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Incorporating Prior Knowledge Regarding the Mean in Bayesian Factor Analysis

In the Bayesian factor analysis model (Press & Shigemasu, 1989), available knowledge regarding the model parameters is incorporated in the form of prior distributions. This has the added consequence of eliminating the ambiguity of rotation found in the traditional factor analysis model. In the model presented by Press and Shigemasu, a vague prior distribution was implicitly specified for the population mean. The sample size was assumed to be large enough to estimate the overall population mean by the sample mean. In this paper, available prior knowledge regarding the population mean is incorporated into the inferences in the form of a prior distribution. The population mean is estimated along with the other parameters by both Gibbs sampling and Iterated Conditional Modes.