What is a "hybrid" model?

[Jeff Shrager]

> Recently, however, I stumbled upon something that I believe may provide
> a fruitful way of looking into this and other related issues.
>...

Well, since you're into this literature, you might as well look at
some real computational psychology.  Permit me a moment of inhumility
in pointing out our work on the development of arithmetic skill in
preschoolers.

Siegler, R.  S., & Shrager, J., (1984).  Strategy choices in addition
  and subtraction: How do children know what to do? In C.  Sophian
  (Ed.), Origins of Cognitive Skills. Hillsdale, NJ: Lawrence Erlbaum
  Associates. 229-294. 

We describe an implemented hybrid (in neo-terminology) model of the
development of small number addition skill (e.g., what's 4+3?) and
validate the model against real children's learning data.  The model
generally correlates with the observed/predicted performance at
greater than .8, and often greater than .9.

It is hybrid in two senses.  (I use the term "mediated" rather than
"hybrid" because "mediated" describes the way in which the components
interact, as follows....)  First, the model has both an explicit
component and a memory component.  The former is discrete (it does
simple addition, which is, well, simple), and the latter is a basic
(continuous) association model.  These components train one another
and the decision about which component to use in a given case is made
in accord with the history of training.  This is one sense of
mediation: the memory component is trained by the discrete component;
that is, the discrete component mediates between the memory and
reality (or, rather, correctness).  The second sense in which the
model is hybrid, or mediated, is in a (computational analog of a)
social sense: Specifically, the model's "environment" -- the
particular distribution of problems that it sees, is based upon real
observations of the distrubution of problems that children are given
by their parents.  Here, too, the parent mediates the child's
performance until the child's own systems are trained up
appropriately.

There.  Now you don't have any excuse for not including this in your
forthcoming TR! :-)

Cheers,
  Jeff

p.s. Anyone who would like a copy of this forthcame-TR may send me an
address label-like email and I'll be happy to send one out.