gaussian(link="cloglog")

[therneau]

An edge case perhaps, but I have data which is quite close to a cloglog curve, though the response is not binomial. This is the accumulation over time for amyloid in the brain, as measured using PET scans with Pittsburgh compound B (PIB). The following lme4 code works (age70 = (age -70)/10 , it makes glmer happier).

fit <- glmer( I(log(pib)/2) ~ age70 + male + apoepos + (1| id), pdata, family= gaussian(link= 'cloglog'), mustart= ....)

(You need mustart or glmer gets unhappy about a response outside of 0/1, but that is just starting estimates.) Subjects follow essentially the same progression curve, but shifted forward and back in time. The presence of one or more e4 alleles on the APOE gene for instance leads to amyloid accumulation about 8 years earlier, on average.

However, I wanted more control over the variance of the random effect, enter rstanarm.
But stan_glmer does not allow this link.

rstanarm_2.32.1
R version 4.3.2 (2023-10-31)
Unix

Priority: low. I'll set up STAN code for this by hand. But rstanarm would have been simpler

Terry Therneau