(From Bruce Abbott [950221.1120 EST])
Rick Marken (950220.1900)
My model is the same as yours except for this peculiar method of computing
model output:
h = h - k * (e*horiz);
Why multiply the error by horiz? What's horiz anyway? I don't think this
was the reason you had problems distinguishing the models, though.
Somehow you are not communicating to me what steps your model takes, with
each variable defined. I tried what I think you (and Bill) suggest is the
proper model and it didn't seem to work (see my post 950220.1540 EST). I
have a feeling that my version and yours are mathematically equivalent.
Horiz is the length of the horizontal line. (In my version the vertical
line is controlled.) H (for "handle") is actually the model's vertical line
length. Because e is an error in the RATIO, you have to multiply by horiz
to convert this to an error in vertical line length. How are you doing this
differently? As a guess, I'd say that you are converting your ratio
reference to an X line length and then just working with X. But if this is
correct, you never made that explicit, or at least I didn't pick up on it.
By the way, who said I had any trouble distinguishing the models? My
results agree with yours in that the model/actual correlation and RMS were
both better for the V/H model, and I said that. I was only suggesting that
comparing correlations is probably not the best way to evaluate the relative
merits of these two models.
If you'd like to try an interesting variation on this task, move the
horizontal line upward on the screen so that is bisects the vertical
one.
Before we do this, I would rather see how changes in r affect the
relative fits of the two model. Just try runs where you ask people (or
yourself) to "keep x equal to y", "keep x a constant amount shorter
than y", "keep x a constant amount longer than y" and then compare
the x-y and x/y model fits in each case. Doing this requires no change in
the program -- just in the subject.
Sounds interesting. I'm not surprised that you had more trouble trying to
maintain a constant offset. How does this change the regression equation
for X on Y? If you were successful in adding a constant offset to your
performance, this should change the intercept without much affecting the
slope. Because the X/Y model does not take the offset into account, the
model/actual RMS error would be expected to suffer (assuming use of the
optimal reference value based on the data). If you merely changed the ratio
reference, the slope of the regression of X on Y should change. I'll give
it a try and report my results.
Regards,
Bruce