Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis

Area of Science:

• Statistics
• Social Sciences
• Computational Statistics

Background:

• Factor analytic models are prevalent in social sciences for analyzing multidimensional data covariance structures.
• Common normal and inverse gamma priors for factor loadings and variances are computationally intensive and require extensive hyperparameter elicitation.
• Existing priors can lead to poorly behaved Gibbs samplers and posterior distribution impropriety issues.

Purpose of the Study:

• To propose a novel default, heavy-tailed prior distribution for factor analytic models.
• To enhance computational efficiency and address challenges associated with traditional prior specifications.
• To develop a method for incorporating uncertainty in the number of factors within these models.

Main Methods:

• A default, heavy-tailed prior distribution is proposed, induced via parameter expansion.
• The approach facilitates efficient posterior computation.
• A method is developed to manage uncertainty regarding the number of factors.

Main Results:

• The proposed heavy-tailed prior specification improves computational efficiency in factor analysis.
• The method effectively handles uncertainty in the number of factors.
• The approach is validated using simulated data and real-world applications in epidemiology and toxicology.

Conclusions:

• The novel prior distribution offers a more robust and computationally feasible alternative for factor analytic modeling.
• This method simplifies the analysis of complex multidimensional data, particularly in applied fields.
• The availability of data and code supports reproducibility and further research.