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Small area estimation with linked data

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  • N. Salvati
  • E. Fabrizi
  • M. G. Ranalli
  • R. L. Chambers

Abstract

Data linkage can be used to combine values of the variable of interest from a national survey with values of auxiliary variables obtained from another source, such as a population register, for use in small area estimation. However, linkage errors can induce bias when fitting regression models; moreover, they can create non‐representative outliers in the linked data in addition to the presence of potential representative outliers. In this paper, we adopt a secondary analyst’s point of view, assuming that limited information is available on the linkage process, and develop small area estimators based on linear mixed models and M‐quantile models to accommodate linked data containing a mix of both types of outliers. We illustrate the properties of these small area estimators, as well as estimators of their mean squared error, by means of model‐based and design‐based simulation experiments. We further illustrate the proposed methodology by applying it to linked data from the European Survey on Income and Living Conditions and the Italian integrated archive of economic and demographic micro data in order to obtain estimates of the average equivalised income for labour market areas in central Italy.

Suggested Citation

  • N. Salvati & E. Fabrizi & M. G. Ranalli & R. L. Chambers, 2021. "Small area estimation with linked data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 78-107, February.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:1:p:78-107
    DOI: 10.1111/rssb.12401
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    References listed on IDEAS

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    1. Annamaria Bianchi & Enrico Fabrizi & Nicola Salvati & Nikos Tzavidis, 2018. "Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation," International Statistical Review, International Statistical Institute, vol. 86(3), pages 541-570, December.
    2. P. Lahiri & Michael D. Larsen, 2005. "Regression Analysis With Linked Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 222-230, March.
    3. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    4. Ray Chambers & Hukum Chandra & Nicola Salvati & Nikos Tzavidis, 2014. "Outlier robust small area estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 47-69, January.
    5. Ray Chambers & Andrea Diniz da Silva, 2020. "Improved secondary analysis of linked data: a framework and an illustration," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 37-59, January.
    6. Kim, Gunky & Chambers, Raymond, 2012. "Regression analysis under incomplete linkage," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2756-2770.
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    Cited by:

    1. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).

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