For next edition, rewrite all JAGS code so that the order/format matches how we write down equations describing our models. E.g.:

response variable ~ statistical distribution(parameters) transformation(parameters) <- linear predictor

In next addition, change: * X_{i,m} to I(sex = male)i * X{i,f} to I(sex = female)_i

Compare to predictSE.gls() in the AICcmodavg package (which I just learned of)! Note, the above only provides SEs for CIs and not PIs.

In next edition, add a note that the way the model is specified can influence how well the MCMC algorithms perform, and that the former approach typically leads to better mixing. Would be even better if the sd random effects were reformulated using a scale parameter multiplied by a standard normal distribution for the random effects. See:

https://elevanth.org/blog/2017/09/07/metamorphosis-multilevel-model/

For next edition, have a look at:

https://esajournals.onlinelibrary.wiley.com/doi/full/10.1002/ecy.4256#

Yes, that would be another option. However, the goal here is to introduce alternative methods specifically developed for count data - rather than compare all options. Also, there are potential reasons to prefer these alternative models - again, see Warton et al. 2016 (though, it is not always going to be a clear cut decision - and, fixing type I error rates may require resorting to atlernative (resampling- and permuation-based methods)..

Highlighting bbrandon's comment /eq typo

Add:

@article{addicott2022toward, title={Toward an improved understanding of causation in the ecological sciences}, author={Addicott, Ethan T and Fenichel, Eli P and Bradford, Mark A and Pinsky, Malin L and Wood, Stephen A}, journal={Frontiers in Ecology and the Environment}, year={2022}, publisher={Wiley Online Library} }

period