Interval data

[From Bill Powers (950716.0730 MDT)]

General note: The scheme that I described last night does work: the model's
curves scale up along both axes as the reference level increases just as
the two Motheral curves do. The detailed shape doesn't fit as well as my
linear model did (the point for FR-80 is too high), but at this point we're
talking about nonlinearities in the cost/benefit function and there's no _a
priori_ way to guess what they would be. I think the model works reasonably
well now.

Samuel Saunders [950716:0055 EDT] --

     Campbell and Dougan examined responding of rats on VI 7.5, 15, 30, and
     480 sec. They determined response rate for each 10 min segment of a
     30 min session. In addition, they ran some 10 min sessions after
     prefeeding the animals the average number of pellets earned in the
     first 20 min of previous sessions on the same VI. Animals were at 80%
     ffw. There were 8 animals, and the figures are not all that large, so
     for now I will only give the mean data (read from Fig. 3). The
     numbers are responses per minute:

      Reinforcers per hour: 7.5 120 240 480

···

___________________________________________________
      First 10 min : 15 25 24 20
      Third 10 min : 9 27 22 15
      Preefeeding : 10 32 23 15

Note: Here is the table multiplied by 60 to show responses/hr, so both
variables are given in the same units:

      Reinforcers per hour: 7.5 120 240 480
     ___________________________________________________
      First 10 min : 900 1500 1440 1200
      Third 10 min : 540 1620 1320 900
      Preefeeding : 600 1920 1380 900

Here is the table showing responses/reinforcement, with an added column
showing the apparent reference level (0 responses per reinf, obtained from
the last two observed points on the right):

      Reinforcers per hour: 7.5 120 240 480 ref
     __________________________________________________________
      First 10 min : 120 12.5 6.0 2.5 651
      Third 10 min : 72 13.5 5.5 1.875 604
      Preefeeding : 80 16.0 5.75 1.875 596

A question: the number of reinforcers per minute seems to be simply 3600
divided by the nominal interval in seconds. In other words, it is the
"scheduled" rate of reinforcement, not the actual rate of reinforcement,
that is shown. It seems unlikely that the actual rate would be exactly that
number. What were the actual (obtained) reinforcement rates? We can't
really compare these data to the FR data without those numbers. The
differences may be small, but we might as well do it right.
--------------------------------------
     In their discussion, Dougan and Campbell say "Because the present
     experiments showed food density to be an important factor, it may be
     tempting to dismiss all reported instances of bitonicity as being
     merely due to an artifactual satiation process." They present
     several arguments against such a conclusion. They note that little is
     known about satiation.

Bruce Abbott, take note: this is exactly what I guessed would be said. The
dropoff of behavior rate with reinforcement rate, as the authors note,
could be attributed to a "satiation process" even though actual satiation
(cessation of behavior) has not occurred. The rise in behavior rate as
reinforcement rate rises from 7.5 to 120 per hour is not considered
problematic (in that it fits the Law of Effect). It is the fall in behavior
rate as reinforcement rate rises above 120/hr that presents a puzzle to
reinforcement theory -- the "bitonicity" of the curve. If the behavior rate
had simply leveled off at 1500-1920 per hour, this would have been called
the maximum possible behavior rate, and there would have been no problem:
the conclusion would be that experimental conditions should be confined to
the range from 7.5 to 120 reinforcements per hour in order to see the
effects clearly. How many experimenters have simply ASSUMED that the
leveling-off represented maximum behavior rate or approaching satiation,
and failed to explore higher reinforcement rates or sizes?

At the longest intervals, we have almost reached the conditions of the FR-1
schedule: By very rough extrapolation, there would be 1 response per
reinforcement at about 560 reinforcers per hour (interval = 6.4 sec), and
the reference level (actual satiation level) would be 617 reinforcements
per hour (average of all three lines of data). These numbers are at least
comparable to those we have seen on the Motheral curves, where the
reference level at 85% of free-feeding weight is about 400 - 420 responses
per session (what was the session length?). At 80% of ffw that reference
level would have been somewhat higher.

It looks to me as though the Motheral curve is seen for interval schedules
as well as ratio schedules, and the same control-system model will work for
either kind of schedule.
-----------------------------------
     Whatever the EAB implications, the results fit nicely with the current
     dicsussion of PCT interpretation of schedules of reinforcement.
     Campbell and Dougan cite 6 previous studies in the literature showing
     "bitonic" functions for interval schedules.

Good, can we get the data for those, too? Gentlemen, I think I smell a
paper coming up here, with at least three authors, two of whom have EAB
credentials. Does it seem that way to you, too?
---------------------------------------------------------------------
Best,

Bill P.