Bayesian inference for graphical factor analysis models (original) (raw)

We de ne graphical factor analysis models as graphical Gaussian models with unobserved variables. We generalise factor analysis models by allowing the concentration matrix of the residuals to have non-zero o -diagonal elements. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the con rmatory and exploratory context. We rst present a su cient condition for global identi ability of this class of models. We then propose a model selection procedure, based on the calculation of the posterior probabilities of the model. Given the analytical intractability of the latter, we construct a reversible jump Markov chain Monte Carlo method. A simulation study to illustrate these ideas is nally presented.