[From Bill Powers (950711.0735 MDT)]
Bruce Abbott (950710.2030 EST) --
here are some data gleaned from Figure 2 of Barofsky, I., &
Hurwitz, D. (1968).
Another good find. I think we need to start a movement to get authors to
present graphic information in tabular form as well, for those who want
to do number-crunching.
I wish the authors had gone all the way down to FR-1 instead of stopping
at FR-10, and that they had increased the ratio high enough for behavior
to drop lower. Also, increasing the ratio requirement systematically
from low to high means that extended learning may be present. In control
situations after the right kind of behavior is found, learning shows up
as a continuing increase in the loop gain. This would work against the
droop in the rate of responding as the ratio increases.
Same question as before: did the authors make any comment about the fact
that decreasing reinforcement _increases_ behavior?
80% deprivation, 45 mg pellets, and low ratios (40 or less) are
typical of operant studies in which the ratio itself was not the
object of study. These conditions are clearly on the _right_ side
of the Motheral curve in these data.
I am really getting curious about how the original conclusion was
reached, the one that associates an increase in amount of reinforcement
with an increase in amount of behavior. Surely there must have been SOME
direct experimental data on which this generalization was based. If most
operant studies are done under conditions appropriate for the right side
of the Motherall curve, why are the results not analyzed on the basis
that increasing reinforcement _decreases_ behavior? Or are they?
The basic conventional assumption applies under one set of conditions
(left of the peak); you're suggesting that most EAB studies are done
under a different set of conditions (right of the peak). Is this true?
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In Staddon's _Adaptive behavior and learning_, on p. 212, Fig. 7.15
shows some data for a range of interval schedules. The Motheral peak
appears there, too, although only one point to the right of the peak is
shown. The suggestion is that an interval schedule gives results similar
to those for a ratio schedule, as I would expect.
In the same figure, results for a range of ratio shedules are also
plotted. The behavior rate on the interval schedule is everywhere less
than the rate for the ratio schedule, which fits Staddon's theoretical
curves but doesn't agree with what Sam Saunders said a few days ago,
that there is more behavior under interval schedules than under ratio
schedules. The ratio data (Boren 1961) is from a different study by a
different author 7 years after the interval data (Wilson, 1954), with no
indicated comparison of reinforcement sizes and no indicated conversion
from interval to ratio -- and of course, using different animals. When
you can shop through the literature for corroborative data, it's not too
hard to support just about any theory. Pretty sloppy.
On the next page is Fig. 7.17. Here we see the Motheral curves for ratio
schedules under two conditions: with and without a running wheel
available. When the running wheel is available, the apparent reference
level is lowered and the whole curve shrinks. This is what is expected
when kt in my model, the percentage of time actually spent on task, is
reduced.
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In the equations for my model, the value parameter kv should apply only
to the average obtained reinforcement rate, not to the reference or
satiation rate. So the equation should read
b = kt*km*(rs - kv*ra)
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I have found other ratio data gathered under just the sort of
conditions a PCT theorist would want: nondeprivation, with the
animals able to eat as much as they wished following completion of
each ratio. The rats were getting their entire daily ration via
lever pressing and lived in the environment 24 hrs/day. I'll
report on these data tomorrow if I can find the time to do so.
Good. I found some similar data from obesity experiments many years ago.
I forget where I mentioned them. One fact I remember is that force-
feeding a rat on such a schedule results in instant but reversible
extinction of bar-pressing behavior, just what is to be expected when
there is a direct disturbance of the controlled variable in the
direction that aids behavior. So increasing the received reinforcement
completely and immediately abolishes behavior! The behavior is
extinguished, in fact, not only faster but far more completely than by
the normal procedure of terminating the reinforcements.
A long time ago Rick sent me a page from some article by Timberlake
called _Behavior regulation and learned performance_. The page shows
data about rats obtaining water by pressing under ratio schedules over a
range from 1 to 300, and (from Collier) obtaining food under ratio
schedules ranging from 1 to a little over 5000. Both food and water
intake are maintained reasonably constant, even though behavior varies
over a factor of 30 (water) or 300 (food). In all cases, the obtained
water or food falls slightly while the behavior increases greatly.
I have one other paper:
Hanson, S. J. and Timberlake, W. (1983); Regulation during challenge: a
general model of learned performance under schedule constraint. Psych
Rev, _90_, 261-282.
The paper starts out with discussions of regulation and set-points, but
rapidly degenerates into a hodgepodge of differential equations and a
"coupled regulation" model. The "coupling" is between an "instrumental
response" and a "contingent response" (a la Staddon). The contingent
response happens to be measured in reinforcements per unit time. The
equations grow page by page, getting bigger and uglier. The object seems
to be to replace Staddon's minimum-distance model which generates
elliptical curves to match the Motheral-type curves with a far more
complex coupled-regulation model that fits the same sort of data with
about the same accuracy.
There are several figures in this paper that show Motheral-type curves
for various ratio schedules, as well as one for fixed and variable
interval schedules. The latter shows only the left side of the Motheral
pattern.
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Best,
Bill P.