A partially confirmatory approach to scale development with the Bayesian Lasso.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Factor analysis encompasses exploratory and confirmatory approaches, with varying levels of researcher input.
• Bayesian regularization methods offer enhanced flexibility in scale development.

Purpose of the Study:

• To propose a partially confirmatory factor analysis approach integrating Bayesian Lasso methods.
• To simultaneously address loading and residual structures in scale development.

Main Methods:

• Utilizing Bayesian Lasso for regression and covariance matrices.
• Implementing a one-step procedure with specified item loadings and a two-step procedure with factor loadings.
• Employing Bayesian hierarchical formulation with Markov Chain Monte Carlo estimation and Lasso or regular priors.

Main Results:

• The proposed approach effectively estimates both loading and residual structures simultaneously.
• Evaluated through simulated and real data, demonstrating validity and robustness.

Conclusions:

• The partially confirmatory approach provides a flexible and powerful method for scale development.
• It enhances the integration of prior knowledge within factor analysis frameworks.