I’m working on a non-linear model using ‘brms’, specifically, a dose-response model.
My response data are binomial, and the model is a four-parameter sigmoid. I’m wondering about an efficient strategy in brms for defining the grouping variance, in the case where parameters are bounded.
For binomial responses the parameters defining the upper and lower bounds EMAX and EMIN are naturally constrained to be (0,1), which can be accommodated using the identity link for the response and, say, beta priors for those population parameters.
What about the grouping parameters? Say for example I have (1|Subject) within my non-linear specification:
bf(Count|trials(Total) ~ EMIN + ((EMAX) /(X+EC50)), EMIN+EMAX+EC50 ~ 1 + (1|Subject), nl = TRUE)
Then the parameter EMAX for example is normally-distributed across ‘Subject’, but I’d like it to be (0,1) constrained. I could specify them in log-space to accommodate a lower zero bound, but is there a simple strategy (logit-transformation?) to work with both lower and upper bounds?