[From Rick Marken (950718.2100)]

Bruce Abbott (950717.1405 EST) --

On a happier note, the effect of satiation on the curve is just what is

expected under the PCT model in which the reference level for rate of

injestion is set by the higher-level system whose job is to control stomach

loading.

This is true; I ran Bill's reinforcement model with a VI rather than a

ratio feedback function. The model (which was not posted to the net,

unfortunately), comes equiped with a ratio feedback function, defined

in the statement:

ra := ba/ratio

where ra is the reinforcement rate and ba is the response rate. To create

a quick and dirty VI feedback function, I changed the above statement to:

if ba>=ratio then

ra := ratio

else

ra := ba/ratio

end;

Now the variable called "ratio" determines reinforcement rate in about the

way a VI schedule determines reinforcement rate, assuming that the organism

responds at regular intervals. The variable "ratio" is the maximum average

rate of reinforcment the organism can get on the schedule. If the response

rate is greater than ratio (by any amount) or equal to it then the organism

gets reinforcements at the maximum average rate at which they can occur.

(VI schedules limit the effect that response rate can have on reinforcement

rate. This is quite different than the situation with ratio schedules where

increases in response rate are directly related to increases in reinforcment

rate -- no matter how high the response rate gets). If the response rate is

less than "ratio" then I assume that the organism gets only a fraction of

the reinforcement rate possible.

When I put this VI feedback function into Bill's model (using the default

parameters used to fit the Motherall data) the result was data that looked

very much like that from interval 3 of the McSweeney VI data for subject 161

(below):

Subject 161 5-Minute Interval

Rft/hr 2nd 3rd 4th 5th

240 1728 1205 878 470

120 1207 1190 1027 643

60 922 1032 1260 914

30 713 775 636 710

15 77 89 204 165

If you lower the model's reference level you get the fall off in response

rate for the 240 (256 in the model) Rft/hr schedule but little fall off

for any of the other response rates. The qualitative fit (in terms of changing

the shape of the response rate by reinforcement rate plots for each interval)

of the model can be imporved by changing the error sensativity parameter

(of the gain change system). When error sensativity is increased, changes

in reference (from about 480 to 280) lead to changes in the response rate

by reinforcemnt rate plots that resemble the shape of these plots for

each interval in the data above.

What is interesting (to me) about this exercise is that this very simple

control of reinforcement rate model accounts (qualitatively) for the data

in two very different situations; in one situation the reinforcement is

food and the feedback function is a ratio schedule; in the other the

reinforcment is water and the feedback function is VI. The SAME model

accounted for the behavior in these two situations; the only change needed

was a change in the feedback function -- which is a property of the

environment rather than the organism component of the model.

I have a strong suspicion that the change in response rate over intervals

when the VI schedule delivers a large number of reinforcemnts (240) is not a

result of a reference level change; rather, I think it will be found that

a better model is a dynamic model that keeps the reference (for reinforcement

rate) constant; the change in response rate over trials probably reflects

the reduction of error as the perception (of reinforcement rate) is brought

closer to the reference --rather than the reference being brought closer to

the perception (as the satiety notion implies).

One reason I think that the dynamic effects are not due to reference

signal changes is that the changes in the reinforcement rate by

response rate curve with changes in reference do not really mirror

the data that well. I can get the steady state data to match the

final interval results pretty well -- but the change in reference signal

with these parameters changes the curves over intervals in a way that

just isn't quite right. Since the model matches the final interval (and

probably close to steady state) data so well, I think what's really going on

over intervals is, indeed, a dynamic change in error signal -- but this

change is probably due to the change in perception of reinforcement rate

-- it goes up-- combined with the change in gain due to the

persistance of error.

How about working on the dynamic version of the control of reinforcement

model while we're at the meeting. Bruce? I think the "plain vanilla"

dynamic version of Bill's model will account for McSweeney's data just

fine. And it will be easy to include a better implementation of the VI

feedback function in a dynamic model. The dynamic behavior of the model

might be quite different for VI and ratio schedules (I bet it is) and

then we can see if this shows up in the data.

Best

Rick