Bayesian inference for factor scores

Bayesian inference for the parameters of the factor model follows directly from the likelihood and the prior distributions for the model parameters. Inference about the factor scores themselves is more complex, but can be accommodated in the “complete data” form of the model using Markov Chain Monte Carlo methods. This approach has interesting connections to the EM algorithm approach to maximum likelihood estimation, and it casts light on the controversy over factor score estimation and factor indeterminacy.