IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i4p1071-1077.html
   My bibliography  Save this article

An alternative REML estimation of covariance matrices in linear mixed models

Author

Listed:
  • Li, Erning
  • Pourahmadi, Mohsen

Abstract

We propose a data-driven procedure for modeling covariance matrices in linear mixed-effects models with minimal distributional assumption on the random effects. It is based on elimination of the random effects using a transformation of the response variable. The approach makes it possible for the first time to disentangle the covariance matrices and model them separately. The performance of the proposed method is assessed via simulations and real data.

Suggested Citation

  • Li, Erning & Pourahmadi, Mohsen, 2013. "An alternative REML estimation of covariance matrices in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1071-1077.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1071-1077
    DOI: 10.1016/j.spl.2012.12.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004877
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.12.028?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. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Erning Li & Naisyin Wang & Nae-Yuh Wang, 2007. "Joint Models for a Primary Endpoint and Multiple Longitudinal Covariate Processes," Biometrics, The International Biometric Society, vol. 63(4), pages 1068-1078, December.
    3. Michael G. Kenward, 1987. "A Method for Comparing Profiles of Repeated Measurements," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 296-308, November.
    4. Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
    5. Erning Li & Daowen Zhang & Marie Davidian, 2004. "Conditional Estimation for Generalized Linear Models When Covariates Are Subject-Specific Parameters in a Mixed Model for Longitudinal Measurements," Biometrics, The International Biometric Society, vol. 60(1), pages 1-7, March.
    6. Lynn LaMotte, 2007. "A direct derivation of the REML likelihood function," Statistical Papers, Springer, vol. 48(2), pages 321-327, April.
    7. Li, Erning & Zhang, Daowen & Davidian, Marie, 2007. "Likelihood and pseudo-likelihood methods for semiparametric joint models for a primary endpoint and longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5776-5790, August.
    8. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, 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. Anasu Rabe & D. K. Shangodoyin & K. Thaga, 2019. "Linear Cholesky Decomposition Of Covariance Matrices In Mixed Models With Correlated Random Effects," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 59-70, December.
    2. Gul Inan & Ozlem Ilk, 2019. "A marginalized multilevel model for bivariate longitudinal binary data," Statistical Papers, Springer, vol. 60(3), pages 601-628, June.
    3. Rabe Anasu & Shangodoyin D. K. & Thaga K., 2019. "Linear Cholesky Decomposition Of Covariance Matrices In Mixed Models With Correlated Random Effects," Statistics in Transition New Series, Statistics Poland, vol. 20(4), pages 59-70, December.

    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. Duchwan Ryu & Erning Li & Bani K. Mallick, 2011. "Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements," Biometrics, The International Biometric Society, vol. 67(2), pages 454-466, June.
    2. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    3. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    4. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Bayesian analysis of joint mean and covariance models for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2504-2514, November.
    5. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    6. Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2021. "Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models," International Statistical Review, International Statistical Institute, vol. 89(1), pages 186-206, April.
    7. Warrington Nicole M. & Tilling Kate & Howe Laura D. & Paternoster Lavinia & Pennell Craig E. & Wu Yan Yan & Briollais Laurent, 2014. "Robustness of the linear mixed effects model to error distribution assumptions and the consequences for genome-wide association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(5), pages 567-587, October.
    8. Daniel McNeish & Jeffrey R. Harring & Denis Dumas, 2023. "A multilevel structured latent curve model for disaggregating student and school contributions to learning," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 545-575, June.
    9. Jacqmin-Gadda, Helene & Sibillot, Solenne & Proust, Cecile & Molina, Jean-Michel & Thiebaut, Rodolphe, 2007. "Robustness of the linear mixed model to misspecified error distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5142-5154, June.
    10. Brent A Coull, 2011. "A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs," Biometrics, The International Biometric Society, vol. 67(2), pages 486-494, June.
    11. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
    12. Laine Thomas & Leonard Stefanski & Marie Davidian, 2011. "A Moment-Adjusted Imputation Method for Measurement Error Models," Biometrics, The International Biometric Society, vol. 67(4), pages 1461-1470, December.
    13. Erning Li & Naisyin Wang & Nae-Yuh Wang, 2007. "Joint Models for a Primary Endpoint and Multiple Longitudinal Covariate Processes," Biometrics, The International Biometric Society, vol. 63(4), pages 1068-1078, December.
    14. Reyhaneh Rikhtehgaran & Iraj Kazemi, 2013. "Semi-parametric Bayesian estimation of mixed-effects models using the multivariate skew-normal distribution," Computational Statistics, Springer, vol. 28(5), pages 2007-2027, October.
    15. Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    16. Weiping Zhang & MengMeng Zhang & Yu Chen, 2020. "A Copula-Based GLMM Model for Multivariate Longitudinal Data with Mixed-Types of Responses," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-379, November.
    17. Loy, Adam & Hofmann, Heike, 2014. "HLMdiag: A Suite of Diagnostics for Hierarchical Linear Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(i05).
    18. Xiao Song & Marie Davidian & Anastasios A. Tsiatis, 2002. "A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 58(4), pages 742-753, December.
    19. Philip S. Boonstra & Bhramar Mukherjee & Jeremy M. G. Taylor & Mef Nilbert & Victor Moreno & Stephen B. Gruber, 2011. "Bayesian Modeling for Genetic Anticipation in Presence of Mutational Heterogeneity: A Case Study in Lynch Syndrome," Biometrics, The International Biometric Society, vol. 67(4), pages 1627-1637, December.
    20. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.

    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:stapro:v:83:y:2013:i:4:p:1071-1077. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.