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Testing variance components in balanced linear growth curve models

Author

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  • Reza Drikvandi
  • Ahmad Khodadadi
  • Geert Verbeke

Abstract

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.

Suggested Citation

  • Reza Drikvandi & Ahmad Khodadadi & Geert Verbeke, 2012. "Testing variance components in balanced linear growth curve models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 563-572, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:3:p:563-572
    DOI: 10.1080/02664763.2011.603294
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    References listed on IDEAS

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    1. Garrett M. Fitzmaurice & Stuart R. Lipsitz & Joseph G. Ibrahim, 2007. "A Note on Permutation Tests for Variance Components in Multilevel Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(3), pages 942-946, September.
    2. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
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    Cited by:

    1. Baey, Charlotte & Cournède, Paul-Henry & Kuhn, Estelle, 2019. "Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 107-122.
    2. Reza Drikvandi & Olamide Lawal, 2023. "Sparse Principal Component Analysis for Natural Language Processing," Annals of Data Science, Springer, vol. 10(1), pages 25-41, February.

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