Synonyms
Definition
A principal component analysis decomposes the covariance (or correlation) matrix into independent components, which comprise decreasing amounts of variance, reflected by their respective eigenvalues.
Introduction
In psychological research, measurement instruments, such as questionnaires or tests, usually comprise a set of items. Typically, these items are thought to belong together, which is statistically reflected by their covariance. To find the common components in the covariance structure of a set of items, principal components can be mathematically identified through analysis of the covariance matrix of these items. All items receive loadings in each of the components that quantify their respective relationships with them in terms of the amount of variance they share. Even though the analysis of the principal components is not yet a procedure to analyze the assumed latent structure of a hypothetical construct that could be responsible for the covariance of...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Guttman, L. (1954). Some necessary conditions for common factor analysis. Psychometrika, 19, 149–162.
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185.
Hubbard, R., & Allen, S. J. (1987). An empirical comparison of alternative methods for principal component extraction. Journal of Business Research, 15(2), 173–190.
Jolliffe, I. (2002). Principal component analysis (2nd ed.). New York: Springer.
Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151.
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston: Pearson.
Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321–327.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this entry
Cite this entry
Hilbert, S., Bühner, M. (2020). Principal Components Analysis. In: Zeigler-Hill, V., Shackelford, T.K. (eds) Encyclopedia of Personality and Individual Differences. Springer, Cham. https://doi.org/10.1007/978-3-319-24612-3_1340
Download citation
DOI: https://doi.org/10.1007/978-3-319-24612-3_1340
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24610-9
Online ISBN: 978-3-319-24612-3
eBook Packages: Behavioral Science and PsychologyReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences