Dimensionality assessment of ordered polytomous items with parallel analysis

Timmerman, M. E. & Lorenzo-Seva, U., Jun-2011, In : Psychological Methods. 16, 2, p. 209-220 12 p.

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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.

Original languageEnglish
Pages (from-to)209-220
Number of pages12
JournalPsychological Methods
Issue number2
Publication statusPublished - Jun-2011


  • number of common factors, exploratory factor analysis, minimum rank factor analysis, principal component analysis, polychoric correlation, tetrachoric correlation, EXPLORATORY FACTOR-ANALYSIS, DATA CORRELATION-MATRICES, 95TH PERCENTILE EIGENVALUES, PRINCIPAL COMPONENTS, LATENT ROOTS, CORRELATION-COEFFICIENT, ANALYSIS CRITERION, ROBUST ESTIMATION, COMMON FACTORS, MONTE-CARLO

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