Evidence for interaction in Bayesian RM ANOVA
Hi, I would like to ask regarding the optimal analysis for interaction (within-by-within) term of two main factors. In particular, I would like to better understand how to estimate BFincl for the interaction and thus whether the effects should be calculated "Across all models" or "Across matched models".
As far as I understand, "matched models" should be preferred to evaluate the interaction term, since this strips the possible influences of main effects. For example, if I have 2 main factors (A,B) +1 interaction, the "matched models" allows me to estimate BFincl by comparing a model (A+B) against (A+B+A*B), thus to evaluate the evidence for (or "additive value" of) the interaction term. Is it correct that one should estimate matched models to get the BF estimate for the interaction term (ad least when the model is relatively simple)? Or is there a situation when "across all models" should be preferred for interaction terms?
Secondarily, following the same rationale, should "matched models" be also preferred for main effects?
I attended the latest JASP Bayesian workshop and did not notice this option, at least not realizing it may be that important to ask about it in more detail, so I hope I can get a kind of beginner-friendly response here. The thing is that reviewers of our paper asked to perform BF for RM ANOVA and "all models" versus "matched models" selection makes a difference (BF incl = 4.67 versus 1.17), i.e., while the former analysis of effects suggest moderate evidence (thus warranting a further investigation), the later suggests absence of evidence (please see the results below).
Thank you for your help,