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A new matrix-based formulation for computing the variance components F-test in linear models with crossed random effects

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  • Yahia S. El-Horbaty

    (Helwan University)

Abstract

This paper considers the problem of testing statistical hypotheses about the variance components under linear models with crossed random effects. The objective here is two-fold. First, new derivations of exactly distributed F test statistics are presented. Second, an alternative Monte Carlo permutation procedure is proposed to approximate the distribution of the F statistics, which shows its usefulness when the error components distributions depart from normality. Transformations that uniquely decompose the covariance structure of the response vector and do not sacrifice any part of the data, as existing methods do, are presented in matrix form. The suggested transformations highlight the exchangeable covariance structure of the model under the null hypotheses of interest and thus motivate the use of the permutation procedure. Comments on the performance of the proposed procedure compared to existing tests as well as using a real data example are provided.

Suggested Citation

  • Yahia S. El-Horbaty, 2024. "A new matrix-based formulation for computing the variance components F-test in linear models with crossed random effects," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(3), pages 3001-3020, June.
    • Handle: RePEc:spr:qualqt:v:58:y:2024:i:3:d:10.1007_s11135-023-01784-8
    DOI: 10.1007/s11135-023-01784-8
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    References listed on IDEAS

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    1. Halekoh, Ulrich & Højsgaard, Søren, 2014. "A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models The R Package pbkrtest," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i09).
    2. Fuller, Wayne A. & Battese, George E., 1974. "Estimation of linear models with crossed-error structure," Journal of Econometrics, Elsevier, vol. 2(1), pages 67-78, May.
    3. Long Qu & Tobias Guennel & Scott L. Marshall, 2013. "Linear Score Tests for Variance Components in Linear Mixed Models and Applications to Genetic Association Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 883-892, December.
    4. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
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