DDM: z or beta?

[DominiqueMakowski]

The starting point is currently named z, but I've also seen a couple of papers and software using $\beta$. Any reason to favour the former? $\beta$ has the advantage that 1) it suggests a link with alpha (which it has) and 2) "b" hints at "bias" so it makes it easier to remember.

[DominiqueMakowski]

In signal detection theory, the bias is also called beta (https://bookdown.org/danbarch/psy_207_advanced_stats_I/signal-detection-theory.html#beta)

[kiante-fernandez]

I have seen both as well. $z$ comes from the DDM tradition where Ratcliff, among others, named it $z$ in influential works. Of note I have also seen $w$ used to indicate the relative versus absolute starting point. $\beta$ could make sense (and I have used $\beta$ in past papers because the JAGS implementation did so), though it may cause some confusion when people specify parameters as linear combinations of predictors, which are in many cases labeled as $\beta$'s.

[itsdfish]

I don't have a strong preference for either, but I do have a slight preference not make breaking changes =)

I will be making some breaking changes sometime in the next couple of months. So that would be a good time to make the change.

[itsdfish]

I'm going to leave the bias parameter as z. I think there is enough convention for using z and it also has the appeal of requiring no additional effort 😄