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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.

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    $\begingroup$ With the glmmTMB R-package your response can follow a zero-inflated binomial distribution with separate linear predictors for the zero-inflation probability and the probability $p$ of the non-zeroinflated component of the distribution. Both linear predictors can include random effects. $\endgroup$
    – Jarle Tufto
    Commented Sep 19, 2019 at 14:23
  • $\begingroup$ Thanks for your comment @JarleTufto! I already had a look at the glmmTMB package and it seems to offer quite a lot of possibilities. Remains the question how to specify the function for the zero-inflated part and how to interpret it, do you have any recommendations? $\endgroup$
    – Ricarda
    Commented Sep 19, 2019 at 19:34

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