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My initial hunch is no, since in case control data (assuming $y_i$ is a binary response, i.e. = 1 for case, 0 for control), we match a control (or several) per case. Meaning the data is very much dependent given the strata. But I saw this question here which made me think I might be wrong.

So, can GLMM be used with Case-Control data?

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