beta() defines a one-response distribution for continuous proportions
strictly inside (0, 1), with formulas for mean mu and scale sigma.
Details
The implemented contract is
logit(mu) = eta_mu, log(sigma) = eta_sigma, and internal precision
phi = 1 / sigma^2. Larger sigma therefore means more variation around
the mean, not more precision.
Ordinary unlabelled random intercepts and independent numeric slopes such as
(1 | id) and (0 + x | id) may enter the logit-mu predictor; sigma
remains fixed-effect in this first slice.
This helper masks base::beta() when drmTMB is attached. Use
base::beta() for the mathematical beta function.