multidimensional classifiers
David Dirlam (ddirlam who-is-at weber.ucsd.edu)
Tue, 18 Nov 1997 10:47:09 -0800 (PST)
Martin Packer and others --
Actually, maybe the understanding impasse was my fault to begin
with. After 25 years of working with the Cartesian Product conception of
dimensions, it sometimes comes too automatically to mind. A Cartesian
Product makes order pairs where each element of one set is paired with
each element of another. When two sets are continuous, the Cartesian
Product gives you the two-dimensional, X-Y plane. The basic issue is that
a dimension does NOT have to be continuous, but can be made of a few
discrete elements or sets. In the extreme simplicity case, one just has
two sets resulting in a binary, information theory, or boolean approach.
You don't have to be restricted to this binary case and sometimes
your research can be greatly enriched by expanding the number of discrete
sets to several. I have found this to be especially true wherever
development is occurring (historical, ontogenetic, or microgenetic). One
set invariably turns out to be a default reaction. Basically, what one
does when one does not know anything about the situation. The requirement
is that each dimension has to exhaustively classify the events that one is
studying and that each set in one dimension has to be logically compatible
with every set in another. Using several sets allows one to test
developmental progressions. A beautiful quality of this approach is that
using several dimensions makes it possible to uniquely classify an
enormous variety of events with a few concepts -- you have generality
without losing particularity.
I've created multidimensional classifiers for children's drawing,
pupil writing, developmental researchers methods, and a variety of other
settings. A thousand samples distributed in time are enough to show the
sort of dynamics that Katherine Goff has aluded to. With the classifiers,
I have been able to uncover changes that normally occur over years and
decades that I could not have uncovered otherwise. They also show that
practices don't replace each other in lock-step fashion, but overlap in
time, competing (much like quantitative and qualitative research methods
have competed here and in the history of developmental research).
The process of creating and using classifiers is not without
pitfalls and after 30 years of working with the process, I am still
learning about them. Just this morning, for example, Mike Cole suggested
that the tendency of some teams of coders to get bogged down in
definitions that allow them to classifier their records is actually a
problem of crossing time-scales (macro and micro). This made a connection
I had never thought of before between the time-scale dimensionality
discussed in response to Jay a few days ago and the classificational
dimensionality described above.
I'd be glad to try to answer anyone's questions about these
classifiers, but there is one thought I'd like to leave you with about
them. Every time I have had a student help me code 100 or more samples,
they have never forgotten the classifier they used (even years later).
Help someone to use a classifier for 100 times and they have it for life.
There is a very interesting responsibility as well as blessing in this
outcome.
David