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Small Area with Multiply Imputed Survey Data

Author

Listed:
  • Runge Marina

    (1 Institute of Statistics and Econometrics, Freie Universität Berlin, Garystraße 21, 14195, Berlin, Germany)

  • Schmid Timo

    (2 Institute of Statistics, Otto-Friedrich-Universität Bamberg, Feldkirchenstraße 21, 96045, Bamberg, Germany)

Abstract

In this article, we propose a framework for small area estimation with multiply imputed survey data. Many statistical surveys suffer from (a) high nonresponse rates due to sensitive questions and response burden and (b) too small sample sizes to allow for reliable estimates on (unplanned) disaggregated levels due to budget constraints. One way to deal with missing values is to replace them by several plausible/imputed values based on a model. Small area estimation, such as the model by Fay and Herriot, is applied to estimate regionally disaggregated indicators when direct estimates are imprecise. The framework presented tackles simultaneously multiply imputed values and imprecise direct estimates. In particular, we extend the general class of transformed Fay-Herriot models to account for the additional uncertainty from multiple imputation. We derive three special cases of the Fay-Herriot model with particular transformations and provide point and mean squared error estimators. Depending on the case, the mean squared error is estimated by analytic solutions or resampling methods. Comprehensive simulations in a controlled environment show that the proposed methodology leads to reliable and precise results in terms of bias and mean squared error. The methodology is illustrated by a real data example using European wealth data.

Suggested Citation

  • Runge Marina & Schmid Timo, 2023. "Small Area with Multiply Imputed Survey Data," Journal of Official Statistics, Sciendo, vol. 39(4), pages 507-533, December.
    • Handle: RePEc:vrs:offsta:v:39:y:2023:i:4:p:507-533:n:4
    DOI: 10.2478/jos-2023-0024
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    References listed on IDEAS

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    1. Shonosuke Sugasawa & Hiromasa Tamae & Tatsuya Kubokawa, 2017. "Bayesian Estimators for Small Area Models Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 150-167, March.
    2. Michael Sverchkov & Danny Pfeffermann, 2018. "Small area estimation under informative sampling and not missing at random non‐response," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 981-1008, October.
    3. Wang, Junyuan & Fuller, Wayne A., 2003. "The Mean Squared Error of Small Area Predictors Constructed With Estimated Area Variances," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 716-723, January.
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