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Weighting in survey analysis under informative sampling

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  • Jae Kwang Kim
  • C. J. Skinner

Abstract

Sampling related to the outcome variable of a regression analysis conditional on covariates is called informative sampling and may lead to bias in ordinary least squares estimation. Weighting by the reciprocal of the inclusion probability approximately removes such bias but may inflate variance. This paper investigates two ways of modifying such weights to improve efficiency while retaining consistency. One approach is to multiply the inverse probability weights by functions of the covariates. The second is to smooth the weights given values of the outcome variable and covariates. Optimal ways of constructing weights by these two approaches are explored. Both approaches require the fitting of auxiliary weight models. The asymptotic properties of the resulting estimators are investigated and linearization variance estimators are obtained. The approach is extended to pseudo maximum likelihood estimation for generalized linear models. The properties of the different weighted estimators are compared in a limited simulation study. The robustness of the estimators to misspecification of the auxiliary weight model or of the regression model of interest is discussed. Copyright 2013, Oxford University Press.

Suggested Citation

  • Jae Kwang Kim & C. J. Skinner, 2013. "Weighting in survey analysis under informative sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 385-398.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:385-398
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    File URL: http://hdl.handle.net/10.1093/biomet/ass085
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    Cited by:

    1. 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.
    2. A. Sikov & J. M. Stern, 2019. "Application of the full Bayesian significance test to model selection under informative sampling," Statistical Papers, Springer, vol. 60(1), pages 89-104, February.
    3. Jae Kwang Kim & J.N.K. Rao & Yonghyun Kwon, 2022. "Analysis of clustered survey data based on two‐stage informative sampling and associated two‐level models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1522-1540, October.
    4. Ray Chambers & Setareh Ranjbar & Nicola Salvati & Barbara Pacini, 2022. "Weighting, informativeness and causal inference, with an application to rainfall enhancement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1584-1612, October.
    5. Robert G. Clark & David G. Steel, 2022. "Sample design for analysis using high‐influence probability sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1733-1756, October.

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