A Model for Bayesian Factor Analysis with Jointly Distributed Means and Loadings

Abstract

In the Bayesian approach to factor analysis, available prior knowledge regarding the model parameters is quantified in the form of prior distributions and incorporated into the inferences along with the data. The incorporation of prior knowledge has the added consequence of eliminating the ambiguity of rotation and the need for model constraints found in the traditional factor analysis model. A focus of recent work (Rowe, 2000a and Rowe 2000b and Rowe, 2000C) has been on quantifying and incorporating available prior knowledge when estimating the population mean. This previous work has considered vague, conjugate, and generalized conjugate distributions for the population mean. In this paper, unlike previous work, the population mean vector and the factor loading matrix are taken to be jointly distributed, which allows available interrelated prior information to be quantified and incorporated with the data. The model parameters are estimated by Gibbs sampling and iterated conditional modes algorithms.

Files

Additional details