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Selection of Fixed Effects in High-dimensional Generalized Linear Mixed Models

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Abstract

The selection of fixed effects is studied in high-dimensional generalized linear mixed models (HDGLMMs) without parametric distributional assumptions except for some moment conditions. The iterative-proxy-based penalized quasi-likelihood method (IPPQL) is proposed to select the important fixed effects where an iterative proxy matrix of the covariance matrix of the random effects is constructed and the penalized quasi-likelihood is adapted. We establish the model selection consistency with oracle properties even for dimensionality of non-polynomial (NP) order of sample size. Simulation studies show that the proposed procedure works well. Besides, a real data is also analyzed.

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Acknowledgements

The authors thank the Editors and the referees for their constructive comments and suggestions that substantially improved an earlier manuscript.

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Authors and Affiliations

  1. School of Science, China University of Mining & Technology (Beijing), Beijing, 100083, P. R. China

    Xi Yun Zhang & Zai Xing Li

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  1. Xi Yun Zhang
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  2. Zai Xing Li
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Correspondence to Zai Xing Li.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11671398), State Key Lab of Coal Resources and Safe Mining (China University of Mining and Technology) (Grant No. SKLCRSM16KFB03) and the Fundamental Research Funds for the Central Universities in China (Grant No. 2009QS02)

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Zhang, X.Y., Li, Z.X. Selection of Fixed Effects in High-dimensional Generalized Linear Mixed Models. Acta. Math. Sin.-English Ser. 39, 995–1021 (2023). https://doi.org/10.1007/s10114-023-2195-6

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  • DOI: https://doi.org/10.1007/s10114-023-2195-6

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