I have proportional data, i.e. number of individuals out of 6 that choose a certain option in a multiple choice experiment, so there are just 7 possible outcomes for each option: 0/6; 1/6; 2/6; 3/6; 4/6; 5/6; 6/6.
I had several replicates and did several trials on each replicate. In order to find out which option was preferred (i.e. which option was chosen more frequently), I applied a GLMM with binomial distribution. Turned out that I had overdispersion (dispersion factor = 2) because there were too many zeros.
Now my question is how to go on with my analysis? Do I have to choose another type of distribution (in this case, which one? Beta, negative binomial, etc.?). And could you recommend any function in R to do so? I’m pretty new to GLM analysis.