A Simple Method for Procrustean Rotation in Factor Analysis Using Majorization Theory.

Area of Science:

• Psychometrics
• Factor Analysis
• Mathematical Statistics

Background:

• Analytical rotation schemes aim to approximate Thurstone's simple structure by separating factor loadings into near-zero and near-unity groups.
• The PROMAX method uses a power transformation to create a target for Procrustean rotation, a common approach in factor analysis.

Purpose of the Study:

• To propose a novel analytical rotation technique based on vector majorization for approximating simple structure.
• To offer a mathematically superior alternative to existing methods like PROMAX for target generation in Procrustean rotation.

Main Methods:

• Development of a new analytical rotation method utilizing principles of vector majorization.
• Application of the proposed method to generate rotation targets for achieving simple structure.
• Comparison with existing techniques, such as the PROMAX method.

Main Results:

• The proposed vector majorization technique provides a mathematically well-motivated approach for approximating simple structure.
• The method effectively splits factor loadings into distinct groups tending toward zero and unity.
• Illustrative examples demonstrate the practical application and effectiveness of the new technique.

Conclusions:

• The vector majorization method offers a robust and theoretically grounded alternative for analytical rotation in factor analysis.
• This approach enhances the approximation of Thurstone's simple structure, a key goal in psychometric research.