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Goodness-of-fit test in parametric mixed effects models based on estimation of the error distribution

Author

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  • Wenceslao González-Manteiga
  • María Dolores Martínez-Miranda
  • Ingrid Van Keilegom

Abstract

We address the problem of testing for a parametric function of fixed effects in mixed models. We propose a test based on the distance between two empirical error distribution functions, which are constructed from residuals calculated under the opposing hypotheses. The proposed test statistic has power against all alternatives, and its asymptotic distribution is derived. A simulation study shows that the test outperforms others in the literature. The test is applied to longitudinal data from an AIDS clinical trial and a growth study.

Suggested Citation

  • Wenceslao González-Manteiga & María Dolores Martínez-Miranda & Ingrid Van Keilegom, 2016. "Goodness-of-fit test in parametric mixed effects models based on estimation of the error distribution," Biometrika, Biometrika Trust, vol. 103(1), pages 133-146.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:133-146.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv061
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    Cited by:

    1. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    2. Cadirci, Mehmet Siddik & Evans, Dafydd & Leonenko, Nikolai & Makogin, Vitalii, 2022. "Entropy-based test for generalised Gaussian distributions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.

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