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On the stationary distribution of iterative imputations

Author

Listed:
  • Jingchen Liu
  • Andrew Gelman
  • Jennifer Hill
  • Yu-Sung Su
  • Jonathan Kropko

Abstract

Iterative imputation, in which variables are imputed one at a time conditional on all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modelling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties, accounting for the conditional models being iteratively estimated from data rather than being prespecified. When the families of conditional models are compatible, we provide sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but valid, we show that the combined imputation estimator is consistent.

Suggested Citation

  • Jingchen Liu & Andrew Gelman & Jennifer Hill & Yu-Sung Su & Jonathan Kropko, 2014. "On the stationary distribution of iterative imputations," Biometrika, Biometrika Trust, vol. 101(1), pages 155-173.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:155-173.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast044
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    Cited by:

    1. Xie, Zilong & Chen, Yunxiao & von Davier, Matthias & Weng, Haolei, 2023. "Variable selection in latent regression IRT models via knockoffs: an application to international large-scale assessment in education," LSE Research Online Documents on Economics 120812, London School of Economics and Political Science, LSE Library.
    2. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    3. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Multiple Imputation for Regression Models with Missing Mixed Continuous-Discrete Covariates," Discussion Paper Series DP2018-15, Research Institute for Economics & Business Administration, Kobe University.
    4. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2023. "Handling Missing Data in Cross-Classified Multilevel Analyses: An Evaluation of Different Multiple Imputation Approaches," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 454-489, August.
    5. Speidel, Matthias & Drechsler, Jörg & Jolani, Shahab, 2018. "R package hmi: a convenient tool for hierarchical multiple imputation and beyond," IAB-Discussion Paper 201816, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    6. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian Instrumental Variables Estimation for Nonignorable Missing Instruments," Discussion Paper Series DP2020-06, Research Institute for Economics & Business Administration, Kobe University.

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