Scientific Reports (Jan 2023)

Joint distribution properties of fully conditional specification under the normal linear model with normal inverse-gamma priors

  • Mingyang Cai,
  • Stef van Buuren,
  • Gerko Vink

DOI
https://doi.org/10.1038/s41598-023-27786-y
Journal volume & issue
Vol. 13, no. 1
pp. 1 – 7

Abstract

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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 priors. 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.