Casey's Method For Fitting Hyperplanes From An Intermediate Orthomax Solution.

Area of Science:

• Psychometrics
• Multivariate Statistics

Background:

• Varimax rotation is a common technique in factor analysis for simplifying complex data structures.
• Orthonormal solutions from varimax rotation may not always represent the underlying theoretical structure accurately.

Purpose of the Study:

• To introduce a novel method, Casey's Method, for deriving oblique factor solutions from varimax solutions.
• To provide a practical procedure for enhancing the interpretability of factor analysis results.

Main Methods:

• Dichotomizing varimax factor loadings into 'large' and 'small' based on a specific criterion involving the mean of square roots of absolute values.
• Fitting test vectors associated with 'small' loadings to a hyperplane, following Tucker's approach.
• Applying this procedure across all varimax factors to generate an oblique solution.

Main Results:

• Casey's Method generates an oblique solution that closely corresponds to the original orthonormal varimax solution.
• The method provides a systematic way to obtain oblique solutions, potentially improving factor interpretability.
• Four illustrative examples demonstrate the application and utility of Casey's Method.

Conclusions:

• Casey's Method offers a valuable alternative for obtaining oblique factor solutions, complementing existing techniques.
• This method facilitates a closer alignment between statistical solutions and theoretical constructs in factor analysis.
• The procedure is practical and demonstrated to be effective across diverse datasets.