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Model averaging for linear mixed models via augmented Lagrangian

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  • Kruse, René-Marcel
  • Silbersdorff, Alexander
  • Säfken, Benjamin

Abstract

Model selection for linear mixed models has been a focus of recent research in statistics. Yet, the method of model averaging has been sparsely explored in this context. A weight finding criterion for model averaging of linear mixed models is introduced, as well as its implementation for the programming language R. Since the optimization of the underlying criterion is non-trivial, a fast and robust implementation of the augmented Lagrangian optimization technique is employed. Furthermore, the influence of the weight finding criterion on the resulting model averaging estimator is illustrated through simulation studies and two applications based on real data.

Suggested Citation

  • Kruse, René-Marcel & Silbersdorff, Alexander & Säfken, Benjamin, 2022. "Model averaging for linear mixed models via augmented Lagrangian," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321001857
    DOI: 10.1016/j.csda.2021.107351
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    References listed on IDEAS

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    1. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    2. Benjamin Säfken & Thomas Kneib, 2020. "Conditional covariance penalties for mixed models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 990-1010, September.
    3. Wensheng Guo, 2002. "Functional Mixed Effects Models," Biometrics, The International Biometric Society, vol. 58(1), pages 121-128, March.
    4. Chengbo Li & Wotao Yin & Hong Jiang & Yin Zhang, 2013. "An efficient augmented Lagrangian method with applications to total variation minimization," Computational Optimization and Applications, Springer, vol. 56(3), pages 507-530, December.
    5. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
    6. Xinyu Zhang & Guohua Zou & Hua Liang, 2014. "Model averaging and weight choice in linear mixed-effects models," Biometrika, Biometrika Trust, vol. 101(1), pages 205-218.
    7. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    9. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    10. Alexander Silbersdorff & Julia Lynch & Stephan Klasen & Thomas Kneib, 2018. "Reconsidering the income‐health relationship using distributional regression," Health Economics, John Wiley & Sons, Ltd., vol. 27(7), pages 1074-1088, July.
    11. Hua Liang & Hulin Wu & Guohua Zou, 2008. "A note on conditional aic for linear mixed-effects models," Biometrika, Biometrika Trust, vol. 95(3), pages 773-778.
    12. Simon N. Wood, 2013. "A simple test for random effects in regression models," Biometrika, Biometrika Trust, vol. 100(4), pages 1005-1010.
    13. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    14. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    15. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    16. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
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