A simulation-based scaled test statistic for assessing model-data fit in least-squares unrestricted factor-analysis solutions
Author(s) / Creator(s)
Lorenzo-Seva, Urbano
Ferrando, Pere J.
Abstract / Description
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.
Keyword(s)
chi square test of fit statistic goodness-of-fit indices principal axis factoring MINRES ULS minimum rank factor analysis unrestricted factor analysis power analysisPersistent Identifier
Date of first publication
2023-06-30
Journal title
Methodology
Volume
19
Issue
2
Page numbers
96–115
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Lorenzo-Seva, U. & Ferrando, P. J. (2023). A simulation-based scaled test statistic for assessing model-data fit in least-squares unrestricted factor-analysis solutions. Methodology, 19(2), 96-115. https://doi.org/10.5964/meth.9839
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Author(s) / Creator(s)Lorenzo-Seva, Urbano
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Author(s) / Creator(s)Ferrando, Pere J.
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PsychArchives acquisition timestamp2023-11-23T11:52:10Z
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Made available on2023-11-23T11:52:10Z
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Date of first publication2023-06-30
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Abstract / DescriptionA 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.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationLorenzo-Seva, U. & Ferrando, P. J. (2023). A simulation-based scaled test statistic for assessing model-data fit in least-squares unrestricted factor-analysis solutions. Methodology, 19(2), 96-115. https://doi.org/10.5964/meth.9839en_US
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ISSN1614-2241
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/9145
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.13665
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Language of contenteng
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PublisherPsychOpen GOLD
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Is version ofhttps://doi.org/10.5964/meth.9839
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Is related tohttps://doi.org/10.23668/psycharchives.12951
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Is related tohttps://doi.org/10.23668/psycharchives.12950
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Keyword(s)chi square test of fit statisticen_US
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Keyword(s)goodness-of-fit indicesen_US
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Keyword(s)principal axis factoringen_US
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Keyword(s)MINRESen_US
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Keyword(s)ULSen_US
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Keyword(s)minimum rank factor analysisen_US
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Keyword(s)unrestricted factor analysisen_US
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Keyword(s)power analysisen_US
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Dewey Decimal Classification number(s)150
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TitleA simulation-based scaled test statistic for assessing model-data fit in least-squares unrestricted factor-analysis solutionsen_US
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DRO typearticle
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Issue2
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Journal titleMethodology
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Page numbers96–115
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Volume19
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Visible tag(s)Version of Recorden_US