I would like to know if is possible to run a model with a categorical response variable plus some categorical predictors (and its interactions) and a random factor in R?
when the response variable is binary or categorical, logistic regression models can accommodate continuous and/or categorical explanatory variables as well as interaction terms to investigate potential combined effects of the explanatory variables.
I think that you can use the glmer() function from lme4 package to made a GLMM where you can include random factors and a logistic regression family link. I've never made It before, but I hope that It Will work.