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An alternative REML estimation of covariance matrices in linear mixed models

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  • 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
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    References listed on IDEAS

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    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. 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.
    6. 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.
    7. 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.
    8. Lynn LaMotte, 2007. "A direct derivation of the REML likelihood function," Statistical Papers, Springer, vol. 48(2), pages 321-327, April.
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    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, Polish Statistical Association, vol. 20(4), pages 59-70, December.

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