In a study I hypothetically conducted, I have the number of times individuals pressed an "A" button and the number of times they pressed a "B" button. I also recorded the numbers of times they made correct and incorrect guesses about which of two chickens weighed more. I recorded this data both before and after pouring a bucket of over them after a certain time. (This is hypothetical, but reflects my actual data.) Individuals were free to press the buttons as many times as they liked and make as many chicken-guesses as they wanted.
I want to see whether the proportion of "A"/"B" button presses affects their success rate when guessing which chicken is heavier, and I want to see if it has an interaction with being drenched with water.
I realize that I can use
cbind() to include the counts of successes and failures as a response variable, and the binomial GLM will weight the proportion of successes by the total number of choices. However, I want to do something similar with my independent variables on the right-hand side.
My model in R is as follows:
glmer(cbind(success.count, failure.count) ~ cbind(A.presses, B.presses)*water.treatment + (1|individual), data=db, family=binomial)
Is this acceptable? I've never seen it used before, and I can't find instances of it happening, but it seems to work when I run the model. If this IS acceptable (and means what I hope it means), how do I interpret the output?
Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.38463 0.10158 3.786 0.000153 *** cbind(A.presses, B.presses)A.presses 0.14501 0.03950 3.671 0.000241 *** cbind(A.presses, B.presses)A.presses -1.33795 0.31068 -4.307 1.66e-05 *** water.treatment1 -0.27075 0.15035 -1.801 0.071738 . . . .
What would the coefficient for
cbind(A.presses, B.presses)A.presses mean in this case?