IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v67y2005i4p531-553.html
   My bibliography  Save this article

Estimated estimating equations: semiparametric inference for clustered and longitudinal data

Author

Listed:
  • Jeng‐Min Chiou
  • Hans‐Georg Müller

Abstract

Summary. We introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions. This estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi‐likelihood regression, where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link, and variance–covariance is an unknown smooth function of the marginal means. We propose to estimate the nonparametric link and variance–covariance functions via smoothing methods, whereas the regression parameters are obtained via the estimated estimating equations. These are score equations that contain nonparametric function estimates. The proposed estimated estimating equations approach is motivated by its flexibility and easy implementation. Moreover, if data follow a generalized linear mixed model, with either a specified or an unspecified distribution of random effects and link function, the model proposed emerges as the corresponding marginal (population‐average) version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model, without the need to specify any other components of this generalized linear mixed model. Among marginal models, the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations. Applications of estimated estimating equations include diagnostics and link selection. The asymptotic distribution of the proposed estimators for the model parameters is derived, enabling statistical inference. Practical illustrations include Poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses.

Suggested Citation

  • Jeng‐Min Chiou & Hans‐Georg Müller, 2005. "Estimated estimating equations: semiparametric inference for clustered and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 531-553, September.
  • Handle: RePEc:bla:jorssb:v:67:y:2005:i:4:p:531-553
    DOI: 10.1111/j.1467-9868.2005.00514.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2005.00514.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-9868.2005.00514.x?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
    ---><---

    Citations

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


    Cited by:

    1. Jun Yan & Jian Huang, 2009. "Partly Functional Temporal Process Regression with Semiparametric Profile Estimating Functions," Biometrics, The International Biometric Society, vol. 65(2), pages 431-440, June.
    2. Lan Wang & Annie Qu, 2009. "Consistent model selection and data‐driven smooth tests for longitudinal data in the estimating equations approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 177-190, January.
    3. Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
    4. Nan Zheng & Brajendra C. Sutradhar, 2018. "Inferences in semi-parametric dynamic mixed models for longitudinal count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 215-247, February.
    5. Li, Gaorong & Lian, Heng & Feng, Sanying & Zhu, Lixing, 2013. "Automatic variable selection for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 174-186.
    6. Jinsong Chen & Inyoung Kim & George R. Terrell & Lei Liu, 2014. "Generalised partial linear single-index mixed models for repeated measures data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 291-303, June.
    7. Yan Sun & Jialiang Li & Wenyang Zhang, 2012. "Estimation and model selection in a class of semiparametric models for cluster data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 835-856, August.
    8. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.
    9. 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.

    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:bla:jorssb:v:67:y:2005:i:4:p:531-553. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.