  Fully conditional specification (FCS) is a convenient and flexible multiple
imputation approach. It specifies a sequence of simple regression models
instead of a potential complex joint density for missing variables. However,
FCS may not converge to a stationary distribution. Many authors have studied
the convergence properties of FCS when priors of conditional models are
non-informative. We extend to the case of informative priors. This paper
evaluates the convergence properties of the normal linear model with
normal-inverse gamma prior. The theoretical and simulation results prove the
convergence of FCS and show the equivalence of prior specification under the
joint model and a set of conditional models when the analysis model is a linear
regression with normal inverse-gamma priors.
