Chris Chatham writes:
I am using multilevel logistic regression to model individuals’ abilties to ‘stop’ a planned motor movement (my binary outcome), based on the delay between the beginning of the trial and the occurrence of the stop signal (my input with 4 different values). As an apriori assumption, I’d like to specify that the fitted model predict perfect ‘stopping’ when the stop signal is provided at 0 delay and no ‘stopping’ whatsoever when the signal is provided at each individual’s maximum reaction time. While these particular delays were not tested, the assumptions are sound; my question is how I can ensure that the model fits these assumptions without including some arbitrary number of made-up observations in my dataset?
My reply: As a person who has difficulty in suppressing motor movements, I’m interested in your example. Getting to the statistics, I can’t understand enough of what you’re saying to give a direct answer, but more generically I’d say try to avoid any hard constraints such as zero intercepts or sharp cutoffs at maximum reaction time. I’d first fit the model straight with no such constraints. Then if the constraints are consistent with your inferences, you could consider setting certain parameters to zero (perhaps in this case you’d be setting main effects to zero while letting interactions vary).
Thanks for the reply; in case it helps (or just satisfies your curiosity) here are the details of the example.
Your job is to press one key for left arrows, and another key for right arrows, and to do so as quickly as possible *unless* i remove the arrow from the screen. Obviously, if I provide this "stop signal" at a short delay – for example, at the very moment the arrow would have appeared on screen – you won't have difficulty stopping, since you never saw the arrow in the first place. Likewise, if I provide this stop signal at a very long delay – for example, at the very moment you're going to press a key – you obviously won't be able to stop. These two examples were my apriori assumptions.
By modeling your stopping accuracy at various delays, we can estimate the delay that would yield 50% stopping accuracy. Using this value, we can calculate the time it takes you to stop (your average reaction time on trials without a stop signal minus the delay that yields 50% accuracy, assuming independent stop and go processes and various other things that I won't get into.)
The problem is that – as you note – people vary widely in "stopping" ability; even the shortest of my delays yield 0% stopping among some people, and even the longest yield 100% stopping among others. Obviously, when my four predictors all predict either 0 or 100% accuracy, I can't meaningfully estimate the delay that would provide 50% accuracy for some individual without some additional apriori assumptions.
I should note that this paradigm and the general method are Gordon Logan's invention, and go under the name "Stop Signal Reaction Time" in the cog psych literature.
Chris, I am abusing Andrew's comment function here… I do not really understand why you want to constrain your model in the way specified in your original question. The constrained model would really be misspecified if you ignore that some people are prone to reacting even in case of an obvious stop signal. I am sure you have a reason for not estimating SSRT adaptively. I guess you will have to change your experimental setup for those people reacting as extremely as you suggest.
In my particular case, if a stop signal is presented at 0 delay, there is never a go stimulus even presented to the subjects. i don't think people would be prone to responding in the presence of a stop signal *and* the ABSENCE of the 2 choice stimulus, unless they sneeze and accidentally press a button or something.
in other words, in my case, a stop signal at 0 delay is not equivalent to a nogo trial in a go/nogo paradigm, as in many stop signal paradgims. instead, it is equivalent to the absence of any trial at all, akin to a null event.
Would you not then expect a discontinuity response probability as a function of stop signal delay at delay = 0?
Corey – one might expect a discontinuity there; but on the other hand, presentations of a stimulus for less than 35ms may be subthreshold aka "subliminal") so it's not clear that 35ms would be any different than 0ms. But maybe i'm missing your point…
I'm assuming that you want to enforce the prior constraint so as to improve the model's performance at nearby points. If there's a discontinuity between the point where you want to constrain the model and the regions you want good model performance, it hardly seems worth it to enforce the prior constraint. But this seems so elementary that I've probably misunderstood something about the problem.