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Fully conditional specification (FCS) is a convenient and flexible multipleimputation approach. It specifies a sequence of simple regression modelsinstead of a potential complex joint density for missing variables. However,FCS may not converge to a stationary distribution. Many authors have studiedthe convergence properties of FCS when priors of conditional models arenon-informative. We extend to the case of informative priors. This paperevaluates the convergence properties of the normal linear model withnormal-inverse gamma prior. The theoretical and simulation results prove theconvergence of FCS and show the equivalence of prior specification under thejoint model and a set of conditional models when the analysis model is a linearregression with normal inverse-gamma priors.

Joint distribution properties of Fully Conditional Specification under the normal linear model with normal inverse-gamma priors