We are trying to identify the pairwise differences using an equivalent to Tukey which we assume cannot be used.
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Does this help you with your question? https://stats.stackexchange.com/questions/332412/negative-binomial-pairwise-comparison-in-r/332413#332413 – Stefan Mar 14 '18 at 21:12
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These models can also be fitted in a Bayesian framework via MCMC with rstanarm or brms which would obviate some of the concern about post hoc tests. The brms package in particular contains a nice function called hypothesis which provides a Bayesian factor and p value for a linear combination. https://github.com/paul-buerkner/brms – bjw Mar 15 '18 at 21:48