good tutorial/textbook chaper/review paper on Poisson regression :
Below are a few readings that discuss how to fit a generalized linear mixed model.
1. Breslow & Clayton (1993), JASA, Approximate Inference in
Generalized Linear Mixed Models.
https://doi.org/10.2307/2290687
A classic statistical paper introducing the Laplace approximation and penalized quasi-likelihood for GLMMs
2. Bates (2011), Mixed models in R using the lme4 package Part 5: Generalized linear mixed models
https://lme4.r-forge.r-project.org/slides/2011-03-16-Amsterdam/5GLMMH.pdf 3. Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of statistical software, 67, 1-48.
https://doi.org/10.18637/jss.v067.i01
4. Bates (2025), Computational methods for mixed models
https://cran.r-project.org/web/packages/lme4/vignettes/Theory.pdf
These are written by the authors of the lme4 package, discussing the details of how a mixed-effects model (more specifically, a generalized linear mixed-effects model) is trained using the PIRLS approach.
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