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Analysis of correlated binary data under partially linear single-index logistic models

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  • Yi, Grace Y.
  • He, Wenqing
  • Liang, Hua
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    Abstract

    Clustered data arise commonly in practice and it is often of interest to estimate the mean response parameters as well as the association parameters. However, most research has been directed to address the mean response parameters with the association parameters relegated to a nuisance role. There is relatively little work concerning both the marginal and association structures, especially in the semiparametric framework. In this paper, our interest centers on the inference of both the marginal and association parameters. We develop a semiparametric method for clustered binary data and establish the theoretical results. The proposed methodology is investigated through various numerical studies.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 2 (February)
    Pages: 278-290

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:2:p:278-290

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    Related research

    Keywords: primary; 62G08; 62G10 secondary; 62G20 Association Binary outcomes Clustered data Estimating equation Marginal mean Semiparametric estimation Undersmooth;

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    References

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    1. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    2. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    3. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1112-1137, December.
    4. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    5. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    6. Sungduk Kim & Ming-Hui Chen & Dipak K. Dey, 2008. "Flexible generalized t-link models for binary response data," Biometrika, Biometrika Trust, vol. 95(1), pages 93-106.
    7. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    8. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    9. Efang Kong & Yingcun Xia, 2007. "Variable selection for the single‐index model," Biometrika, Biometrika Trust, vol. 94(1), pages 217-229.
    10. Yi G.Y. & Cook R.J., 2002. "Marginal Methods for Incomplete Longitudinal Data Arising in Clusters," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1071-1080, December.
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    Cited by:
    1. Grace Yi & Wenqing He & Hua Liang, 2011. "Semiparametric marginal and association regression methods for clustered binary data," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 511-533, June.
    2. Xu, Peirong & Zhu, Lixing, 2012. "Estimation for a marginal generalized single-index longitudinal model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 285-299.
    3. Graciela Boente & Daniela Rodriguez, 2012. "Robust estimates in generalized partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(2), pages 386-411, June.

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