Response competition as signal detection

[Erik M. Altmann]

I believe it's a general finding that the more distractors or 
response mappings there are, or the less time that old ones have had 
to decay, the greater the time to retrieve the current target from 
memory.  I'm replicating this in the serial attention paradigm, and 
am able to track the effect in my ACT-R simulation.   However, I'd 
like to get better handle on the mathematics of this, and would 
appreciate any pointers.  I'd also appreciate pointers to data sets 
that help to quantify the relationship between extra distractors or 
response mappings and increased retrieval time for the target.

I've been approaching the problem conceptually in terms of signal 
detection theory.  The target is the signal, and the distractors are 
the noise.  Assuming logistic noise, multiple distractors can be 
represented by a single (right-shifted) noise distribution.  The 
retrieval threshold is simply beta, and the higher the retrieval 
threshold the longer the retrieval time (assuming multiple retrieval 
attempts per trial).

The mapping gets more complicated because the SDT noise distribution 
shifts as a function of circumstances.  Retrieval errors have a 
conditional probability, in that one error makes the next more 
likely, in effect shifting the noise distribution rightwards.  Time 
(decay) has the opposite effect, shifting the noise distribution 
leftwards.  Error frequency also has an effect, by making the noise 
distribution increasingly stable in terms of resistance to decay.

I'm specifically interested in finding (or approximating) the optimal 
location of beta, given an estimate of the expected rightward shift 
of the noise distribution due to a single retrieval error (say). 
This optimal beta would seem to be to the right of the optimal beta 
in a simple SDT analysis (where the distributions don't shift), but 
that's about as far as I've gotten.

I'm also interested in whether anyone else has used ACT-R to address 
how people adjust their retrieval threshold (beta) dynamically, say 
in response to metacognitive information or performance feedback. 
This seems related to the question of how people maintain and adjust 
speed-accuracy tradeoffs (e.g., Rabbitt & Vyas), but also to 
production-utility computations.  In general it seems to be very much 
a question of how the memory system adapts in the short term to 
demands of the environment.

Erik.

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Erik M. Altmann, PhD
Psychology 2E5
George Mason University
Fairfax, VA 22030
703-993-1326 (voice)
703-993-1330 (fax)
altmann at gmu.edu
hfac.gmu.edu/~altmann
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