Conceptual interpretation drift intercept

[Johannes Algermissen]

Dear HDDM users,

this is a more theoretical question that moves away from the particular HDDM implementation. I've recently fit a series of different DDMs and wondered about the conceptual interpretation of a "drift rate intercept" in such cases.

In value-based DDMs, I'd normally model the trial-by-trial drift like this: 

drift = drift_slope * (value_left - value_right)

While for all other parameters of the DDM, zero is an impossible/ highly unlikely number, the drift might actually be zero, e.g. when both choice options are of identical value.

However, I've come across a few papers that include a "drift intercept":

drift = drift_intercept * drift_slope * (value_left - value_right)

It seems to me that the drift intercept serves a highly similar function to the starting point bias. In fact, I've observed both drift intercept and starting point to negatively tradeoff. Also, parameter values of the starting point end up quite low (not in accordance with the overall "bias" observed in descriptive statistics on both responses). 

 

I've now fitted models with/ without such an intercept and the range of fit indices overall doesn't change (it doesn't seem that models with such an intercept lead to overall better/worse fit), but the hierarchy of which model wins (starting point vs. drift rate modulation by another external input) changes quite a bit.

Has someone else observed & thought about this before?
Is there a benefit in fitting or a theoretical interpretation that motivates including such a drift intercept?
Any suggestions/ pointers appreciated!

Best regards,

Johannes

[Carina Forster]

Hi Johannes and HDDM users,

I recently fitted the hddm to data with a manipulation of the decision criterion. I included a parameter for drift rate bias, I am not sure if you are refering to that with a drift rate intercept? The model with varying drift rate bias between conditions gave me the best model fit, however also a varying starting point accounted well for the data. I think I am also not sure what is the reason to fit a drift rate bias versus a starting point bias? 

Best,

Carina

Virenfrei. www.avast.com

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[Mads Lund Pedersen]

Hi,

This is something I've thought quite a bit about myself. I think the best approach depends on the design of the task, especially whether stimuli are of the same type, and what scale of values you use. In recent work I've done, where we modeled approach-avoidance conflict, I included an intercept on drift and slopes for the amount of reward and aversiveness offered (as well as other things that are not important in this context). Here the intercept for drift can account for the fact that drift rate is not necessarily 0 when the mean of both reward and aversiveness (using standardized values) are both 0. However, for a task in which stimuli are on the same scale (e.g. learnt values for arbitrary stimuli) then I think it makes sense to force the drift rate to be 0 when both stimuli are 0. What type of design does your task have, and have you standardized values?

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Best, 

Mads

[Johannes Algermissen]

Hi Mads and Carina,

thanks for your answers!

@Mads okay, if it depends on the set-up, I'll go into some more detail, although I wondered whether this question could be answered more generally... especially since I feel that the drift rate intercept does part of "the job" of the starting point bias.

I'm currently busy with a bunch of data sets on the same task. It's a motivational Go/NoGo Task as first used by Guitart-Masip et al. (e.g. https://www.sciencedirect.com/science/article/pii/S105381191200420X ) and in parallel used by Hanneke den Ouden and colleagues (closest to the data sets I'm work on is this version in van Nuland et al. 2020 Brain, https://academic.oup.com/brain/article/143/11/3422/5956227 , see Figure 1). In short, participants learn Go or NoGo responses for a range of stimuli, some of which can give you rewards for correct responses while others can give you punishments for incorrect responses. Previous RL modeling with a softmax link function has suggested that the valence of cues (Win points vs. avoid losing points) biases action values (see papers above).

A previous paper ( http://www.mitpressjournals.org/doi/abs/10.1162/jocn_a_01224 ) with an adapted version of the task (no rewards) has tried to test whether these biases are better explained by an RLDDM with separate starting points or an RLDDM with separate drift rate intercepts for rewards and punishments. The model with separate drift rates contains a drift slope (multiplied with the difference in Q-values) and two separate drift rate intercepts for Win and Avoid cues (I think that comes close to what you report). The model with separate starting points contains a drift slope and a single drift intercept (see code under https://github.com/sjgershm/GoNoGo ). I've wondered why to include that single drift intercept. If I include it, the model with separate starting points seems to win; if I drop it, the model with separate drift rates seems to win (by quite a margin, though these results are all still preliminary and I'm still looking into fit indices and posterior predictive checks)...

