Is it possible to have brms do the following model:
y ~ N(exp(log_mu), exp(log_sigma))
log_mu = X * Beta
log_sigma = alpha0 + alpha1 * log_mu
clearly the log link on the mean and variance is easy and well documented but I wasn’t sure if I was able to utilize the mean in predicting the variance.
I think you can achieve this readily though the nonlinear modeling syntax in brms. Do the examples here clarify the way forward?
Btw, I’ve found location-scale models tend to behave better when modelling the log-variance (rather than log-sd as you have).
Isn’t the log variance just exactly twice the log sd, which would just rescale the coefficients?
Lol, I never realized that, but of course! 🤦♂️ I guess my “better behaved” anecdote is spurious
Thanks that’s what I needed
Oh wait! I just remembered why I like log-variance; because then a std_normal() prior has a nice pushforward density for the standard deviation: