Rotation to Sparse Loadings Using Losses and Related Inference Problems.

Area of Science:

• Statistics
• Psychometrics

Background:

• Exploratory Factor Analysis (EFA) is crucial for uncovering latent structures in multivariate data.
• Rotation and regularized estimation are common EFA techniques for interpretable loading matrices.

Purpose of the Study:

• Propose a new family of oblique rotations for EFA.
• Develop model selection and post-selection inference procedures.
• Enhance statistical accuracy and computational efficiency, especially for sparse data.

Main Methods:

• Introduced component-wise loss functions for oblique rotations, closely linked to regularized estimators.
• Developed an iteratively reweighted gradient projection algorithm for nonsmooth optimization.
• Established theoretical consistency for estimation, model selection, and post-selection inference.

Main Results:

• The proposed method demonstrates superior performance over traditional rotation and regularized estimation for sparse loading matrices.
• Simulation studies confirm the method's effectiveness.
• Application to the Big Five personality assessment illustrates practical utility.

Conclusions:

• The novel oblique rotation method offers a statistically accurate and computationally efficient approach to EFA.
• It provides robust model selection and post-selection inference capabilities.
• This method advances the analysis of latent structures, particularly in sparse scenarios.