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Using an Approximate Bayesian Bootstrap to multiply impute nonignorable missing data

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  • Siddique, Juned
  • Belin, Thomas R.

Abstract

An Approximate Bayesian Bootstrap (ABB) offers advantages in incorporating appropriate uncertainty when imputing missing data, but most implementations of the ABB have lacked the ability to handle nonignorable missing data where the probability of missingness depends on unobserved values. This paper outlines a strategy for using an ABB to multiply impute nonignorable missing data. The method allows the user to draw inferences and perform sensitivity analyses when the missing data mechanism cannot automatically be assumed to be ignorable. Results from imputing missing values in a longitudinal depression treatment trial as well as a simulation study are presented to demonstrate the method's performance. We show that a procedure that uses a different type of ABB for each imputed data set accounts for appropriate uncertainty and provides nominal coverage.

Suggested Citation

  • Siddique, Juned & Belin, Thomas R., 2008. "Using an Approximate Bayesian Bootstrap to multiply impute nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 405-415, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:405-415
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    References listed on IDEAS

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    1. Demirtas, Hakan & Arguelles, Lester M. & Chung, Hwan & Hedeker, Donald, 2007. "On the performance of bias-reduction techniques for variance estimation in approximate Bayesian bootstrap imputation," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4064-4068, May.
    2. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 287-296, July.
    3. Schenker, Nathaniel & Taylor, Jeremy M. G., 1996. "Partially parametric techniques for multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 425-446, August.
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    Cited by:

    1. Sullivan, Danielle & Andridge, Rebecca, 2015. "A hot deck imputation procedure for multiply imputing nonignorable missing data: The proxy pattern-mixture hot deck," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 173-185.
    2. Tian Li & Julian M. Somers & Xiaoqiong J. Hu & Lawrence C. McCandless, 2019. "Bayesian Sensitivity Analysis for Non-ignorable Missing Data in Longitudinal Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 184-205, April.
    3. Vijayan K. Pillai & Fang-Hsun Wei & Arati Maleku, 2013. "International Non-Governmental Organizations in Latin America and Social Capital," SAGE Open, , vol. 3(4), pages 21582440135, December.
    4. Bailey, Michael & Hopkins, Daniel J. & Rogers, Todd, 2013. "Unresponsive and Unpersuaded: The Unintended Consequences of Voter Persuasion Efforts," Working Paper Series rwp13-034, Harvard University, John F. Kennedy School of Government.
    5. Ferrari, Pier Alda & Annoni, Paola & Barbiero, Alessandro & Manzi, Giancarlo, 2011. "An imputation method for categorical variables with application to nonlinear principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2410-2420, July.

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