Testing interactions: global test using F test with approximate degrees of freedom instead of LRT

[giulianonetto]

Hello!

Thank you for this amazing methodology and package! Please, I have a question about .ancombc_global_LRT.

From the source code, .ancombc_global_LRT seems to be doing a LRT between full and reduced models using two corresponding lmerTest::lmerModLmerTest objects.

From my understanding of the lmerTest paper and corresponding docs, the authors suggest using the anova.lmerModLmerTest method on the full model directly so that you can benefit from the implemented F tests with approximately correct degrees of freedom, avoiding the anti-conservativeness of the LRT in this setting.

Is this compatible with the ANCOMBC2 methodology? It seems to be a matter of removing the reduced model from .ancombc_global_LRT and adjusting downstream parsing accordingly (happy to PR if needed).

My motivation for this question is that I wanted to test the significance of interaction effects. I planned to implement this by running a global test using a model matrix from a fixed-effects formula of the form ~ x + time_point + x:time_point, where I would append a prefix "interaction" on the interaction terms and set group="interaction". Does this make sense? (sorry for the double question).

Thank you very much!