Question about eta transformation in hBayesDM bart_ewmv

[Haoyu Nie]

Hi all,

I am currently working with the EWMV model in hBayesDM::bart_ewmv and had a question regarding the implementation of the updating parameter.

In the Stan code, I noticed that:

• the subject-level parameter eta is transformed as eta = Phi_approx(mu_pr[2] + sigma[2] * eta_pr);

• this appears to constrain eta to the interval [0, 1]

However, in Park et al. (2021), the corresponding parameter in the EW/EWMV framework is described as an updating exponent ξ > 0, which does not seem to imply an upper bound of 1.

Could this mean that the bounded eta in bart_ewmv is mainly a package-specific implementation choice, for example for estimation stability or regularization, rather than a direct theoretical requirement of the original model?

I am asking because I am fitting a custom EW model alongside the packaged hBayesDM EWMV model, and I am trying to understand how closely I should align the parameter transformation across models.

Any clarification would be greatly appreciated.

Kind regards,

Haoyu Nie

PhD Candidate, University of Vienna

SCAN Unit

[Jinwoo Jeong]

Dear Haoyu,

The upper bound of the updating exponent ξ can be considered a package-specific implementation choice. Although the parameter is theoretically unbounded, the Stan code is assuming that value range of 0–1 is reasonable.

While this is not explicitly specified in the paper, the parameter recovery results reported in Park et al. (2021) also show that ξ values can be very low and an upper bound of 1 is big enough. I suggest you fit your data with the hBayesDM first and see if the the upper bound of the parameter need to be adjusted (e.g., check whether the parameter value is close to 1).

FYI, if you know how to program in Stan, you can adjust or remove this value range as needed in your custom EW model implementation. Same goes for other models and parameters in our package.

Best regards,
Jinwoo Jeong