Science China Mathematics

, Volume 61, Issue 7, pp 1303–1318 | Cite as

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

  • Xinmin Li
  • Haiyan Su
  • Hua Liang


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.


fiducial distribution generalized pivotal quantity generalized test variable penalized spline additive models restricted likelihood ratio test structural equation zero-variance components 


62J10 62G10 


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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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQingdao UniversityQingdaoChina
  2. 2.Department of Mathematical SciencesMontclair State UniversityMontclairUSA
  3. 3.Department of StatisticsGeorge Washington UniversityWashingtonUSA

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