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A Simulation-Based Scaled Test Statistic for Assessing Model-Data Fit in Least-Squares Unrestricted Factor-Analysis Solutions

  • Identification data

    Identifier: imarina:9326008
    Authors:
    Lorenzo-Seva, UrbanoFerrando, Pere J
    Abstract:
    A shortcoming of least-squares unrestricted factor analysis (UFA) procedures, which are widely used in psychometric applications is that a test statistic for assessing model-data fit cannot be easily derived from the minimum fit function value. This paper proposes a chi-square type goodness-of-fit test statistic intended for the principal-axis, MINRES, and minimum-rank UFA procedures. The statistic is empirically obtained via intensive simulation based on a two-stage approach. First, a distribution of minimum fit function values is obtained from a scenario in which the null hypothesis of perfect model-data fit holds. Second, the obtained statistic is non-linearly transformed so that it has its first four moments equal to those of the theoretical reference chi-square distribution with the appropriate degrees of freedom. Extensions of the basic statistic are next proposed that include comparative and relative indexes based on it. Tests of close-fit and power assessment derived from the basic statistic are 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: Unrestricted factor analysis Uls Principal axis factoring Power analysis Minres Minimum rank factor analysis Goodness-of-fit indices Chi square test of fit statistic
    Abstract: A shortcoming of least-squares unrestricted factor analysis (UFA) procedures, which are widely used in psychometric applications is that a test statistic for assessing model-data fit cannot be easily derived from the minimum fit function value. This paper proposes a chi-square type goodness-of-fit test statistic intended for the principal-axis, MINRES, and minimum-rank UFA procedures. The statistic is empirically obtained via intensive simulation based on a two-stage approach. First, a distribution of minimum fit function values is obtained from a scenario in which the null hypothesis of perfect model-data fit holds. Second, the obtained statistic is non-linearly transformed so that it has its first four moments equal to those of the theoretical reference chi-square distribution with the appropriate degrees of freedom. Extensions of the basic statistic are next proposed that include comparative and relative indexes based on it. Tests of close-fit and power assessment derived from the basic statistic are also proposed.
    Thematic Areas: Social sciences, mathematical methods Social sciences (miscellaneous) Social sciences (all) Psychology, mathematical Psychology (miscellaneous) Psychology (all) Psicología General social sciences General psychology Ciencias sociales
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    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://meth.psychopen.eu/index.php/meth/article/view/9839
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Methodology-European Journal Of Research Methods For The Behavioral And Social Sciences. 19 (2): 96-115
    APA: Lorenzo-Seva, Urbano; Ferrando, Pere J (2023). A Simulation-Based Scaled Test Statistic for Assessing Model-Data Fit in Least-Squares Unrestricted Factor-Analysis Solutions. Methodology-European Journal Of Research Methods For The Behavioral And Social Sciences, 19(2), 96-115. DOI: 10.5964/meth.9839
    Article's DOI: 10.5964/meth.9839
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2023
    Publication Type: Journal Publications
  • Keywords:

    Psychology (Miscellaneous),Psychology, Mathematical,Social Sciences (Miscellaneous),Social Sciences, Mathematical Methods
    Unrestricted factor analysis
    Uls
    Principal axis factoring
    Power analysis
    Minres
    Minimum rank factor analysis
    Goodness-of-fit indices
    Chi square test of fit statistic
    Social sciences, mathematical methods
    Social sciences (miscellaneous)
    Social sciences (all)
    Psychology, mathematical
    Psychology (miscellaneous)
    Psychology (all)
    Psicología
    General social sciences
    General psychology
    Ciencias sociales
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