Minimum average partial correlation and parallel analysis: The influence of oblique structures

ABSTRACT

Parallel analysis (Horn 1965) and the minimum average partial correlation (MAP; Velicer 1976) have been widely spread as optimal solutions to identify the correct number of axes in principal component analysis. Previous results showed, however, that they become inefficient when variables belonging to different components strongly correlate. Simulations are used to assess their power to detect the dimensionality of data sets with oblique structures. Overall, MAP had the best performances as it was more powerful and accurate than PA when the component structure was modestly oblique. However, both stopping rules performed poorly in the presence of highly oblique factors.

KEYWORDS:

• Monte Carlo simulations
• minimum average partial correlation
• parallel analysis
• principal component analysis
• stopping rules

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H25
• 11K45

Acknowledgement

The author would like to thank André Achim and Anne-Josée Piazza for their helpful comments on the manuscript.