🚀 go-pugleaf

[From Rick Marken (950218.1530)]

Bruce Abbott (950216.1040 EST)--

Thanks for the Inverted T Turbo code, Bruce. It's up and running,
but I haven't had time to put the analysis or model fitting code
into it so I wrote up a quick version of the Inverted T in QuickBasic
for the Mac just to get a rough idea of which model works best.

In my program the mouse determines the length of the horizontal (x) line
and the disturbance determines the length of the verticle (y) line.
I compared my performance on the task to that of models that controlled
perceptual variables proportional to x-y and x/y. I didn't do any fancy
parameter fitting for the models (which were identical except for the
perceptual variables and reference values). Because of the illusion,
the reference value that gave the best fit for the model controlling
x-y was 50; x had to be made longer than it should be (by 50 pixels in
my case) to be considered equal to y. The reference value that gave the
best fit for the model controlling x/y was 1.5; x had to be 1.5 times the
length of y to be considered equal to it.

The main result was that the model controlling x/y always fit the
subject's (my) data better than the one controlling x-y. The difference
in the fit of the models to subject data (measured by correlation) was
not large, but it was consistently in favor of the x/y model. When control
was good (the disturbance was slow) the correlation between subject
and x-y model was typically about .982; the correlation between subject and
x/y model was typically about .997. The models are highly correlated
with each other so it is expected that one model will do well if the other
does well. But the consistent improvement of fit with the x/y compared to
the x-y suggests that the variable I (the subject) was controlling in this
experiment was proportional to x/y rather than x-y. The difference
in the fit of the models could probably be made clearer by using a
disturbance with a greater dynamic range than the one I used.

I'm pretty confident that x/y is the controlled perception in this situation
but I have not yet given both models their best shot; I didn't use any
fancy parameter estimation techniques to try to find the best fit of
each model to the data; it may be possible to find an integration
factor that improves the fit of the x-y model; but I have a feeling that
the improvement in fit will not be large; the x-y model is already doing
pretty well (correlation of ,98+) and improvements in fit now are likely
to be in the third decimal place.

So my tentative conclusion is that when I try to match the horizontal to
thye vertical line lengths of the inverted T experiment, I am controlling
the ratio of the line lengths, x/y, not the difference, x-y.

It would be interesting to see if this is true for others who do the
Inverted T. What was the result when you did it, Bruce?

Best

Rick