IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v64y2002i1p101-117.html
   My bibliography  Save this article

Robust estimation in generalized linear mixed models

Author

Listed:
  • Kelvin K. W. Yau
  • Anthony Y. C. Kuk

Abstract

Generalized linear mixed models (GLMMs) are widely used to analyse non‐normal response data with extra‐variation, but non‐robust estimators are still routinely used. We propose robust methods for maximum quasi‐likelihood and residual maximum quasi‐likelihood estimation to limit the influence of outlying observations in GLMMs. The estimation procedure parallels the development of robust estimation methods in linear mixed models, but with adjustments in the dependent variable and the variance component. The methods proposed are applied to three data sets and a comparison is made with the nonparametric maximum likelihood approach. When applied to a set of epileptic seizure data, the methods proposed have the desired effect of limiting the influence of outlying observations on the parameter estimates. Simulation shows that one of the residual maximum quasi‐likelihood proposals has a smaller bias than those of the other estimation methods. We further discuss the equivalence of two GLMM formulations when the response variable follows an exponential family. Their extensions to robust GLMMs and their comparative advantages in modelling are described. Some possible modifications of the robust GLMM estimation methods are given to provide further flexibility for applying the method.

Suggested Citation

  • Kelvin K. W. Yau & Anthony Y. C. Kuk, 2002. "Robust estimation in generalized linear mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 101-117, January.
  • Handle: RePEc:bla:jorssb:v:64:y:2002:i:1:p:101-117
    DOI: 10.1111/1467-9868.00327
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00327
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1467-9868.00327?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. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.
    2. Kelvin Yau & Karen Yip & H. K. Yuen, 2003. "Modelling repeated insurance claim frequency data using the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 857-865.
    3. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    4. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2009. "Robust empirical likelihood inference for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2101-2108, October.
    5. Qin, Guo You & Zhu, Zhong Yi & Fung, Wing K., 2008. "Robust estimating equations and bias correction of correlation parameters for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4745-4753, June.
    6. Whasoo Bae & Soonyoung Hwang & Choongrak Kim, 2008. "Influence diagnostics in the varying coefficient model with longitudinal data," Computational Statistics, Springer, vol. 23(2), pages 185-196, April.
    7. Guoyou Qin & Zhongyi Zhu & Wing Fung, 2012. "Robust estimation of the generalised partial linear model with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 517-530.
    8. David I. Ohlssen & Linda D. Sharples & David J. Spiegelhalter, 2007. "A hierarchical modelling framework for identifying unusual performance in health care providers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 865-890, 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:bla:jorssb:v:64:y:2002:i:1:p:101-117. 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.