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Combining data from two independent surveys: a model-assisted approach

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  • Jae Kwang Kim
  • J. N. K. Rao

Abstract

Combining information from two or more independent surveys is a problem frequently encountered in survey sampling. We consider the case of two independent surveys, where a large sample from survey 1 collects only auxiliary information and a much smaller sample from survey 2 provides information on both the variables of interest and the auxiliary variables. We propose a model-assisted projection method of estimation based on a working model, but the reference distribution is design-based. We generate synthetic or proxy values of a variable of interest by first fitting the working model, relating the variable of interest to the auxiliary variables, to the data from survey 2 and then predicting the variable of interest associated with the auxiliary variables observed in survey 1. The projection estimator of a total is simply obtained from the survey 1 weights and associated synthetic values. We identify the conditions for the projection estimator to be asymptotically unbiased. Domain estimation using the projection method is also considered. Replication variance estimators are obtained by augmenting the synthetic data file for survey 1 with additional synthetic columns associated with the columns of replicate weights. Results from a simulation study are presented. Copyright 2012, Oxford University Press.

Suggested Citation

  • Jae Kwang Kim & J. N. K. Rao, 2012. "Combining data from two independent surveys: a model-assisted approach," Biometrika, Biometrika Trust, vol. 99(1), pages 85-100.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:85-100
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    File URL: http://hdl.handle.net/10.1093/biomet/asr063
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    Citations

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    Cited by:

    1. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    2. Jae Kwang Kim & Zhonglei Wang & Zhengyuan Zhu & Nathan B. Cruze, 2018. "Combining Survey and Non-survey Data for Improved Sub-area Prediction Using a Multi-level Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 175-189, June.
    3. Seho Park & Jae Kwang Kim & Diana Stukel, 2017. "A measurement error model approach to survey data integration: combining information from two surveys," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 345-357, December.
    4. Alleva Giorgio & Petrarca Francesca & Falorsi Piero Demetrio & Righi Paolo, 2021. "Measuring the Accuracy of Aggregates Computed from a Statistical Register," Journal of Official Statistics, Sciendo, vol. 37(2), pages 481-503, June.
    5. Yves G. Berger & Ewa Kabzińska, 2020. "Empirical Likelihood Approach for Aligning Information from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 88(1), pages 54-74, April.
    6. Paolo Righi, 2016. "Estimation procedure and inference for component totals of the economic aggregates in the “Frame SBS”," Rivista di statistica ufficiale, ISTAT - Italian National Institute of Statistics - (Rome, ITALY), vol. 18(1), pages 83-97.
    7. Jerry J. Maples, 2017. "Improving small area estimates of disability: combining the American Community Survey with the Survey of Income and Program Participation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1211-1227, October.
    8. Jae Kwang Kim & Seho Park & Yilin Chen & Changbao Wu, 2021. "Combining non‐probability and probability survey samples through mass imputation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 941-963, July.
    9. Perchinunno, Paola & Mongelli, Lucia & d’Ovidio, Francesco D., 2020. "Statistical matching techniques in order to plan interventions on socioeconomic weakness: An Italian case," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).

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