Hi,
sorry for not getting to you earlier, your question is relevant and well written.
Sigmoids are generally very hard to fit, I’ve spent substantial time working with them and I still have no idea how to fit them reliably in all cases. I would expect a lot of the issues to have to do with the sigmoid part and less with the centering/non-centering.
Some discussion of problems with sigmoids can be found at:
- Identifying non-identifiability
- Dose Response Model with partial pooling on maximum value - #3 by martinmodrak
- There was a cool presentation at the online StanCon 2020 about fitting growth curves to Icelandic Covid data, the Q&A is in a separate video. he main idea was to fit the derivative of the curve to differences between consecutive data points instead of fitting the sigmoid directly. I never tried this myself, but I can see how it could sometimes make your life easier.
I don’t have a good answer to your general question. I think the fact that your model is able to fit only some simulated datasets is often an interesting information not to be thrown away. However , you often don’t believe your real datasets have as much variability as the simulated ones so finding better prior or other ways to only simulate datasets that you would care about is often helpful. As a last resort I would try to develop heuristics to pick a model based on the data.
Best of luck with your model