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Bootstrap ICC estimators in analysis of small clustered binary data

Author

Listed:
  • Bei Wang

    (Arizona State University)

  • Yi Zheng

    (Arizona State University
    Arizona State University)

  • Kyle M. Irimata

    (Arizona State University)

  • Jeffrey R. Wilson

    (Arizona State University)

Abstract

Survey data are often obtained through a multilevel structure and, as such, require hierarchical modeling. While large sample approximation provides a mechanism to construct confidence intervals for the intraclass correlation coefficients (ICCs) in large datasets, challenges arise when we are faced with small-size clusters and binary outcomes. In this paper, we examine two bootstrapping methods, cluster bootstrapping and split bootstrapping. We use these methods to construct the confidence intervals for the ICCs (based on a latent variable approach) for small binary data obtained through a three-level or higher hierarchical data structure. We use 26 scenarios in our simulation study with the two bootstrapping methods. We find that the latent variable method performs well in terms of coverage. The split bootstrapping method provides confidence intervals close to the nominal coverage when the ratio of the ICC for the primary cluster to the ICC for the secondary cluster is small. While the cluster bootstrapping is preferred when the cluster size is larger and the ratio of the ICCs is larger. A numerical example based on teacher effectiveness is assessed.

Suggested Citation

  • Bei Wang & Yi Zheng & Kyle M. Irimata & Jeffrey R. Wilson, 2019. "Bootstrap ICC estimators in analysis of small clustered binary data," Computational Statistics, Springer, vol. 34(4), pages 1765-1778, December.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:4:d:10.1007_s00180-019-00885-z
    DOI: 10.1007/s00180-019-00885-z
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    References listed on IDEAS

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    1. Guangyong Zou & Allan Donner, 2004. "Confidence Interval Estimation of the Intraclass Correlation Coefficient for Binary Outcome Data," Biometrics, The International Biometric Society, vol. 60(3), pages 807-811, September.
    2. Tak K. Mak, 1988. "Analysing Intraclass Correlation for Dichotomous Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(3), pages 344-352, November.
    3. C. A. Field & A. H. Welsh, 2007. "Bootstrapping clustered data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 369-390, June.
    4. Shiquan Ren & Hong Lai & Wenjing Tong & Mostafa Aminzadeh & Xuezhang Hou & Shenghan Lai, 2010. "Nonparametric bootstrapping for hierarchical data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1487-1498.
    5. McMahon, James M. & Pouget, Enrique R. & Tortu, Stephanie, 2006. "A guide for multilevel modeling of dyadic data with binary outcomes using SAS PROC NLMIXED," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3663-3680, August.
    6. Kyle M. Irimata & Jeffrey R. Wilson, 2018. "Identifying intraclass correlations necessitating hierarchical modeling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(4), pages 626-641, March.
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