[Simon Anders]

No, because due to the use of an empirical-Bayes estimation method for dispersion estimation, you do not consume DoFs as usual.

Otherwise, it would be completely impossible to perform comparisons between groups with only two to four samples per group. For details, see Gordon Smyth's original 2004 paper on limma, which introduced this whole idea of understanding empirical-Bayes shrinkage estimation as a way of "saving degrees of freedom" by sharing information across genes.

[moritzhess]

Hi Simon,

thank's for your response. That's very interesting I might need to study the matter more in detail to fully understand.
Moritz

[Ariana G.]

More concerns

If we model random effects as fixed effects and put bayes prior on the fixed effects to get shrunken estimates, more concerns are:

(1) When the design is complex with nested designs (such as split-plot) and blocking effects, etc. how to correctly estimate variation merely due to sampling/replication; i.e. so-called "error variation"? The size of error variation is crucial for significance test. Is there any research to assess the nearly equivalence of "fixed effects with empirical bayes" and "random effects with empirical bayes"? Because you can also put prior on random effects also to borrow information across genes.

I once analyzed a gene expression data with complex designs. I first use edgeR GLM and DESeq also. edgeR and DESeq results are very similar. Then I used GLMM (no shrinkage, but random effects), I got a lot more significant differentially expressed genes than edgeR and DESeq by controlling FDR at 0.05. So, the above two things "fixed with empirical bayes" and "random effects" are not quite equal from this experience I have.

(2) Correlation among observations. Does the "fixed effects with empirical bayes" correctly model correlations among observations? Bayes prior does put correlations among genes, but within a gene, how does it model correlations among observations within a gene where split-plot or blocking happen?

Thanks,
Ariana G.

No, because due to the use of an empirical-Bayes estimation method for dispersion estimation, you do not consume DoFs as usual.

Otherwise, it would be completely impossible to perform comparisons between groups with only two to four samples per group. For details, see Gordon Smyth's original 2004 paper on limma, which introduced this whole idea of understanding empirical-Bayes shrinkage estimation as a way of "saving degrees of freedom" by sharing information across genes.

[Simon Anders]

Not sure whetehr ther's mich point in reviving this old thread, hence just to clarify:

Of course, fixed models with empirical Bayes shrinkage cannot replace any form of mixed models. Especially they cannot account for nested designs, repeated-measure designs, or other designs which cause the strength of correlation between samples within a treatment group to depend on sub-structure.

My point back then (as far as I can say now) was merely that quite often, people think they need mixed models but don't.