I fitted the same linear mixed model with changing response variables:
lmer(Response ~ categorical predictor 1 * categorical predictor 2 + (1|random effect1/random effect2)
(one predictor has 2 levels the other 3)
Afterwards I used the anova to check for signficant effects of the 2 predictors. Model validation tells me for one response, that the variances are not homogenous. Now I was thinking about the next steps. I thought about using a Kruskal-Wallis test, but that does not work with my 2 predictors in one line. Is it correct to do one Kruskal-test for the one predictor and an other for the other one? I am pretty new to statistics and it is really difficult when things are not following a typical recipe. So sorry if the question is a bit stupide.
I have read this question: General approach for non-parametric two-way ANOVA but this is for only one predictor