Hi, I'm using BiSeq for finding relevant features in my targeted bisulfite sequencing data. Th response is the methylation and I want to find out wich features are relevant for distingishing between the two groups: case and control. Therefore I did a beta regression with the function betaRegression(), used "probit" as link function and set type to "BR" for maximum likelyhood bias reduction. But considering the Wald test for me it is not clear which test ist used!?

If I think about the problem, for me it's clear that if I want to test if there is a group effect in my model, I have to test the hypothesis of the F-Test: H0: ß1 = ß2 = ... = ßk = 0. This test tests if at least one of the fatures has an impact on the separation of the two groups: case and control.

But for me it is not clear why the output of the betaRegression() function provides a p value for evry single feature.

E.g. in the biSeq tutorial on page 19 https://bioconductor.org/packages/release/bioc/vignettes/BiSeq/inst/doc/BiSeq.pdf you can see this output:

I already read the documentation for BiSeq, for betareg and waldtest, but all I could find is the information that it uses either the finite sample F statistic or the asymptotic Chi-squared statistic.

Considering all the p values for me it makes more sense, that betaRegression() uses the Chi-squared test. Or are there multiple Wald tests: For each feature a test if the whole model is better than the model without the feature? Or the empty model against the model with the feature? Or ...?

Please can somebody explain? Thanks a lot.