variance for cloglog link

[jebyrnes]

trafficstars

Love this package. I was working with a beta regression with a cloglog link recently, but cannot get an R2. Here is a reproducible example. Thoughts?

library(insight)
library(betareg)
library(glmmTMB)

data("GasolineYield", package = "betareg")

## Table 1
gy <- glmmTMB(yield ~ batch + temp, 
              data = GasolineYield,
              family = beta_family(link = "cloglog"))

insight::get_variance(gy)

This yields

[1] NA
Warning message:
Model link 'cloglog' is not yet supported for the beta distribution. 

It looks like, though, Nakagawa et al. have worked this out - see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636267/pdf/rsif20170213.pdf

The distribution specific-variance is (pi^2)/6 and the observation level variance is defined in a table in the paper.

Any chance this will make it into a new version anytime soon?

[strengejacke]

I'm not sure if the cloglog-link for the beta-family can be treated in the same way as for betabinomial familiies?