More SDTEST3 2-Level Analysis

[From Bruce Abbott (950320.1940 EST)]

My two-level control model analysis for SDTEST3 now has an iterative
procedure for finding the k-values for both levels--and it takes forever for
it to complete its analysis (or at least long enough not only to HAVE a cup
of coffee, but to MAKE one as well!). We'll probably want to find some
short cuts to cut down the number of required iterations. As presently
constituted, the analysis starts with an arbitrary value of 0.05 for both
k-values, then iterates the level 1 model (cursor-target distance control)
to find the k value yielding the lowest rms error. It then changes the
level 2 k-value and repeats. Both loops use a binary search procedure. If
it takes an average of 20 iterations at each level to find the minimum rms,
then on average it would take 20 * 20 = 400 iterations to find the optimal
k-values for both levels.

While I was still doing this by hand, I tried entering a level 1 k-value
from the previous best-fit delay run to get a first-estimate level 2
k-value. I then entered this level 2 k-value and iterated to find the best
level 1 k-value, and so on, going back and forth between entering the level
1 or level 2 k as the fixed value and finding the best-fit value for the
other. Interestingly, this process converged in the two cases in which I
tested it. For run 008, for example, the process went like this:

Entered Computed
kc = 0.0290 k = 0.0830
k = 0.0830 kc = 0.0303
kc = 0.0303 k = 0.0713
k = 0.0713 kc = 0.0303

Thus, entering either final k-value produces the other as best-fit value.
However,--and this is surprising-- these two values do NOT yield the fit
with the smallest rms error:

       Best: 0.0290 0.0830 14.31 0.993
Convergence: 0.0303 0.0713 14.50 0.992

Perhaps someone with a better mathematical brain than mine can explain why.

The convergence phenomenon suggests that it might be possible to quickly
find, if not the best, than probably nearly the best values for the two k's.
I'll have to try starting with values farther from the optimum to determine
whether convergence depends on starting with nearly ideal values in the
first place.

I've just completed a "playback" program that allows you to watch the
participant's cursor movements being replayed, along with the changes in
cursor color, on a modified version of the original SDTEST3 display.
Immediately below the original target positions is displayed a second cursor
which displays the MODEL's cursor movements. It's fascinating to watch the
actual versus model cursors move in near synchrony around the same target
and between targets. On one run I ran my daughter's data (run 017) and
entered the two k values based on my own performance on run 008. When the
cursor color changed, Cyndi's cursor flashed to the alternate target, while
the "my" cursor (actually, the model of my performance) lagged conspicuously
behind. I'm now wondering at exactly what time I became "old." (Or maybe I
was always this wonder I've never been any good at sports!)

I plan to post the two-level iterative analysis program and the playback
program after I've had a chance to test them a bit for bugs. This may not
be before I get back from the BAAM meeting, which I will be attending
Thursday and Friday.

By the way, there has been no CSG-L mail (other than mine) since Saturday.
Is everyone on vacation?