A Bayesian Model to Incorporate Jointly Distributed Generalized Prior Information on Means and Loadings in Factor Analysis

Abstract

A Bayesian factor analysis model is outlined in which prior knowledge regarding the model parameters is quantified using prior distribution and incorporated into the inferences along with the data. Recent work (Rowe, 2000a; Rowe, 2000b; Rowe, 2000c) has focused on the population mean and considered vague, conjugate and generalized conjugate distributions when it was taken to be independent of the factor loadings. More recent work (Rowe, 2001) has taken the population mean and factor loadings to be jointly distributed and used a conjugate prior distribution. In this paper, the population mean vector and the factor loadings are taken to be jointly distributed and a generalized conjugate distribution is used. As mentioned in Press (1982), Rothenburg (1963) pointed out that with a conjugate prior distribution, the elements in the covariance matrices are constrained and may not be rich enough to permit complete freedom of assessment. The generalized conjugate distribution permits complete freedom of assessment. Parameters are estimated by Gibbs sampling and iterated conditional modes algorithms.