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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?

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    $\begingroup$ I've never seen it done before, but that doesn't mean it is wrong. $\endgroup$ – william3031 Oct 17 at 8:43

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