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Updated: May 17, 2026
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
A new look at Horn's parallel analysis with ordinal variables.
Luis Eduardo Garrido1, Francisco José Abad1, Vicente Ponsoda1
1Departamento de Psicologia Social y Metodologia.
Psychological Methods
|October 11, 2012
Summary
Parallel analysis (PA) with polychoric correlations is recommended for assessing ordinal data dimensionality. While PA with Pearson correlations can be inaccurate with skewed data, polychoric correlations offer greater robustness and accuracy in factor retention.
Area of Science:
- Psychometrics
- Statistical analysis
- Data science
Background:
- Horn's parallel analysis (PA) is a factor retention method.
- Previous studies showed unexpected results using PA with ordinal variables and Pearson correlations compared to polychoric correlations.
Purpose of the Study:
- To clarify the performance of PA with ordinal data.
- To investigate the impact of data and method factors on PA accuracy.
Main Methods:
- A comprehensive simulation study was conducted.
- Manipulated 7 data factors (sample size, factor loading, variables/factor, number of factors, factor correlation, response categories, skewness) and 3 PA method factors (correlation type, extraction method, eigenvalue percentile).
Main Results:
- PA performance is sensitive to sample size, factor loadings, variables per factor, and factor correlations.
- PA with polychoric correlations is robust to skewness.
- PA with Pearson correlations is inaccurate with high skewness, often retaining spurious factors.
Conclusions:
- Recommend using PA with polychoric correlations for dimensionality assessment of ordinal data.
- Polychoric correlations provide more accurate factor retention with skewed ordinal variables.
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