IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v38y2011i5p1063-1072.html
   My bibliography  Save this article

Leverage analysis for linear mixed models

Author

Listed:
  • Juvêncio S. Nobre
  • Julio M. Singer

Abstract

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Suggested Citation

  • Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:5:p:1063-1072
    DOI: 10.1080/02664761003759016
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664761003759016
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664761003759016?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. Jiang, Jiming, 1999. "On unbiasedness of the empirical BLUE and BLUP," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 19-24, January.
    2. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    3. Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, 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. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    2. Duarte Nubia E. & Giolo Suely R. & Pereira Alexandre C. & de Andrade Mariza & Soler Júlia P., 2014. "Using the theory of added-variable plot for linear mixed models to decompose genetic effects in family data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 359-378, June.
    3. Pinho, Luis Gustavo B. & Nobre, Juvêncio S. & Singer, Julio M., 2015. "Cook’s distance for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 126-136.
    4. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Mayor-Gallego, J.A. & Moreno-Rebollo, J.L., 2015. "A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 18-33.

    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. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    2. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    3. Patriota, Alexandre G., 2011. "A note on influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 218-225, January.
    4. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    5. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    6. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    7. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    8. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    9. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    10. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    11. 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.
    12. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    13. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    14. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    15. Emami, Hadi, 2015. "Influence diagnostic in ridge semiparametric models," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 106-113.
    16. Andréa Rocha & Alexandre Simas, 2011. "Influence diagnostics in a general class of beta regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 95-119, May.
    17. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    18. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    19. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    20. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.

    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:taf:japsta:v:38:y:2011:i:5:p:1063-1072. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.