Update on the parallel analysis criterion for determining the number of principal components

Area of Science:

• Multivariate statistics
• Psychometrics
• Data analysis

Background:

• Principal component analysis (PCA) is a common dimensionality reduction technique.
• Determining the optimal number of components is crucial for valid interpretation.
• Parallel analysis is a widely used criterion for this purpose.

Purpose of the Study:

• To review recent advancements in parallel analysis methods.
• To illustrate the application of the parallel analysis criterion with practical examples.
• To highlight potential discrepancies between different approaches to parallel analysis.

Main Methods:

• Review of literature on parallel analysis techniques.
• Application and comparison of parallel analysis with unities in the diagonal.
• Illustration using three distinct datasets or scenarios.

Main Results:

• Parallel analysis, particularly with unities in the diagonal, is a valuable tool.
• Discrepancies were observed between the results of various parallel analysis approaches.
• The effectiveness of parallel analysis can vary depending on the specific dataset and method.

Conclusions:

• The parallel analysis criterion is recommended for component selection in PCA.
• Investigators should utilize parallel analysis in conjunction with other criteria.
• A multi-criterion approach ensures more reliable decisions regarding the number of principal components.