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This is an addendum to the other answer that is too long for a comment. The original question regarded overdispersion in generalized linear mixed models models (I assume, given OP is using lme4). In this case there are covariates that will induce variation in excess of what would be expected for iid binomial data. This is actually a primary motivation for ...


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If you would like another explanation of the procedure, you can read the original paper by Tarone (1979), but the blog actually gives a longer and clearer explanation than the original paper. In any case, the function you have programmed does not correspond to the formula for Tarone's Z statistic. I would recommend writing a function that directly ...


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