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Sample design for analysis using high‐influence probability sampling

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  • Robert G. Clark
  • David G. Steel

Abstract

Sample designs are typically developed to estimate summary statistics such as means, proportions and prevalences. Analytical outputs may also be a priority but there are fewer methods and results on how to efficiently design samples for the fitting and estimation of statistical models. This paper develops a general approach for determining efficient sampling designs for probability‐weighted maximum likelihood estimators and considers application to generalized linear models. We allow for non‐ignorable sampling, including outcome‐dependent sampling. The new designs have probabilities of selection closely related to influence statistics such as dfbeta and Cook's distance. The new approach is shown to perform well in a simulation based on data from the New Zealand Health Survey.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:185:y:2022:i:4:p:1733-1756
    DOI: 10.1111/rssa.12916
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    References listed on IDEAS

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    1. Oǧuz-Alper, Melike & Berger, Yves G., 2020. "Modelling multilevel data under complex sampling designs: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    2. Sophia Rabe‐Hesketh & Anders Skrondal, 2006. "Multilevel modelling of complex survey data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 805-827, October.
    3. Jae Kwang Kim & C. J. Skinner, 2013. "Weighting in survey analysis under informative sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 385-398.
    4. D. Pfeffermann & C. J. Skinner & D. J. Holmes & H. Goldstein & J. Rasbash, 1998. "Weighting for unequal selection probabilities in multilevel models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 23-40.
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