Independent component analysis as a rotation method: a very different solution to Thurstone's box problem

Area of Science:

• Multivariate statistics
• Psychometrics
• Machine learning

Background:

• The Thurstone box problem is a classic challenge in exploratory factor analysis.
• Principal component analysis (PCA) is commonly used for initial component extraction.
• Traditional methods focus on simple loadings, which may not always recover underlying dimensions accurately.

Purpose of the Study:

• To investigate the application of independent component analysis (ICA) to the Thurstone box problem.
• To demonstrate how rotating components towards independence, rather than simplicity, can improve dimension recovery.
• To provide an introduction to ICA from a factor analysis perspective.

Main Methods:

• Utilizing principal component analysis (PCA) for initial extraction of loadings and components.
• Applying component rotation towards independence as a criterion.
• Employing a general rotation algorithm for component transformation.
• Leveraging methods from independent component analysis (ICA).

Main Results:

• Rotation towards component independence accurately recovers the dimensions of each box.
• This approach also successfully produces simple loadings.
• Demonstrates the efficacy of ICA in solving the Thurstone box problem.

Conclusions:

• Independent component analysis (ICA) offers a powerful alternative for solving the Thurstone box problem.
• Rotating components for independence is superior to rotating for simplicity in this context.
• This work bridges factor analysis and independent component analysis.