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In this post I see how they calculate the confidence interval on the theta parameter of a negative binomial GLM: Confidence Interval for the Dispersion parameter of negbin distribution. I typically take into account overdispersion either using a quasibinomial GLM or using a binomial GLMM by incorporating an observation-level random effect (from which one could calculate the intraclass correlation as a measure of overdispersion, cf. https://royalsocietypublishing.org/doi/10.1098/rsif.2017.0213) though.

Would anyone happen to know how to calculate the confidence intervals on the dispersion coefficients if overdispersion is taken into account in those ways? Via nonparametric bootstrapping, or is there other faster approaches?

kjetil b halvorsen
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Tom Wenseleers
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  • One thought is that the quasilikelihood models treat the dispersion parameter as a nuissance parameter. Consequently, you can't derive reliable confidence interval estimates from such models, even by bootstrapping the dataset. I'd conjecture such intervals would be conservative, because you maximize the likelihood in the fixed parameters first. – AdamO Feb 16 '21 at 19:22
  • @AdamO And what if you model overdispersion via a GLMM with an observation-level random effect and calculate the intraclass correlation? Methods to calculate the confidence intervals of random effects are available at least, right? Or maybe via bootstrapping? – Tom Wenseleers Feb 16 '21 at 19:26

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