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Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution

  • Identification data

    Identifier: imarina:6184566
    Authors:
    Lorenzo-Seva, UrbanoFerrando, Pere J
    Abstract:
    Least-squares exploratory factor analysis based on tetrachoric/polychoric correlations is a robust, defensible and widely used approach for performing item analysis, especially in the first stages of scale development. A relatively common problem in this scenario, however, is that the inter-item correlation matrix fails to be positive definite. This paper, which is largely intended for practitioners, aims to provide a didactic discussion about the causes, consequences and remedies of this problem. The discussion is more applied than statistical and based on the factor analysis model, and the problem is linked to that of improper solutions. Solutions for preventing the problem from occurring, and the smoothing corrections available at present are described and discussed. A new smoothing algorithm is also proposed.
  • Others:

    Author, as appears in the article.: Lorenzo-Seva, Urbano; Ferrando, Pere J
    Department: Psicologia
    URV's Author/s: Ferrando Piera, Pere Joan / Lorenzo Seva, Urbano
    Keywords: Smoothing method Robust estimation Polychoric correlation Not positive definite Heywood cases
    Abstract: Least-squares exploratory factor analysis based on tetrachoric/polychoric correlations is a robust, defensible and widely used approach for performing item analysis, especially in the first stages of scale development. A relatively common problem in this scenario, however, is that the inter-item correlation matrix fails to be positive definite. This paper, which is largely intended for practitioners, aims to provide a didactic discussion about the causes, consequences and remedies of this problem. The discussion is more applied than statistical and based on the factor analysis model, and the problem is linked to that of improper solutions. Solutions for preventing the problem from occurring, and the smoothing corrections available at present are described and discussed. A new smoothing algorithm is also proposed.
    Thematic Areas: Sociology and political science Sociologia i política Social sciences, mathematical methods Psychology Psicología Modeling and simulation Mathematics, interdisciplinary applications Matemática / probabilidade e estatística General o multidisciplinar General economics,econometrics and finance General decision sciences Economics, econometrics and finance (miscellaneous) Economics, econometrics and finance (all) Economia Decision sciences (miscellaneous) Decision sciences (all) Ciencias sociales
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 1070-5511
    Author's mail: urbano.lorenzo@urv.cat perejoan.ferrando@urv.cat
    Author identifier: 0000-0001-5369-3099 0000-0002-3133-5466
    Record's date: 2024-10-12
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.tandfonline.com/doi/full/10.1080/10705511.2020.1735393
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Structural Equation Modeling-A Multidisciplinary Journal. 28 (1): 138-147
    APA: Lorenzo-Seva, Urbano; Ferrando, Pere J (2021). Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution. Structural Equation Modeling-A Multidisciplinary Journal, 28(1), 138-147. DOI: 10.1080/10705511.2020.1735393
    Article's DOI: 10.1080/10705511.2020.1735393
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    Publication Type: Journal Publications
  • Keywords:

    Decision Sciences (Miscellaneous),Economics, Econometrics and Finance (Miscellaneous),Mathematics, Interdisciplinary Applications,Modeling and Simulation,Social Sciences, Mathematical Methods,Sociology and Political Science
    Smoothing method
    Robust estimation
    Polychoric correlation
    Not positive definite
    Heywood cases
    Sociology and political science
    Sociologia i política
    Social sciences, mathematical methods
    Psychology
    Psicología
    Modeling and simulation
    Mathematics, interdisciplinary applications
    Matemática / probabilidade e estatística
    General o multidisciplinar
    General economics,econometrics and finance
    General decision sciences
    Economics, econometrics and finance (miscellaneous)
    Economics, econometrics and finance (all)
    Economia
    Decision sciences (miscellaneous)
    Decision sciences (all)
    Ciencias sociales
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