Response competition as signal detection

[Christian Lebiere]

> 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.

The effect of the number of distractors on response time has often been
accounted for in terms of the fan effect in the strengths of association,
but a more general account can be found in terms of a competitive latency
function:

Ti = F*(Sum_j e^f*Aj)/e^f*Ai

This latency function can be seen as a straightforward generalization of
the Retrieval Time Equation.  Its derivation results from the same analysis
as in Appendix B of Chapter 3 of ACT98 if one assumes basic interactions
between the chunks competing for retrieval.  Alternatively, it can also be
seen as resulting from a scaling of the activation values to enforce the
condition that activations are log odds of the probabilities of retrieval.
Finally, it has an appealing symmetry with the Chunk Choice Equation.

This latency function and other changes to the architecture being
considered will be discussed at the ACT-R SIG at ICCM2000 in Groningen and
at the 2000 ACT-R workshop.

Christian Lebiere
John Anderson