individual a z t parameters are negative value when using hierarchical model

[YuanboBQ]

HSSM version
v0.2.0b1

Hi,
Thanks for updating the package. I am currently working with the v0.2.0b1 version of HSSM package, and I have encountered an issue while handling my own data. Specifically, when using hierarchical models with the sampler set to "nuts_numpyro", I am facing the following problem:
When I did not set link_settings = "log_logit", the sampling process was slow, and resulting in high values for r_hat. When I set link_settings = "log_logit", the sampling process was normal, and the r_hat was below 1.05. But the individual a z t parameters are negative value (See the below fig). How to fix this issue? Thanks!

[digicosmos86]

Hi @YuanboBQ:

Setting link_settings to "log-logit" adds link functions between the linear combination in the regressions and the response in the regressions. We added this setting so that the regressions on a, z, t are always within the defined domains for the likelihood function. However, doing so does change the interpretation of the regression estimates. Therefore, from how I understand the outputs, it's not surprising for some parameter values to be negative. For example, if you have a regression y ~ ax + by, and if you set the link function to log, then the regression becomes log(y) = ax + by.

If this is not desired behavior, we recommend that you set link_settings to None, and set prior_settings to safe. That way we apply safe priors to the regression parameters for more efficient sampling.

I defer to @AlexanderFengler for more detailed explanation.

[YuanboBQ]

Hi, Paul
Thanks for your reply. As I described above, if I set link_settings to None, the sampling process was slow, and resulting in high values of r_hat. I also try to updated the package to v0.2.0, and found that even using the latest version, it still result in high values of r_hat, and when using loglik_kind = "approx_differentiable", the samling process is very slow compare to previous version.

[digicosmos86]

Will convert this into a discussion. In HSSM v0.2.1, we made some enhancements to help with the convergence issue. It will be released soon. Please try it out and let us know if that doesn't resolve this issue