2010–2019 by Applying Dynamic Relative Taxonomy to Interval-Valued Data," Sustainability, MDPI, vol. 15(4), pages 1-21, February.
    12. Öztürk, Elif Göksu & Guimarães, Paulo & Tavares Silva, Sandra, 2024. "Building a composite index using the multi-objective approach: An application to the case of human development," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    13. 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).
    14. Ruiz, Francisco & El Gibari, Samira & Cabello, José M. & Gómez, Trinidad, 2020. "MRP-WSCI: Multiple reference point based weak and strong composite indicators," Omega, Elsevier, vol. 95(C).
    15. 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.
    16. Paola Annoni & Manuela Scioni, 2022. "The Unbalance Penalisation Method for Metrics of Social Progress," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 162(3), pages 1093-1115, August.
    17. 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.
    18. 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.
    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. Matheus Pereira Libório & Lívia Maria Leite Silva & Petr Iakovlevitch Ekel & Letícia Ribeiro Figueiredo & Patrícia Bernardes, 2022. "Consensus-Based Sub-Indicator Weighting Approach: Constructing Composite Indicators Compatible with Expert Opinion," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(3), pages 1073-1099, December.

    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_s11336-021-09799-6. 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.