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A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure

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  • Craiu, Radu V.
  • Duchesne, Thierry

Abstract

A new model selection criterion for mixed effects regression models is introduced. The criterion is computable even when the model is fitted with a two-step method or when the structure and the distribution of the random effects are unknown. The criterion is especially useful in the early stage of the model building process when one needs to decide which covariates should be included in a mixed effects regression model, but has no knowledge of the random effect structure. This is particularly relevant in substantive fields where variable selection is guided by information criteria rather than regularization. The calculation of the criterion requires only the evaluation of cluster-level log-likelihoods and does not rely on heavy numerical integration. Theoretical and numerical arguments are used to justify the method and its usefulness is illustrated by analysing data from a youth behaviour study.

Suggested Citation

  • Craiu, Radu V. & Duchesne, Thierry, 2018. "A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 154-161.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:154-161
    DOI: 10.1016/j.csda.2017.07.011
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    References listed on IDEAS

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    1. 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).
    2. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    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. 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.
    5. Inna Chervoneva & Boris Iglewicz & Terry Hyslop, 2006. "A General Approach for Two-Stage Analysis of Multilevel Clustered Non-Gaussian Data," Biometrics, The International Biometric Society, vol. 62(3), pages 752-759, September.
    6. Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    7. M. C. Donohue & R. Overholser & R. Xu & F. Vaida, 2011. "Conditional Akaike information under generalized linear and proportional hazards mixed models," Biometrika, Biometrika Trust, vol. 98(3), pages 685-700.
    8. 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.
    9. Molenberghs, Geert & Verbeke, Geert & Iddi, Samuel, 2011. "Pseudo-likelihood methodology for partitioned large and complex samples," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 892-901, July.
    10. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    11. Renard, Didier & Molenberghs, Geert & Geys, Helena, 2004. "A pairwise likelihood approach to estimation in multilevel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 649-667, January.
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