Permutimin: Factor Rotation to Simple Structure with Permutation of Variables

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Factor rotation aims to achieve a simple structure in loading matrices.
• Thurstone's definition of simple structure specifies zero and nonzero elements.
• Existing methods may not optimally align target structures with loading matrices.

Purpose of the Study:

• To introduce Permutimin, a new factor rotation technique.
• To directly implement Thurstone's simple structure definition.
• To address the challenge of associating target matrix rows with loading matrix rows.

Main Methods:

• Developed a novel rotation technique named Permutimin.
• Simultaneously rotates a loading matrix and permutes a target matrix.
• Optimally matches the rotated loading matrix to the permuted target matrix in a least squares sense.
• Modified Thurstone's definition to uniquely specify the target matrix.

Main Results:

• Permutimin provides a direct implementation of Thurstone's simple structure.
• The technique effectively handles the association between target and loading matrix rows.
• Illustrations with real data demonstrate Permutimin's application and effectiveness.

Conclusions:

• Permutimin offers a new approach to factor rotation.
• The method's novelty lies in its use of permutation for optimal matching.
• Further discussion explores Permutimin's relationship with Procrustes rotation.