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Generalised calibration with latent variables for the treatment of unit nonresponse in sample surveys

Author

Listed:
  • M. Giovanna Ranalli

    (University of Perugia)

  • Alina Matei

    (University of Neuchâtel)

  • Andrea Neri

    (Banca d’Italia, DG Economics, Statistics and Research)

Abstract

Sample surveys may suffer from nonignorable unit nonresponse. This happens when the decision of whether or not to participate in the survey is correlated with variables of interest; in such a case, nonresponse produces biased estimates for parameters related to those variables, even after adjustments that account for auxiliary information. This paper presents a method to deal with nonignorable unit nonresponse that uses generalised calibration and latent variable modelling. Generalised calibration enables to model unit nonresponse using a set of auxiliary variables (instrumental or model variables), that can be different from those used in the calibration constraints (calibration variables). We propose to use latent variables to estimate the probability to participate in the survey and to construct a reweighting system incorporating such latent variables. The proposed methodology is illustrated, its properties discussed and tested on two simulation studies. Finally, it is applied to adjust estimates of the finite population mean wealth from the Italian Survey of Household Income and Wealth.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00646-1
    DOI: 10.1007/s10260-022-00646-1
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    References listed on IDEAS

    as
    1. Kott, Phillip S. & Chang, Ted, 2010. "Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1265-1275.
    2. Ted Chang & Phillip S. Kott, 2008. "Using calibration weighting to adjust for nonresponse under a plausible model," Biometrika, Biometrika Trust, vol. 95(3), pages 555-571.
    3. 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.
    4. Andrea Neri & Roberta Zizza, 2010. "Income reporting behaviour in sample surveys," Temi di discussione (Economic working papers) 777, Bank of Italy, Economic Research and International Relations Area.
    5. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    6. Linzer, Drew A. & Lewis, Jeffrey B., 2011. "poLCA: An R Package for Polytomous Variable Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i10).
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