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Dimensionality assessment of ordered polytomous items with parallel analysis

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Timmerman, Marieke E., Lorenzo-Seva, Urbano·2011·Psychological Methods

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Abstract

Parallel analysis (PA) is an often-recommended approach for assessment of the dimensionality of a variable set. PA is known in different variants, which may yield different dimensionality indications. In this article, the authors considered the most appropriate PA procedure to assess the number of common factors underlying ordered polytomously scored variables. They proposed minimum rank factor analysis (MRFA) as an extraction method, rather than the currently applied principal component analysis (PCA) and principal axes factoring. A simulation study, based on data with major and minor factors, showed that all procedures consistently point at the number of major common factors. A polychoric-based PA slightly outperformed a Pearson-based PA, but convergence problems may hamper its empirical application. In empirical practice, PA-MRFA with a 95% threshold based on polychoric correlations or, in case of nonconvergence, Pearson correlations with mean thresholds appear to be a good choice for identification of the number of common factors. PA-MRFA is a common-factor-based method and performed best in the simulation experiment. PA based on PCA with a 95% threshold is second best, as this method showed good performances in the empirically relevant conditions of the simulation experiment.

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Authors: Timmerman, M. E., & Lorenzo-Seva, U.
Affiliations: University of Groningen (NL)
ORCID: Timmerman, Marieke E.
Lorenzo-Seva, Urbano
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 2011-06
Volume: 16
Issue: 2
Pages: 209-220
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/a0023353
OpenAlex: W2100515418
Cited by: 1,634
References: 58
Citations by year: 2026: 104 · 2025: 143 · 2024: 158 · 2023: 181 · 2022: 179 · 2021: 183 · 2020: 154 · 2019: 102 · 2018: 114 · 2017: 81 · 2016: 76 · 2015: 68 · 2014: 37 · 2013: 35 · 2012: 16
FWCI: 38.22
Type: journal article
Language: en
Open access: green
research.rug.nl
Licence: other-oa
Locations: Psychological Methods (publishedVersion)
PubMed (publishedVersion)
University of Groningen research database (University of Groningen / Centre for Information Technology) (publishedVersion, other-oa)
University of Groningen research database (University of Groningen / Centre for Information Technology) (submittedVersion)
Funders: Ministry of Universities (2009SGR1549)
Spanish Ministry of Education and Science (PSI2008-00236/PSIC)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
Keywords: parallel analysis, dimensionality analysis, polychoric correlation, Pearson correlation, principal component analysis
MeSH terms: Data Interpretation, Statistical, Factor Analysis, Statistical, Humans, Mathematical Computing, Psychology, Research, Research Design, Statistics as Topic, Models, Statistical, Sample Size, Principal Component Analysis

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Dimensionality assessment of ordered polytomous items with parallel analysis

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