IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i12p4186-4197.html
   My bibliography  Save this article

Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data

Author

Listed:
  • Li, Jialiang
  • Xia, Yingcun
  • Palta, Mari
  • Shankar, Anoop

Abstract

Semiparametric models are becoming increasingly attractive for longitudinal data analysis. Often there is lack of knowledge of the covariance structure of the response variable. Although it is still possible to obtain consistent estimators for both parametric and nonparametric components of a semipatrametric model by assuming an identity structure for the covariance matrix, the resulting estimators may not be efficient. We conducted extensive simulation studies to investigate the impact of an unknown covariance structure on estimators in semiparametric models for longitudinal data. In some situations the loss of efficiency could be substantial. A two-step estimator is thus proposed to improve the efficiency. Our study was motivated by a population based data analysis to examine the temporal relationship between systolic blood pressure and urinary albumin excretion.

Suggested Citation

  • Li, Jialiang & Xia, Yingcun & Palta, Mari & Shankar, Anoop, 2009. "Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4186-4197, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4186-4197
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00195-9
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    2. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    3. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    4. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    5. 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.
    6. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    7. 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.
    8. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    9. 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.
    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. Chen, Ziqi & Shi, Ning-Zhong & Gao, Wei & Tang, Man-Lai, 2011. "Efficient semiparametric estimation via Cholesky decomposition for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3344-3354, December.
    2. Tao Huang & Jialiang Li, 2018. "Semiparametric model average prediction in panel data analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 125-144, January.
    3. Tuglus Catherine & van der Laan Mark J., 2011. "Repeated Measures Semiparametric Regression Using Targeted Maximum Likelihood Methodology with Application to Transcription Factor Activity Discovery," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-31, January.

    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. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    2. Chen, Huaihou & Paik, Myunghee Cho & Dhamoon, Mandip S. & Moon, Yeseon Park & Willey, Joshua & Sacco, Ralph L. & Elkind, Mitchell S.V., 2012. "Semiparametric model for the dichotomized functional outcome after stroke: The Northern Manhattan Study," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2598-2608.
    3. Cho, Hyunkeun & Kim, Seonjin, 2017. "Model specification test in a semiparametric regression model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 105-116.
    4. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    5. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    6. Jia Chen & Degui Li & Yingcun Xia, 2015. "New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models," Discussion Papers 15/17, Department of Economics, University of York.
    7. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 617-638, August.
    8. Yixin Chen & Weixin Yao, 2017. "Unified Inference for Sparse and Dense Longitudinal Data in Time-varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 268-284, March.
    9. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    10. Jia, Shengji & Zhang, Chunming & Lu, Haoran, 2022. "Covariance function versus covariance matrix estimation in efficient semi-parametric regression for longitudinal data analysis," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    11. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    12. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.
    13. Yi, Grace Y. & He, Wenqing & Liang, Hua, 2009. "Analysis of correlated binary data under partially linear single-index logistic models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 278-290, February.
    14. 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;The Institute of Statistical Mathematics, vol. 63(3), pages 511-533, June.
    15. Al Kadiri, M. & Carroll, R.J. & Wand, M.P., 2010. "Marginal longitudinal semiparametric regression via penalized splines," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1242-1252, August.
    16. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    17. Şentürk, Damla & Ghosh, Samiran & Nguyen, Danh V., 2014. "Exploratory time varying lagged regression: Modeling association of cognitive and functional trajectories with expected clinic visits in older adults," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 1-15.
    18. Tuglus Catherine & van der Laan Mark J., 2011. "Repeated Measures Semiparametric Regression Using Targeted Maximum Likelihood Methodology with Application to Transcription Factor Activity Discovery," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-31, January.
    19. Qiu, Jia & Li, Degao & You, Jinhong, 2015. "SCAD-penalized regression for varying-coefficient models with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 100-118.
    20. Li, Lexin & Yin, Xiangrong, 2009. "Longitudinal data analysis using sufficient dimension reduction method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4106-4115, October.

    More about this item

    Statistics

    Access and download statistics

    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:eee:csdana:v:53:y:2009:i:12:p:4186-4197. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.