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Model selection in linear mixed-effect models

Author

Listed:
  • Simona Buscemi

    (University of Palermo)

  • Antonella Plaia

    (University of Palermo)

Abstract

Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or random), the dimensionality of models and the structure of variance and covariance matrices, and also, wherever possible, the existence of an implemented application of the methodologies set out.

Suggested Citation

  • Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:4:d:10.1007_s10182-019-00359-z
    DOI: 10.1007/s10182-019-00359-z
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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. Yali Fan & Guoyou Qin & Zhong Yi Zhu, 2014. "Robust Variable Selection in Linear Mixed Models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4566-4581, November.
    3. Francisco M. M. Rocha & Julio M. Singer, 2018. "Selection of terms in random coefficient regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 225-242, January.
    4. Yuki Kawakubo & Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Conditional AIC under Covariate Shift with Application to Small Area Prediction," CIRJE F-Series CIRJE-F-944, CIRJE, Faculty of Economics, University of Tokyo.
    5. Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
    6. Francis K. C. Hui & Samuel Müller & A. H. Welsh, 2017. "Joint Selection in Mixed Models using Regularized PQL," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1323-1333, July.
    7. Shang, Junfeng & Cavanaugh, Joseph E., 2008. "Bootstrap variants of the Akaike information criterion for mixed model selection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2004-2021, January.
    8. Srivastava, Muni S. & Kubokawa, Tatsuya, 2010. "Conditional information criteria for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1970-1980, October.
    9. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    10. 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.
    11. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    12. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    13. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    14. Chen, Fei & Li, Zaixing & Shi, Lei & Zhu, Lixing, 2015. "Inference for mixed models of ANOVA type with high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 382-401.
    15. Shakhawat Hossain & Trevor Thomson & Ejaz Ahmed, 2018. "Shrinkage estimation in linear mixed models for longitudinal data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 569-586, July.
    16. Rohart, Florian & San Cristobal, Magali & Laurent, Béatrice, 2014. "Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 209-222.
    17. 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.
    18. 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.
    19. Cheng Wenren & Junfeng Shang, 2016. "Conditional conceptual predictive statistic for mixed model selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 585-603, March.
    20. Julia Braun & Leonhard Held & Bruno Ledergerber, 2012. "Predictive Cross-validation for the Choice of Linear Mixed-Effects Models with Application to Data from the Swiss HIV Cohort Study," Biometrics, The International Biometric Society, vol. 68(1), pages 53-61, March.
    21. Jiang, Jiming & Nguyen, Thuan & Rao, J. Sunil, 2009. "A simplified adaptive fence procedure," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 625-629, March.
    22. 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.
    23. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    24. Abhik Ghosh & Magne Thoresen, 2018. "Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 179-210, April.
    25. 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.
    26. 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.
    27. 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.
    28. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    29. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    30. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    31. Dimova, Rositsa B. & Markatou, Marianthi & Talal, Andrew H., 2011. "Information methods for model selection in linear mixed effects models with application to HCV data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2677-2697, September.
    32. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    33. M. Revan Özkale & Funda Can, 2017. "An evaluation of ridge estimator in linear mixed models: an example from kidney failure data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2251-2269, September.
    34. Xinyu Zhang & Hua Liang & Anna Liu & David Ruppert & Guohua Zou, 2016. "Selection Strategy for Covariance Structure of Random Effects in Linear Mixed-effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 275-291, March.
    35. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
    36. Sorensen, G. & Barbeau, E. & Stoddard, A.M. & Hunt, M.K. & Kaphingst, K. & Wallace, L., 2005. "Promoting behavior change among working-class, multiethnic workers: Results of the healthy directions - Small business study," American Journal of Public Health, American Public Health Association, vol. 95(8), pages 1389-1395.
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