Issues in the graphical representation of the DDM in the README file

[dkatsimpokis]

The README file contains a figure of a hierarchical DDM model with trial-to-trial variability in the drift rate, on top of the the mean drift-rate, threshold and non-decision time parameters. Although the Figure is informative and gives a succinct depiction of how hierarchical models work, it contains some issues that need to be addressed.

Specifically, in the Wiener distribution of error responses, the threshold parameter is given as -α and the bias parameter as z. However, these are both mistakes because, first, the valence of the threshold does not change across error/correct RT distributions and, second, the bias parameter needs to be 1-z (it adds up to 1 across the error/correct RT distributions).

[mar-wir]

Hi!

-α and the bias parameter as z. However, these are both mistakes because, first, the valence of the threshold does not change across error/correct RT distributions and, second, the bias parameter needs to be 1-z

I followed the implementation of https://compcogscisydney.org/publications/NavarroFuss2009.pdf and subsequently

Ahn, Woo-Young, Nathaniel Haines, and Lei Zhang. 2016. “Revealing Neuro-Computational Mechanisms of Reinforcement Learning and Decision-Making with the hBayesDM Package.” bioRxiv. Cold Spring Harbor Laboratory. doi:10.1101/064287.

Can you confirm that my implementation diverges from those?

[dkatsimpokis]

Hi Marco!

Sorry for the late response. I think your implementation (in the code) follows the references you cited. What is problematic I think is the Figure in the readme file. According to the figure, the wiener distribution statement for wrong responses (when S = 0) has a negative drift rate (which is correct) but also a negative threshold parameter (alpha) and a bias parameter (zeta). Nevertheless, alpha should not be negative and zeta should be (1 - zeta) since zeta should add up to one across the correct/error responses.

In your code you have implemented it correctly. For example, in the simplest case of the pure DDM, the code is (StanDDM_NCEN_Pure.r, lines: 84-85):

log_lik[i] = wiener_lpdf(RTu[i, :Nu[i]] | alpha[i], tau[i], beta[i], delta[i]);

log_lik[i] = log_lik[i] + wiener_lpdf(RTl[i, :Nl[i]] | alpha[i], tau[i], 1-beta[i], -delta[i]);

As you see in the second line, the bias is constrained to 1-beta and alpha is not negative. This should also be reflected in the Figure of the readme file.

[mar-wir]

You are right, sorry for the delay! I did make a note, cannot find the original tex file for the graphic. Thanks again for pointing it out!