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

TL;DR

This paper investigates the convergence properties of Fully Conditional Specification (FCS) in the normal linear model with normal-inverse gamma priors, extending previous work to informative priors and proving convergence and prior equivalence.

Contribution

It extends the analysis of FCS convergence to the case of informative priors, providing theoretical and simulation evidence of convergence and prior equivalence.

Findings

FCS converges under the normal linear model with normal-inverse gamma priors.

Prior specification under the joint model and conditional models are equivalent in this setting.

Theoretical and simulation results support the convergence of FCS with informative priors.

Abstract

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.