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Review and comparison of measures of explained variation and model selection in linear mixed-effects models

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  • Cantoni, Eva
  • Jacot, Nadège
  • Ghisletta, Paolo

Abstract

In linear mixed-effects models, several frequentist and Bayesian measures have been proposed to evaluate model adequacy or/and to perform model selection. First, a large set of these measures are selected, presented with comparable notations, discussed in their strengths, weaknesses, and applicability range, and finally commented upon regarding their limitations. Then, these measures are illustrated on the home radon levels data (Gelman & Pardoe, Technometrics, 241-251, 48, 2006). Next, an extensive simulation study is carried out, to evaluate their sensitivity in selecting the correct model from a series of simpler models containing fewer parameters. Finally, recommendations on the use of these different measures are provided.11Additional results are available in the Supplementary Material.

Suggested Citation

  • Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.
    • Handle: RePEc:eee:ecosta:v:29:y:2024:i:c:p:150-168
    DOI: 10.1016/j.ecosta.2021.05.005
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Wheeler, David C. & Hickson, DeMarc A. & Waller, Lance A., 2010. "Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1657-1671, June.
    3. Ko, Vinnie & Hjort, Nils Lid, 2019. "Copula information criterion for model selection with two-stage maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 12(C), pages 167-180.
    4. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    5. Orelien, Jean G. & Edwards, Lloyd J., 2008. "Fixed-effect variable selection in linear mixed models using R2 statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1896-1907, January.
    6. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    7. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
    8. 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.
    9. Kiviet, Jan F., 2020. "Microeconometric dynamic panel data methods: Model specification and selection issues," Econometrics and Statistics, Elsevier, vol. 13(C), pages 16-45.
    10. Honghu Liu & Yan Zheng & Jie Shen, 2008. "Goodness-of-fit measures of R2 for repeated measures mixed effect models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1081-1092.
    11. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    12. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    13. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    14. Gruber, Lutz F. & West, Mike, 2017. "Bayesian online variable selection and scalable multivariate volatility forecasting in simultaneous graphical dynamic linear models," Econometrics and Statistics, Elsevier, vol. 3(C), pages 3-22.
    15. 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.
    16. Pu, Wenji & Niu, Xu-Feng, 2006. "Selecting mixed-effects models based on a generalized information criterion," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 733-758, March.
    17. Howard D. Bondell & Arun Krishna & Sujit K. Ghosh, 2010. "Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models," Biometrics, The International Biometric Society, vol. 66(4), pages 1069-1077, December.
    18. 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.
    19. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    20. Wataru Sakamoto, 2019. "Bias‐reduced marginal Akaike information criteria based on a Monte Carlo method for linear mixed‐effects models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 87-115, March.
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