Multinomial mixed effect regression? I have data regarding level of damage in tissue samples, using a Likert scale. Our main goal is to understand if there is a difference in the levels between two groups - control and treated.
An example of a dataset:
df<-data.frame(Class=as.character(sample(1:5,size = 50,replace=T)),
               Trt=sample(c("Ctrl","Exp"),size = 50,replace=T),
               Exp=rep(paste0("Exp",1:5,sep=""),each=10))

Edit: We will have data from 5-7 independent experiment, which lead us to think mixed effect regression as the ideal approach (to account for among-experiment variability). Per experiment, we are expecting at most 12 observations but, might be less (<10).
I was thinking to perform a multinomial mixed effect regression. Do you agree? Or is it any other recommended alternative? Any package recommendation for this type of analysis?
Thanks in advance!
 A: It's good to be asking questions about data analysis before you collect the data.
First, with ordered categorical outcomes you should be considering a form of ordinal regression. It comes in two major versions, briefly summarized here, and it's possible in both versions to choose link functions besides the standard logit for logistic regression. This UCLA web page has a helpful introduction, via a proportional-odds logistic-regression fixed-effects model.
Second, experiment numbers of 5 to 7 are close to a common decision boundary for using random effects versus mixed effects to account for such differences. I'll point you to the GLMM FAQ and this Cross Validated page (among many others) for discussion of the issues. With 5 to 7 experiments you are unlikely to get a good estimate of the variance among experiments, if that's of interest in itself.
Third, you have to think carefully about what type of "among-experiment variability" you are trying to "account for." A simple fixed or random effect would only "account for" baseline (intercept) variability in Damage. It wouldn't "account for" variability in the association between Treatment and Damage. To account for that you would have to add interaction terms between Treatment and fixed experiment effects, or random "slopes" with respect to Treatment (along with an assumption about random intercept-slope correlations).
The R ordinal package can handle proportional-odds logistic regression mixed models, or similar models with other cumulative link functions. This page shows how to format and analyze data for continuation-ratio mixed models with tools in the GLMMadaptive package.
As you seem to still be in the study design phase, it would make sense to simulate outcomes of the type you expect, to get a handle on these analyses and to ensure that your design has enough power to answer your question. In particular, evaluate different scenarios for the variability among experiments. That would seem to be a big potential limiting factor. You might consider tradeoffs between the number of experiments and the number of cases per experiment, as inter-experiment variability changes.
