Rotation Criteria and Hypothesis Testing for Exploratory Factor Analysis: Implications for Factor Pattern Loadings and Interfactor Correlations

• Published in: Educational and psychological measurement 2011-02, Vol.71 (1), p.95-113
• Main Authors: Schmitt, Thomas A., Sass, Daniel A.
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Correlation; Criteria; Discriminant analysis; Error of Measurement; Factor Analysis; Factor Structure; Fundamental and applied biological sciences. Psychology; Hypotheses; Hypothesis Testing; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Researchers; Statistics. Mathematics
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164410387348

Exploratory factor analysis (EFA) has long been used in the social sciences to depict the relationships between variables/items and latent traits. Researchers face many choices when using EFA, including the choice of rotation criterion, which can be difficult given that few research articles have discussed and/or demonstrated their differences. The goal of the current study is to help fill this gap by reviewing and demonstrating the utility of several rotation criteria. Furthermore, this article discusses and demonstrates the importance of using factor pattern loading standard errors for hypothesis testing. The choice of a rotation criterion and the use of standard errors in evaluating factor loadings are essential so researchers can make informed decisions concerning the factor structure. This study demonstrates that depending on the rotation criterion selected, and the complexity of the factor pattern matrix, the interfactor correlations and factor pattern loadings can vary substantially. It is also illustrated that the magnitude of the factor loading standard errors can result in different factor structures. Implications and future directions are discussed.