(From Bruce Abbott [950221.2000 EST])
Bill Powers (950220.2330 MST)
You got the the model to give the "right" answer in one iteration by
writing k*e*horiz, but in doing so you introduced a role for the
horizontal size of the bar that makes no sense model-wise. Why should
that perceived size multiply the error signal? Unless you can come up
with a justification, all that can be said is that by doing this, you
can make convergence happen in a single iteration with k set arbitrarily
to 1.0 and the initial value of h and c set to less than the reference
value.
Yes, that was what was bothering me about it, but I couldn't see any other
way around it that made sense.
Try just running my model as stated, but using a value of k of 200
instead of 1.
Ah-HA!! So THAT's the problem! In our previous discussions of the 3CV1
model you indicated that k would be a number between 0 and 1, so I have been
thinking of k as reflecting the _proportion_ of error corrected in one
iteration. I used k=1.0 in my example because, given this interpretation of
k, the proper set of equations for the model should cancel all error in one
step when k has that value. (The fitted k was always much less.)
Using the corrected V/H model I do get slightly different fits (I'm still
using h = vert rather than h = c where vert = 159 + c, which is comparable
to Rick's program except for the reversal of which axis is under control.)
The revised stats for V/H (with old-model values in parentheses):
Run r mv rms best ref k k/Mean H
000 0.969(0.971) 12.57(12.41) 12.6(12.3) 0.853 12.646(0.059) 0.060
001 0.962(0.956) 12.53(13.43) 12.1(13.0) 0.833 5.289(0.031) 0.025
002 0.985(0.985) 10.20(10.41) 10.1(10.4) 0.717 17.141(0.088) 0.078
Except for k, these are very close to the values given by the old model.
The last column provides a comparable k value after rescaling (Mean H is the
average horizontal line length).
I have been deriving the participant's reference value by computing observed
V/H or V-H from the data. Is this how you are doing it? These values do
seem to give the best fits according to the spot checks I've made.
Is there any utility to looking at the rates of change of the two lines? I
have a procedure that does this and, as might be expected, these are also
correlated, although not as well as the absolute lengths are.
Regards,
Bruce