Bayesian factor analysis when only a sample covariance matrix is available

Abstract

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing the posterior estimates of Bayesian factor analysis using only the sample variance-covariance matrix without the entire data set. The method is verified in terms of an existing data set. With our method, researchers will be able to apply Bayesian factor analysis when they find either a variance-covariance or a correlation matrix with standard deviations in the existing literature.