2-parameter search in ACT-R (e.g. Slow Kendler)

[Niels Taatgen]

I think you address an interesting aspect of parameter fitting: if one tries to
fit four datapoints using two variables, one can expect trouble. It also points
at what many people consider a weakness of ACT-R: there are so many parameters
that you can fit any data with it. So to defend the model, I will briefly sketch
some of the background of it.
The first version of the Kendler model I made was truely a zero-parameter model,
in the sense that it was actually a model I made for a completely different
task, namely a variant of the balanced-beam task. In that model I attempted to
make the model as independent of the task as possible, by writing productions
that could be applicable to any task that somehow resembled the balanced-beam.
That is how I started with the Kendler task: by reusing the model of the
balanced-beam. The model acted in the "older child/adult" version of the model.
So the next question I asked myself was: what if I just remove a number of the
criticial production rules in the model, will it change its behavior to the
"younger child" version? This turned out to be the case. Up to than I hadn't
been bothered by parameter fitting, and indeed the absolute fit between the
Kendler data and my model wasn't great. But the qualitative result, adults are
better at reversal but worse at extra-dimensional versus children are better
extra-dimensional was clearly there.
The version that ended up in the book was much more readable than my original
version, as it was simplified to just do the Kendler task, and the parameters
were fitted to the data. Although these to changes improve presentation, it also
gives rise to the "one can fit any set of data you like"-criticism.

Niels