Hello all!

My question could have either a very easy or relatively complex answer, but I am currently lost and would appreciate some helpful insight.

I've been given a dataset with results from a binary-choice experiment in which a certain cue was introduced (and the side of introduction was randomized). In summary this is what I have:

>4 treatment groups

>4 replicate groups inside each treatment

>Cue input side (2 sides)

> two interdependent response variables:

> proportion of responsive inds (PR)

> proportion of inds that responded correctly (PC)

PR = nr of inds that responded (R) / total nr of inds tested (T)

PC = nr of inds that responded correctly (C) / nr of inds that responded (R)

Since I want to compare both response variables (response and choice), between treatments, I was planning on applying a Binomial GLM (possibly GLMM if test side or replicate could have any effect, and would add them as random effect).

Shouldn't I apply some kind of hierarchical test, since my response variables are directly dependent of each other?

(from the animals that responded, some exhibited a correct choice and others a wrong one).

Perhaps GLMMM? (but is it a rabbit hole?).

Thank you in advance!

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