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Indirect Sampling: A Review of Theory and Recent Applications

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Abstract

Survey practitioners regularly face the task to draw a sample from a (sub-) population for which no sampling frame exists. Indirect sampling might be a way out in such situations, given that connections exist between the target population and another population for which probability sampling is feasible. While the theory of indirect sampling originated in the context of household panel studies, a wider area of applications emerged during the last decade. We first give a short review of the theory of indirect sampling, show that estimators from indirect samples might have smaller variance than the corresponding direct estimators (contrary to some claims in the literature), summarize recent applications and discuss some issues that are relevant for applying indirect sampling in practice. We also present some theory for unbiased estimation after an additional subsampling stage that was necessary for sampling kindergarten children in the German National Educational Panel Study (NEPS).

Zusammenfassung

In der Umfragepraxis stellt sich oft das Problem, eine Stichprobe aus einer (Sub-)Population zu ziehen, für die kein vollständiger Auswahlrahmen existiert. In dieser Situation kann ein indirektes Auswahlverfahren eine Lösung sein, falls gewisse Verbindungen bestehen zwischen der Zielpopulation und einer anderen Gesamtheit, für die wiederum ein Auswahlrahmen existiert. Die nötige Theorie zur indirekten Auswahl wurde im Kontext von Haushaltsstichproben entwickelt; in den letzten Jahren ergaben sich aber zahlreiche weitere Anwendungsmöglichkeiten. Dieser Beitrag gibt einen Überblick über die Methodik der indirekten Auswahl, beschreibt einige Anwendungen aus jüngerer Zeit und diskutiert praktische Aspekte. Gezeigt wird zudem, dass Schätzer für indirekte Auswahlen durchaus kleinere Varianzen als direkte Schätzer haben können. Schließlich wird ein zusätzlicher Substichprobenschritt für eine Anwendung im Nationalen Bildungspanel (NEPS) beschrieben.

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Notes

  1. Kalton and Brick (1995, p.37) look at the expected value of \(\hat{t}_{Y,\mathop{\mathrm{IS}}}\) given a sample \(s_{B}\) and write (in our notation): \(E(\hat{t}_{Y,\mathop{\mathrm{IS}}}|s_{B})=E(\sum_{i\in U_{B}}w_{i_{s}}y_{i}|s_{B})=\sum_{i\in s_{B}}E(w_{i_{s}}|i\in s_{B})y_{i}=\hat{t}_{Y,HT}\). The next-to-last equality is wrong. \(E(w_{i_{s}}|s_{B})\) is not equal to \(E(w_{i_{s}}|i\in s_{B})\): the first expectation is over all direct samples \(s_{A}\) which lead to the specified indirect sample \(s_{B}\), the second expectation is over all direct samples which lead to any indirect sample that contains unit \(i\). There is no reason why these expectations should be equal, and, in fact, they are usually different.

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  1. Fakultät Informatik und Mathematik, OTH Regensburg, 93025, Regensburg, Germany

    Hans Kiesl

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  1. Hans Kiesl
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Correspondence to Hans Kiesl.

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This work was partially funded by the German Research Foundation (DFG), Priority Programme “Education as a lifelong process” (SPP 1646) under the grant KI 1646/1-1.

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Kiesl, H. Indirect Sampling: A Review of Theory and Recent Applications. AStA Wirtsch Sozialstat Arch 10, 289–303 (2016). https://doi.org/10.1007/s11943-016-0183-3

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