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Accounting for model uncertainty in multiple imputation under complex sampling

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  • Gyuhyeong Goh
  • Jae Kwang Kim

Abstract

Multiple imputation provides an effective way to handle missing data. When several possible models are under consideration for the data, multiple imputation is typically performed under a single‐best model selected from the candidate models. This single‐model selection approach ignores the uncertainty associated with the model selection and so leads to underestimation of the variance of multiple imputation estimator. In this article, we propose a new multiple imputation procedure incorporating model uncertainty in the final inference. The proposed method incorporates possible candidate models for the data into the imputation procedure using the idea of Bayesian model averaging. The proposed method is directly applicable to handling item nonresponse in survey sampling. Asymptotic properties of the proposed method are investigated. A limited simulation study confirms that our model averaging approach provides better estimation performance than the single‐model selection approach.

Suggested Citation

  • Gyuhyeong Goh & Jae Kwang Kim, 2021. "Accounting for model uncertainty in multiple imputation under complex sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 930-949, September.
  • Handle: RePEc:bla:scjsta:v:48:y:2021:i:3:p:930-949
    DOI: 10.1111/sjos.12473
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    References listed on IDEAS

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    1. Jae Kwang Kim & J. Michael Brick & Wayne A. Fuller & Graham Kalton, 2006. "On the bias of the multiple‐imputation variance estimator in survey sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 509-521, June.
    2. S. Yang & J. K. Kim, 2016. "A note on multiple imputation for method of moments estimation," Biometrika, Biometrika Trust, vol. 103(1), pages 244-251.
    3. J. K. Kim & S. Yang, 2017. "A note on multiple imputation under complex sampling," Biometrika, Biometrika Trust, vol. 104(1), pages 221-228.
    4. Z Wang & J K Kim & S Yang, 2018. "Approximate Bayesian inference under informative sampling," Biometrika, Biometrika Trust, vol. 105(1), pages 91-102.
    5. Dey, Dipak K. & Birmiwal, Lea R., 1994. "Robust Bayesian analysis using divergence measures," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 287-294, July.
    6. Jeremy York & David Madigan & Ivar Heuch & Rolv Terje Lie, 1995. "Birth Defects Registered by Double Sampling: A Bayesian Approach Incorporating Covariates and Model Uncertainty," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 227-242, June.
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