Use z-distribution for GLMs with dispersion parameter fixed to 1

[matthewravery]

At present, many GLM methods use t-distributions rather than z-distributions for GLMs where the dispersion parameter is fixed at 1. (See Section 2.6.2 of Applied generalized linear mixed models: Continuous and discrete data, 2010.) These methods should use a standard normal instead. See add_ci.glm, add_pi.glm, etc.

[jthaman]

atm add_pi.glm is doing a simulation via arm::sim, but I will keep this in mind when I try to write a parametric solution for GLM PIs.

[jthaman]

Note to remind myself to make a list of GLMs with dispersion param = 1.

[jthaman]

I looked in the code of summary.glm and found that you are correct: poisson and binomial GLMs are the only families where the dispersion param is set to one.