Dose Response Model with partial pooling on maximum value

Yes, I’ve worked with sigmoids in models a bit. They can be challenging to fit.

But first think you might want to check out is “non-centered parametrization” of the hierarchical component, i.e. have parameters var_d_raw ~ normal(0,1); and then derive transformed parameter var_d = var_d_raw * d_var_sigma. (see e.g. https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html for more details).

I’ve found the direct parametrization of the sigmoid problematic, primarily because if your data don’t cover the whole “dynamic range” of the sigmoid (i.e. data close to both lower and upper plateau and to the middle), some of the parameters can become basically unconstrained by data. My other guess here is that when you have a single d the data cover the whole dynamic range, while when you let d (and hence the whole sigmoid) vary by group (variety), this ceases to be the case for some groups. I would expect that you would see in the posterior is that as d_var_sigma gets larger, all of the sigmoid parameters are allowed to vary wildly.

I worked with @stemangiola on fitting sigmoids in a different context, you might want to check out the parametrization we used in a preprint: https://doi.org/10.1101/2020.03.16.993162, also discussed at Difficulties with logistic population growth model

I also wrote about some of the considerations at Hierarchical Gompertz model

Best of luck with your model!

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