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Uniformly valid inference based on the Lasso in linear mixed models

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  • Kramlinger, Peter
  • Schneider, Ulrike
  • Krivobokova, Tatyana

Abstract

Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics, and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are based on Lasso-type estimators. Aside from providing confidence regions, this also allows for quantification of the joint uncertainty of both variable selection and parameter estimation in the procedure. To show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter spaces of both the regression coefficients and the covariance parameters, we also prove the novel result on uniform Cramér consistency of the restricted maximum likelihood (REML) estimators of the covariance parameters. The superiority of the constructed confidence sets to naïve post-selection procedures is validated in simulations and illustrated with a study of the acid-neutralization capacity of lakes in the United States.

Suggested Citation

  • Kramlinger, Peter & Schneider, Ulrike & Krivobokova, Tatyana, 2023. "Uniformly valid inference based on the Lasso in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x23000763
    DOI: 10.1016/j.jmva.2023.105230
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    References listed on IDEAS

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    1. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    2. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. 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.
    4. Lynn LaMotte, 2007. "A direct derivation of the REML likelihood function," Statistical Papers, Springer, vol. 48(2), pages 321-327, April.
    5. Ali Charkhi & Gerda Claeskens, 2018. "Asymptotic post-selection inference for the Akaike information criterion," Biometrika, Biometrika Trust, vol. 105(3), pages 645-664.
    6. 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.
    7. Cressie, N. & Lahiri, S. N., 1993. "The Asymptotic Distribution of REML Estimators," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 217-233, May.
    8. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(2), pages 163-185, June.
    9. 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.
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