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Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

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Abstract

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

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Acknowledgements

This work was supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2014AM019), National Natural Science Foundation of China (Grant Nos. 11171188 and 11529101), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China, and National Science Foundation of USA (Grant Nos. DMS-1418042 and DMS-1620898). The authors thank two reviewers for their valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Xinmin Li

  2. Department of Mathematical Sciences, Montclair State University, Montclair, NJ, 07043, USA

    Haiyan Su

  3. Department of Statistics, George Washington University, Washington, DC, 20052, USA

    Hua Liang

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  1. Xinmin Li
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  2. Haiyan Su
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  3. Hua Liang
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Correspondence to Hua Liang.

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Li, X., Su, H. & Liang, H. Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models. Sci. China Math. 61, 1303–1318 (2018). https://doi.org/10.1007/s11425-016-9068-8

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