Question about interpretation of the individual intercepts in m11.4

[thai1491]

In model m11.4, the model allows each monkey to have their own intercept but common treatment effect. I am not sure about the interpretation of the individual intercept when the treatment variable has index contrast. Does the intercept indicate the logit(p left) of an individual monkey when there is no treatment, and does this make sense when the smallest coding value of treatment is 1?

Sorry if the answer is obvious, but I haven't been able to wrap my head around this.

Thank you.

[ellen-ying]

Hi, I happen to work on the same chapter these days. My understanding is that the intercepts indicate the logit(p) of an individual chimp when there is no treatment (and this explains why Richard calls them the baseline probability for each chimp when converted back to the prob scale). I do think this makes sense because these are the values of alpha and they contribute to logit(p) independently of beta (the treatment effect). It's just like in a linear model, we interpret the intercept as if all other predictors are equal to 0.

(This being said, I feel that the interpretation here does lack a realistic meaning because chimps can't pull the lever without any treatment condition. To me, this is similar to fitting a linear model of, say, wage regressed on age without centering age. In this case, the intercept indicates the wage when age is zero, but this does not make any sense since babies can't earn anything yet.)

This is my interpretation and may not reflect how Richard thinks of his approach. Happy to chat!