Parallel analysis approach for determining dimensionality in canonical correlation analysis

ABSTRACT

Canonical correlations are maximized correlation coefficients indicating the relationships between pairs of canonical variates that are linear combinations of the two sets of original variables. The number of non-zero canonical correlations in a population is called its dimensionality. Parallel analysis (PA) is an empirical method for determining the number of principal components or factors that should be retained in factor analysis. An example is given to illustrate for adapting proposed procedures based on PA and bootstrap modified PA to the context of canonical correlation analysis (CCA). The performances of the proposed procedures are evaluated in a simulation study by their comparison with traditional sequential test procedures with respect to the under-, correct- and over-determination of dimensionality in CCA.

KEYWORDS:

• Canonical correlations
• dimensionality
• parallel analysis
• bootstrap
• simulation

AMS SUBJECT CLASSIFICATION:

• 62H20
• 65C05

Acknowledgments

We would like to thank the editor for his encouragement and the anonymous referee, whose comments and suggestions have improved the presentation of the paper and have provided us new perspectives.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Gülhayat Gölbaşı Şimşek  http://orcid.org/0000-0002-8790-295X