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June 10, 2026Journal of Data Science1 citationsOpen Access

An Estimation Framework for Combining Probability and Non-probability Samples

MEMahmoud ElkasabiTLTaylor LewisMWMatthew Williams

Key Points

  • The aim is to develop a framework for making population estimates using hybrid sampling strategies that combine probability and non-probability data.
  • Utilized public data from the National Health and Nutrition Examination Survey.
  • Combined data from a stratified, multistage probability sample with a non-probability sample.
  • Outlined analytical methods for hybrid sampling structures, including case study and supplementary R code.
  • Demonstrated successful estimation of population parameters using hybrid sampling methods.
  • Highlighted the effectiveness of combining probability and non-probability samples for rare populations.
  • Provided insights into the advantages of reduced costs and improved statistical efficiency.

Abstract

Survey researchers are increasingly adopting hybrid sampling designs to address the limitations of traditional probability sampling, especially when studying rare or hard-to-reach populations. Challenges such as high screening costs, low statistical efficiency, and operational constraints make purely probability-based approaches impractical in many contexts. This article uses public data from the National Health and Nutrition Examination Survey to demonstrate how one can make population estimates from a hybrid sampling strategy that combines data from a stratified, multistage probability sample with data from a non-probability sample within the same primary sampling units as the probability sample. We outline a framework and discuss methods for analyzing data from a hybrid sample such as this, where covariates and survey outcomes are observed in both the probability and non-probability samples. We present a case study to illustrate the framework. We provide the case study R code in the supplementary material.

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Cite This Study

Elkasabi et al. (2026) studied this question.

synapsesocial.com/papers/6a2900886f82f25be989d1d8https://doi.org/10.6339/26-jds1234
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