Fully and partially exploratory factor analysis with bi-level Bayesian regularization.

Area of Science:

• Statistics
• Psychometrics
• Machine Learning

Background:

• Exploratory Factor Analysis (EFA) is crucial for identifying underlying structures in data.
• Existing EFA methods can struggle with factor selection and simultaneous parameter estimation.
• Incorporating prior knowledge into EFA models remains an area for development.

Purpose of the Study:

• To introduce novel fully and partially exploratory factor analysis (EFA) models utilizing bi-level Bayesian regularization.
• To enable robust factor selection and parameter estimation through sparse modeling.
• To allow incorporation of partial prior knowledge and handle an unknown number of factors in partially EFA.

Main Methods:

• Development of bi-level Bayesian regularization for both fully and partially exploratory factor analysis.
• Conceptualization of factors at the group level and loadings at the individual level for sparse modeling.
• Simultaneous estimation of model parameters and tuning parameters, providing interval estimates.

Main Results:

• Both fully and partially EFA models demonstrated satisfactory performance under reasonable conditions.
• The models exhibited robustness against the interference of local dependence.
• Partially EFA, when supplied with appropriate information, outperformed the fully EFA version and performed well under extreme conditions.

Conclusions:

• The proposed bi-level Bayesian regularization models offer a unified approach for factor extraction and parameter estimation in EFA.
• Partially EFA provides a flexible framework for incorporating prior information and handling uncertainty in the number of factors.
• The R package LAWBL implements these advanced EFA techniques for practical application.