Roy Levy posted on Tuesday, July 08, 2014 - 8:35 pm
I have a question about how imposing constraints on factor variances when using an inverse-Wishart prior distribution in Bayesian analyses. The situation is one in which there are multiple factors, each with a variance constrained to 1, but the covariances are unknown, much like in example 5.31 from the user guide where the variance for the general factor (fg) is constrained to 1. When the factor variances are not fixed, draws for the covariance matrix are obtained from the inverse-Wishart full conditional distribution, as in (8) on p. 7 of the paper Bayesian Analysis Using Mplus: Technical Implementation (version 3). My understanding is that when the factor variances are fixed to 1, the draws are obtained in the same manner, and each drawn value for the covariance matrix is transformed such that the factor variances are each 1. Is that correct? If not, can you explain how the draws for the factor covariance matrix are obtained when the factor variances are fixed?