Welcome to the forum!
Just to be clear, I think most people here believe that for the kind of analysis you have in mind, Bayesian analysis, using a mixed model, with packages based on Stan (most likely
rstanarm , possibly
brms ) are the best you can get. For such use cases we also provide support here. Depending on the exact scientific question you have, it is likely most people here would also advise you against doing a “test” with a yes/no answer and instead just try to estimate the effect size and its associated uncertainty. If you absolutely have to, you might want to do a hypothesis test with a Bayes factor using the
bridgesampling package, but Bayes factors may be tricky to get right (I’ve never used them myself, just know this is what people I respect say about them).
We will be able to help you most effectively, if you include more information about your ultimate scientific question (the “big picture”) and what exactly are your dependent and independent variables and how are they measured.
Unfortunately, if you, for whatever reason, want/need to stay within a frequentist framework (p-values, ANOVA, …), that would be outside the scope of this forum and we would ask you to move your question elsewhere. Even though I sympathize that getting an answer on Cross Validated is hard (I think I never got one unless I put a bounty on the question).
Best of luck with your analysis!