[From Bruce Abbott (950711.1615 EST)]
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'll second that motion. Actually, many of the JEAB articles on the
matching law and its relations include an appendix giving the overall rates
of responding and reinforcement for the stable sessions of each experimental
condition for each bird. I wish all the articles included an appendix like
that.
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.
The study has been criticized for not counterbalancing the ratio order. In
practical terms, however, it is usually necessary to begin at a lower ratio
and work up in steps to a high one; otherwise behavior does not persist long
enough on the high ratio to produce reinforcement, and extinguishes. What
these researchers should have done is revisit the lower ratios after
reaching the highest one.
Same question as before: did the authors make any comment about the fact
that decreasing reinforcement _increases_ behavior?
They noted that response rate varied inversely with rate of reinforcement
and that this is opposite to what had been reported in previous research for
interval schedules.
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?
You keep asking this question, and I keep answering it. See my previous
posts on this topic, and my next comment below.
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?
Apples and oranges. In learning one would expect that following a response
with a so-called reinforcing consequence would "strengthen" the behavior
(relative to other behaviors not so reinforced). Maintained performance is
another game altogether--a dynamic equilibrium involving all sorts of
effects. You don't necessarily expect _rate_ or responding to be directly
related to _rate_ of reinforcement under these conditons. There are too
many other factors to consider and could alter this simple relationship.
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.
I'll have to order the reports on which these data are based. Other, more
recent data with pigeons show rate of responding increasing with rate of
reinforcement over a range from 8.4 (VI 427-s) to 300 (VI 12-s)
reinforcements/hour in a manner that resembles the left limb of the Motheral
curves (Catania, A. C., & Reynolds, G. S. (1968). A quantitative analysis
of the responding maintained by interval schedules of reinforcement.
_JEAB_, _11_, 327-383). These authors also plot data from two other studies
in which the data follow the same curves as theirs. Those studies included
an 1800 rft/hr point which showed a further increase, as if the curve were
approaching an asymptote from below rather than curving back downward as in
the right limb of the Motheral-type curves.
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.
I believe what Sam may have said was that response rates _increase_ with
increasing rate of reinforcement on interval schedules. When you compare
ratio and interval schedules on which the rate of reinforcement is the same,
ratio schedules support a higher rate of responding.
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.
Yes, this sort of comparison is of little value--too many confounded
variables to make comparison meaningful. But when you're writing a book,
you can get away with stuff like that--who's to question you? It's harder
to get away with that kind of thing in a reviewed article, if the reviewers
are doing their job.
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.
I'd like to see your model extended so that kt emerges from the competition
of the two systems rather than being fit to the data. But perhaps that can
wait.
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.
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.
These are the data to which I refer. I spent some time at the library today
obtaining copies of the original reports; it will take me a bit of time to
reduce the relevant figures to numbers.
The reason these rats continued to respond on the ratio schedule at ratios
up to 5000 is that this was their only way to obtain food--it's that or
starve. Food deprived rats working on a ratio schedule in a 1-hr session
will give up responding on ratio schedules far less demanding. It's
interesting to think about why.
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.
I just obtained this paper and I can see what you mean about the mess of
equations. I'll read it in my "spare" time... (;->
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.
That would fit the Catania and Reyolds data. The interesting question is,
does the curve just continue to climb to an asymptote or is it an inverted
U-shaped function, as Staddon's analysis suggests? My guess is that rates
of responding decline monotonically (more or less exponentially) as size of
the interreinforcement interval increases, from a maximum at CRF.
Regards,
Bruce