Bayesian factor analysis has gained prominence in statistical MODELING, particularly in handling parameter uncertainty and small sample sizes. This study presents a Metropolis- Hastings within Gibbs sampling algorithm for estimating a factor analysis model, incorporating Cauchy priors for factor loadings and log-normal priors for residual errors. Unlike traditional approaches, the proposed methodology effectively addresses heavy-tailed distributions in factor loadings and captures the skewness in residual variances. A geriatric dataset comprising 25 items related to locomotive function is used to illustrate the implementation of this Bayesian framework. Model fit is assessed using standard fit indices such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error of Approximation (RMSEA), Comparative Fit Index (CFI), and Standardized Root Mean Square Residual (SRMR). The results demonstrate that incorporating non-conjugate priors improves model flexibility and enhances interpretability in factor structure identification. The findings suggest that Cauchy and log-normal priors outperform conventional normal priors in capturing latent structures, providing a robust alternative for Bayesian factor analysis in geriatric research.
Jagulin et al. (Mon,) studied this question.