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

  • Datos identificativos

    Identificador: imarina:6184566
    Autores:
    Lorenzo-Seva, UrbanoFerrando, Pere J
    Resumen:
    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.
  • Otros:

    Autor según el artículo: Lorenzo-Seva, Urbano; Ferrando, Pere J
    Departamento: Psicologia
    Autor/es de la URV: Ferrando Piera, Pere Joan / Lorenzo Seva, Urbano
    Palabras clave: Smoothing method Robust estimation Polychoric correlation Not positive definite Heywood cases
    Resumen: 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.
    Áreas temáticas: 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
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 1070-5511
    Direcció de correo del autor: urbano.lorenzo@urv.cat perejoan.ferrando@urv.cat
    Identificador del autor: 0000-0001-5369-3099 0000-0002-3133-5466
    Fecha de alta del registro: 2024-10-12
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://www.tandfonline.com/doi/full/10.1080/10705511.2020.1735393
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Structural Equation Modeling-A Multidisciplinary Journal. 28 (1): 138-147
    Referencia de l'ítem segons les normes 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
    DOI del artículo: 10.1080/10705511.2020.1735393
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2021
    Tipo de publicación: Journal Publications
  • Palabras clave:

    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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