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All statistical tests were conducted with a modified F-statistic (Fs) that that shrinks variance components based on information from all the probe sets on the array [ 82].
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Similar to ANOVA and F-test, FS test is based on generalized linear model to estimate shrinking variance to determine DEGs.
In several papers, EB methods were designed to stabilize the expression values/ratios for genes with extreme values or else the variance of genes or gene groups by shrinking variances across all other genes, possibly diminishing the effects of artifacts in the data [ 6, 12- 19].
One well-known solutions to these problems is LASSO, which shrinks the variance of the coefficients and makes other coefficients zero [ 19].
Given that carotenoid traits are likely largely explained by a small number of moderate- to large-effect loci (Wong et al. 2004; Chander et al. 2008; Kandianis et al. 2013), we hypothesized that a variable selection method that shrinks the variance explained by noncontributing markers to near or equal to zero, such as LASSO or elastic net analysis, would show higher predictive ability.
Our results (shown in Supplementary Materials) confirmed that shrinking the variance leads to inferior performance.
This capability of shrinking the variance across all genes has been shown in several publications [ 36- 43].
This approach has the same effect as shrinking the variance towards a pooled estimate and thus reduces the probability of large test statistics arising due to underestimations of the sample variances.
Our justification for the use of limma is that it shrinks sample variances towards a pooled estimate, giving more stable results when the sample size is small [ 43], as is the case with our test data.
Accounting for shrinking grade variances and course selection also explains the convergence in grades for a group where we would expect catch up to not occur: legacies.
LIMMA employs an empirical Bayes methodology that effectively shrinks the sample variances towards a pooled estimate.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com