IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-022-00281-8.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-022-00281-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-022-00281-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Brajendra C. Sutradhar, 2024. "Inferences for Fixed Effects Based Regression Parameters in a Finite Population Setup Using Two-stage Cluster Sample," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 951-991, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brajendra C. Sutradhar, 2022. "Multinomial Logistic Mixed Models for Clustered Categorical Data in a Complex Survey Sampling Setup," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 743-789, August.
    2. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    3. Brajendra C. Sutradhar & R. Prabhakar Rao, 2023. "Asymptotic Inferences in a Multinomial Logit Mixed Model for Spatial Categorical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 885-930, February.
    4. D. Todem & Y. Zhang & A. Ismail & W. Sohn, 2010. "Random effects regression models for count data with excess zeros in caries research," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1661-1679.
    5. Brajendra C. Sutradhar, 2023. "Regression analysis for exponential family data in a finite population setup using two-stage cluster sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 425-462, June.
    6. Brajendra C. Sutradhar, 2023. "Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1452-1488, August.
    7. Hyunju Dan & Jiyoung Kim & Oksoo Kim, 2020. "Effects of Gender and Age on Dietary Intake and Body Mass Index in Hypertensive Patients: Analysis of the Korea National Health and Nutrition Examination," IJERPH, MDPI, vol. 17(12), pages 1-9, June.
    8. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    9. Chaubert, F. & Mortier, F. & Saint André, L., 2008. "Multivariate dynamic model for ordinal outcomes," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1717-1732, September.
    10. Daniel Nevo & Deborah Blacker & Eric B. Larson & Sebastien Haneuse, 2022. "Modeling semi‐competing risks data as a longitudinal bivariate process," Biometrics, The International Biometric Society, vol. 78(3), pages 922-936, September.
    11. Sutradhar, Brajendra C., 2021. "Block-band behavior of spatial correlations: An analytical asymptotic study in a spatial exponential family data setup," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    12. Celine Marielle Laffont & Marc Vandemeulebroecke & Didier Concordet, 2014. "Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 955-966, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00281-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.