A Bayesian Factor Analysis Model with Generalized Prior Information

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. The incorporation of prior knowledge has the added consequence of eliminating the ambiguity of rotation found in the traditional factor analysis model. Previous Bayesian factor analysis work (Press & Shigemasu 1989, & Press 1998, Rowe 2000a, and Rowe 2000b), has considered mainly natural conjugate prior distributions for the model parameters. As is mentioned in Press (1982), Rothenburg (1963) pointed out that with a natural conjugate prior distribution, the elements in the covariance matrices are constrained and thus may not be rich enough to permit freedom of assessment. In this paper, generalized natural conjugate distributions are used to quantify and incorporate available prior information which permit complete freedom of assessment.