Any idea/ intuition for why that is? Which extra flexibility is afforded by this drift rate intercept?
I feel that dropping the single drift intercept is more plausible, but curious to hear others' opinions.

Best regards,

Johannes

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[Anne Urai]

Hi Johannes, all,

especially since I feel that the drift rate intercept does part of "the job" of the starting point bias.

You’re right, starting point and drift biases can lead to similar proportion of biased choices; both can capture an overall tendency towards one response vs. another for stimuli where the external information is 0 (value difference, visual contrast, etc). Note that this only applies to stimulus-coded models, where either a starting point or drift intercept can be interpreted as such an overall choice bias. These choice biases can depend on the task or instructions, and can be quite strongly idiosyncratic between individuals (e.g. in yes-no paradigms: https://elifesciences.org/articles/54014)

However, the starting point and drift bias can be dissociated based on RT distributions, and have a rather different interpretation neurally (work in prep :)). In this paper, we explain how to tease them apart: https://elifesciences.org/articles/46331.  In this case the biases are not modelled as an intercept but as a dependence on choice history, but the idea is the same. See Figure 1 for a general overview, and Figure 7 - Supplement 3 for some simulations on how to tease them apart. There is also some discussion on different manipulations (in perceptual DM) that load onto drift bias vs. starting point. HDDM code for these different models is here https://github.com/anne-urai/2019_Urai_choice-history-ddm

Happy to chat about this further.

Best,

—
Anne E. Urai, PhD
Assistant Professor | Cognitive Psychology | Leiden University

CoCoSys lab | @AnneEUrai | Meet with me

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[Johannes Algermissen]

Hi Anne,

thanks so much for your answer! Very much looking forward to the stuff you are working on!

I'm familiar with both papers, and you do show convincingly that with good data, you can distinguish both biases based on the mode vs. trailing edge of the RT distribution... (I'm actually trying that out in a different data set, testing whether reward and punishment magnitudes modulate starting point or drift rate, and was recently looking for posterior predictive checks, so your paper was very helpful for that!)

However, from a parameter estimation perspective, in my data, in presence of a drift intercept, the starting point bias takes (rather low) values that I find hard to interpret... in the HDDM implementation, unbiased starting points should be around 0.5; but with the drift intercept, the bias gets values around 0.25... so I wonder if interpreting individual differences in this parameter still makes any sense...?

I'm very curious about your ideas about "neural implementation"! For the history biases you look at, there seems some candidate plausible explanations for a drift rate intercept (e.g. stimulus- or motor-priming, i.e. your accumulate evidence for a certain stimulus/ response more easily if you've just seen/ executed it). However, in an RL-DDM context, what would the drift intercept mean? That people accumulate evidence for one choice option (left/ right or Go/NoGo) more easily, overall? Which begs the question of what "evidence" gets actually accumulated in such choices... I'm just worried that I'll get this question once I submit it, and I find it hard to motivate the drift intercept for my kind of task/ data...

Best regards,

Johannes

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[Carina Forster]

Hello Anne, hello Johannes,

I am very interested in this conversation. I recently fittted data from a behavioral paradigm where I manipulated stimulus expectations and thereby introduced a change in decision criterion (SDT). I wanted to see wether this correlates with a drift rate bias or starting point in DDM. I found a stronger correlation with drift rate bias and the model including drift rate bias also gave me a better fit. However, I am also not entirely convinced, as the starting point also correlates with criterion. I am also very interested about the "neural implementation" as I am currently collecting EEG data with this paradigm.  Also very much looking forward to your work Anne. 

Happy to chat about this via zoom if you would be interested.

Best,

Carina

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