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Cluster Correlations and Complexity in Binary Regression Analysis Using Two-stage Cluster Samples

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  • Brajendra C. Sutradhar

    (Memorial University)

Abstract

In a two-stage cluster sampling setup for binary data, a sample of clusters such as hospitals is chosen at the first stage from a large number of clusters belonging to a finite population, and in the second stage a random sample of individuals such as nurses is chosen from the selected cluster and the binary responses along with covariates are collected from the selected individuals. Because the hypothetical binary responses from the individuals in a given cluster/hospital under the first stage sample are correlated (as they share a common cluster effect), this correlation plays a complex role in developing the second stage sample based estimating equations for the underlying regression parameters. Moreover, the correlation parameters have to be consistently estimated too. In this paper, unlike the existing studies, we demonstrate how to accommodate (1) the so-called inverse correlation weights arising from a finite population based generalized quasi-likelihood (GQL) estimating function, on top of (2) the sampling weights, to develop a survey sample based doubly weighted (SSDW) estimation approach, for consistent estimation of both regression and correlation parameters. For simplicity, we refer to this GQL cum SSDW approach as the SSDW approach only. The method of moments (MM) cum SSDW approach will be simpler but less efficient, which is not included in the paper. The estimating function involved in the proposed SSDW estimating equation has the form of a sample total, which unbiasedly estimate the corresponding finite population total that arises from the aforementioned generalized quasi-likelihood function for the targeted finite population parameter. The resulting SSDW estimators, thus, become consistent for the respective parameters. This consistency property for the SSDW estimator for both regression and cluster correlation parameters is studied in details.

Suggested Citation

  • Brajendra C. Sutradhar, 2023. "Cluster Correlations and Complexity in Binary Regression Analysis Using Two-stage Cluster Samples," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 829-884, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00281-8
    DOI: 10.1007/s13171-022-00281-8
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    References listed on IDEAS

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    1. Sutradhar, Brajendra C. & Mukerjee, Rahul, 2005. "On likelihood inference in binary mixed model with an application to COPD data," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 345-361, February.
    2. E.A. Molina & T.M.F. Smith & R.A. Sugden, 2001. "Modelling Overdispersion for Complex Survey Data," International Statistical Review, International Statistical Institute, vol. 69(3), pages 373-384, December.
    3. Thomas R. Ten Have & Alfredo Morabia, 1999. "Mixed Effects Models with Bivariate and Univariate Association Parameters for Longitudinal Bivariate Binary Response Data," Biometrics, The International Biometric Society, vol. 55(1), pages 85-93, March.
    4. Chris Skinner, 2019. "Analysis of Categorical Data for Complex Surveys," International Statistical Review, International Statistical Institute, vol. 87(S1), pages 64-78, May.
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