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A Cautionary Tale on Instrumental Calibration for the Treatment of Nonignorable Unit Nonresponse in Surveys

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  • Éric Lesage
  • David Haziza
  • Xavier D’Haultfœuille

Abstract

Response rates have been steadily declining over the last decades, making survey estimates vulnerable to nonresponse bias. To reduce the potential bias, two weighting approaches are commonly used in National Statistical Offices: the one-step and the two-step approaches. In this article, we focus on the one-step approach, whereby the design weights are modified in a single step with two simultaneous goals in mind: reduce the nonresponse bias and ensure the consistency between survey estimates and known population totals. In particular, we examine the properties of instrumental calibration, a special case of the one-step approach that has received a lot of attention in the literature in recent years. Despite the rich literature on the topic, there remain some important gaps that this article aims to fill. First, we give a set of sufficient conditions required for establishing the consistency of instrumental calibration estimators. Also, we show that the latter may suffer from a large bias when some of these conditions are violated. Results from a simulation study support our findings. Supplementary materials for this article are available online.

Suggested Citation

  • Éric Lesage & David Haziza & Xavier D’Haultfœuille, 2019. "A Cautionary Tale on Instrumental Calibration for the Treatment of Nonignorable Unit Nonresponse in Surveys," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 906-915, April.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:526:p:906-915
    DOI: 10.1080/01621459.2018.1458619
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    Citations

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    Cited by:

    1. Denis Devaud & Yves Tillé, 2019. "Deville and Särndal’s calibration: revisiting a 25-years-old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1033-1065, December.
    2. M. Giovanna Ranalli & Alina Matei & Andrea Neri, 2023. "Generalised calibration with latent variables for the treatment of unit nonresponse in sample surveys," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 169-195, March.
    3. Denis Devaud & Yves Tillé, 2019. "Rejoinder on: Deville and Särndal’s calibration: revisiting a 25-year-old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1087-1091, December.
    4. Rueda, M. & Martínez, S. & Illescas, M., 2021. "Treating nonresponse in the estimation of the distribution function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 136-144.
    5. Zhan Liu & Chaofeng Tu & Yingli Pan, 2022. "Model-assisted calibration with SCAD to estimated control for non-probability samples," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 849-879, October.
    6. L. Castell & P. Sillard, 2021. "Le traitement du biais de sélection endogène dans les enquêtes auprès des ménages par modèle de Heckman," Documents de Travail de l'Insee - INSEE Working Papers m2021-02, Institut National de la Statistique et des Etudes Economiques.

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