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A note on conditional aic for linear mixed-effects models

Author

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  • Hua Liang
  • Hulin Wu
  • Guohua Zou

Abstract

The conventional model selection criterion, the Akaike information criterion, aic , has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida & Blanchard (2005) demonstrated that such a marginal aic and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested the use of conditional aic . Their conditional aic is derived under the assumption that the variance-covariance matrix or scaled variance-covariance matrix of random effects is known. This note provides a general conditional aic but without these strong assumptions. Simulation studies show that the proposed method is promising. Copyright 2008, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:773-778
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    Citations

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    Cited by:

    1. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    2. 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.
    3. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.
    4. 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.
    5. Overholser, Rosanna & Xu, Ronghui, 2014. "Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 160-170.
    6. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    7. Yunquan Song & Minmin Zhan & Yue Zhang & Yongxin Liu, 2024. "Huber Loss Meets Spatial Autoregressive Model: A Robust Variable Selection Method with Prior Information," Networks and Spatial Economics, Springer, vol. 24(1), pages 291-311, March.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. Rahul Govind & Rabikar Chatterjee & Vikas Mittal, 2018. "Segmentation of Spatially Dependent Geographical Units: Model and Application," Management Science, INFORMS, vol. 64(4), pages 1941-1956, April.
    13. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
    14. 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.
    15. 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.
    16. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    17. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    18. 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.
    19. Braun, Julia & Sabanés Bové, Daniel & Held, Leonhard, 2014. "Choice of generalized linear mixed models using predictive crossvalidation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 190-202.
    20. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.

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