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

Yahia S. El-Horbaty ()
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Yahia S. El-Horbaty: Helwan University

Quality & Quantity: International Journal of Methodology, 2024, vol. 58, issue 3, No 43, 3020 pages

Abstract: 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.

Keywords: ANOVA; Variance components; Idempotent matrix; Crossed random effects (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11135-023-01784-8

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