Thanks @ReneTwo for your quick response.
Regarding point 1, are you suggesting just adding the estimate of the variance in intercepts for each subject to the overall sigma given in the model output, and then using that as the divisor of the difference between groups?
No offence taken about the size of the effect - I agree it is very large, perhaps questionably so. On the other hand, it is ratings of emotion in a very high vs a low fear group, and they are told they are just about to be confronted with the feared object, so in the one group they really are freaking out, and the other group are just not bothered - the responses they give are totally different.
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For this shrinkage consideration, I used a rather vague prior as I knew the differences could be very large. Could this issue however be addressed with a sensitivity analysis - trying some alternative priors for the effect that are increasingly conservative, and confirming at which point, if at all, the estimates change?
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I think I follow you, but I’m not sure. Indeed if we did the effect size the standard way in frequentist stats we would get grp1 sd and grp2 sd separately, then do a pooled estimate to divide the group difference. In a separate regression, I did look at whether overall sigma varied by group (but not the variance in intercepts of subjects), and sigma seemed the same for each group, so I thought an overall sigma value might be possible. However, I did not ask for separate intercept sds per group.
I don’t think I completely understand what the code you noted would do - I think provide separate intercept variances for each group? Would you then pool these estimates, and add them to the overall sigma, or just use them on their own as the divisor of the group difference? Is gr a function?
Best,
Jamie