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Joint Selection in Mixed Models using Regularized PQL

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  • Francis K. C. Hui
  • Samuel Müller
  • A. H. Welsh

Abstract

The application of generalized linear mixed models presents some major challenges for both estimation, due to the intractable marginal likelihood, and model selection, as we usually want to jointly select over both fixed and random effects. We propose to overcome these challenges by combining penalized quasi-likelihood (PQL) estimation with sparsity inducing penalties on the fixed and random coefficients. The resulting approach, referred to as regularized PQL, is a computationally efficient method for performing joint selection in mixed models. A key aspect of regularized PQL involves the use of a group based penalty for the random effects: sparsity is induced such that all the coefficients for a random effect are shrunk to zero simultaneously, which in turn leads to the random effect being removed from the model. Despite being a quasi-likelihood approach, we show that regularized PQL is selection consistent, that is, it asymptotically selects the true set of fixed and random effects, in the setting where the cluster size grows with the number of clusters. Furthermore, we propose an information criterion for choosing the single tuning parameter and show that it facilitates selection consistency. Simulations demonstrate regularized PQL outperforms several currently employed methods for joint selection even if the cluster size is small compared to the number of clusters, while also offering dramatic reductions in computation time. Supplementary materials for this article are available online.

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  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1323-1333
    DOI: 10.1080/01621459.2016.1215989
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    1. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    3. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
    4. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
    5. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    6. Vonesh E. F. & Wang H. & Nie L. & Majumdar D., 2002. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 271-283, March.
    7. 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.
    8. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    9. 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.
    10. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    11. Francis K. C. Hui & David I. Warton & Scott D. Foster, 2015. "Tuning Parameter Selection for the Adaptive Lasso Using ERIC," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 262-269, March.
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    Cited by:

    1. Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2021. "Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models," International Statistical Review, International Statistical Institute, vol. 89(1), pages 186-206, April.
    2. Liu, Li & Xiang, Liming, 2019. "Missing covariate data in generalized linear mixed models with distribution-free random effects," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 1-16.
    3. 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.
    4. 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.
    5. De La Maza, Cristóbal & Davis, Alex & Azevedo, Inês, 2021. "Welfare analysis of the ecological impacts of electricity production in Chile using the sparse multinomial logit model," Ecological Economics, Elsevier, vol. 184(C).

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