Fundamental question : Can drift rate be varied with stimulus type in accuracy coding?

[Lipika-T]

Hello,

I am trying to fit a DDM to responses from an emotion categorization task with 3 emotions - Happy, Fear and Neutral. I'm using accuracy coding and I am varying drift rate, threshold and non-decision time with the emotion condition. Is this approach correct for a task where there are 3 possible responses? I read in this paper that in accuracy coding the drift rate should not be varied by the stimulus type.
https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2015.00336/full

["Optimally, diffusion model tasks should comprise two response keys that are linked in the analyses to the upper vs. lower threshold. It is also possible to recode responses as correct (upper threshold) vs. incorrect (lower threshold). However, this mapping requires some attention: (a) One needs to be sure that drift rates do not differ between stimulus types; (b) there should be no decision bias, and the relative starting point has to be fixed to 0.5; and (c) it has to be considered that results might be less robust in case of low error numbers (because then the distribution of responses at the lower threshold is absent or small). If these requirements are not met, the linear ballistic accumulator model should be preferred because it allows mapping data with multiple responses"]

The accuracy is also high for this task, is that an issue for accuracy coding?

I also wanted to understand what 'z' means for accuracy coding. I read that it should be fixed to 0.5. I first tried to fit this model keeping 'z' as a free parameter. But for multiple models 'z' was estimated to be around 0.3 - 0.4. What could this mean? These models did converge (r-hat of z < 1.01).

[AlexanderFengler]

Few thoughts:

1. Why do prefer accuracy coding here to begin with?
2. The interpretation of z != 0.5 can simply be a bit unnatural since it conceptually implies that you are a priori biased to be accurate/inaccurate. Usually doesn't make sense.
3. I don't immediately understand why you couldn't/shouldn't allow the drift to vary by stimulus here, even though I can acknowledge that the cited paper does mention that.
4. Low error numbers will make parameter inference more tricky, often produces severe parameter trade-offs, which then either make sampling difficult and/or render the interpretation of marginal parameter estimates hard to interpret (a given tradeoff will "smear" the posteriors over implicated parameters, so marginal posterior mean and variance become less useful to report).

Re point 1: If you have n>2 choice options, and you don't want to use accuracy coding, but instead follow an approach where you model one accumulator per choice, as the paper you cite suggests, you could use the LBA3, or one or e.g. the Race model we have available in HSSM.

We are aiming to increase model coverage quite a bit over the next few months.

[Lipika-T]

Thank you for your reply. Regarding the first point, I used accuracy coding here because there are 3 possible responses. I was wondering if it is conceptually wrong to use accuracy coding like that and vary the parameters with the emotion (which also becomes the response here). The models do converge.
Also regarding point 4, I'm a bit unclear about this part - "(a given tradeoff will "smear" the posteriors over implicated parameters, so marginal posterior mean and variance become less useful to report)." Is my understanding correct that a tradeoff might lead to some parameter reflecting all differences and seeing no difference in other parameters?
I'm also not sure about the sampling part you mentioned. Are the low errors, and therefore sampling considered problematic even if the models converge?

[AlexanderFengler]

Hi @Lipika-T ,

The core idea behind accuracy coding is that you break things down into 'correct' and 'incorrect' answers in a binary way. The way you model parameters e.g. the bias, you just need to make sure that logically this makes sense (having an 'accuracy bias').

If you actually have three options that could be modeled individually, you loose some information. It's neither globally right or globally wrong depends on your case.

Whether or not the models converge is only part of the story, the logical questions concerning overall interpretation of what the parameters mean is the other.

Interpretation is a bit more straightforward if one instead models options, with associated dedicated accumulators, explicitly.

Regarding point 4:

A trade-off in parameters just couples two (or more) parameters in the posterior. This most often shows up quite directly as high posterior correlations. The idea here is that the setting of some parameter X determines the setting of parameter Y in the posterior, so they can't be analyzed independently, they move together. The degenerate example is that these parameter move exactly on a line, so you can always make up for a setting of X with another exact setting of Y. In that case, you get marginal posterior distributions that are very very wide, and you can get a wrong idea of whether or not a parameter actually matters in your model. You can usually drop parameter in the model as a result.

If the example is not extremely pathological, sampling (and convergence) can still work, but it's worth checking for this phenomenon regardless.

[Lipika-T]

Thank you for your inputs. I will check for these in my data