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Repeated-measures analysis with count data following a negative-binomial distribution

Just on the GEE vs GLMM question, this is a really nice clear article explaining the differences and how to choose:

Marginal or conditional regression models for correlated non?normal data?
Muff et al. 2016 MEE.
https://doi.org/10.1111/2041-210X.12623

Remarkably it has been cited only once in 2 years (Google Scholar).

To summarise their recommendations: in most cases you'll want a conditional (GLMM) model.