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Analysis of clustered survey data based on two‐stage informative sampling and associated two‐level models

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  • Jae Kwang Kim
  • J.N.K. Rao
  • Yonghyun Kwon

Abstract

This paper deals with making inference on parameters of a two‐level model matching the design hierarchy of a two‐stage sample. In a pioneering paper, Scott and Smith (Journal of the American Statistical Association, 1969, 64, 830–840) proposed a Bayesian model based or prediction approach to estimating a finite population mean under two‐stage cluster sampling. We provide a brief account of their pioneering work. We review two methods for the analysis of two‐level models based on matching two‐stage samples. Those methods are based on pseudo maximum likelihood and pseudo composite likelihood taking account of design weights. We then propose a new method for analysis of two‐level models based on a normal approximation to the estimated cluster effects and taking account of design weights. This method does not require cluster sizes to be constants or unrelated to cluster effects. We evaluate the relative performance of the three methods in a simulation study. Finally, we apply the methods to real data obtained from 2011 Nepal Demographic and Health Survey (NDHS).

Suggested Citation

  • Jae Kwang Kim & J.N.K. Rao & Yonghyun Kwon, 2022. "Analysis of clustered survey data based on two‐stage informative sampling and associated two‐level models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1522-1540, October.
    • Handle: RePEc:bla:jorssa:v:185:y:2022:i:4:p:1522-1540
    DOI: 10.1111/rssa.12805
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    References listed on IDEAS

    as
    1. D Lee & J K Kim & C J Skinner, 2019. "Within-cluster resampling for multilevel models under informative cluster size," Biometrika, Biometrika Trust, vol. 106(4), pages 965-972.
    2. Jae Kwang Kim & C. J. Skinner, 2013. "Weighting in survey analysis under informative sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 385-398.
    3. E. Benhin & J. N. K. Rao & A. J. Scott, 2005. "Mean estimating equation approach to analysing cluster-correlated data with nonignorable cluster sizes," Biometrika, Biometrika Trust, vol. 92(2), pages 435-450, June.
    4. Damião Nóbrega Da Silva & Chris Skinner & Jae Kwang Kim, 2016. "Using Binary Paradata to Correct for Measurement Error in Survey Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 526-537, April.
    5. D. Pfeffermann & C. J. Skinner & D. J. Holmes & H. Goldstein & J. Rasbash, 1998. "Weighting for unequal selection probabilities in multilevel models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 23-40.
    6. Da Silva, Damião Nóbrega & Skinner, Chris J. & Kim, Jae Kwang, 2016. "Using binary paradata to correct for measurement error in survey data analysis," LSE Research Online Documents on Economics 64763, London School of Economics and Political Science, LSE Library.
    7. Laura Dumitrescu & Wei Qian & J. N. K. Rao, 2021. "A Weighted Composite Likelihood Approach to Inference from Clustered Survey Data Under a Two-Level Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 814-843, August.
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