[From Bill Powers (950702.0915 MDT)]
Rick Marken (950701.1200)--
Psychological research is based on a causal model of organisms; it
assumes that o = f(d). PCT shows that the causal relationship
between o and d reveals nothing at all about f. The implication is
clear, even if unspoken: all research results based on the
assumption that o = f(d) tell us nothing about the nature of
organisms. Since all psychological research is based on this
assumption, it is not surprising that PCT has made no inroads in
conventional psychology.
This might be clearer if you also pointed out that the controlled
variable qi has to be known before the control system can be (a)
recognized, and (b) analyzed. The relationship o = (h^-1)(d) is an
_apparent_ relationship brought about by the operation of the control
system: it is explained by the joint effect of o and d on qi, the
variable that is being controlled by the control system.
In reality it is unlikely that an observer unaware of control theory
would choose a definition of either a behavior (o) or a disturbance (d,
the "stimulus") that would be maximally consistent with the operation of
the system. Steering a car in a crosswind is done, roughly speaking, by
turning the steering wheel opposite to the direction of the wind, but
this loose description is insufficient to idenfity the functions
connecting either o or d to the controlled variable, the car's lateral
position. If you measured the steering wheel position in degrees and the
wind's velocity in miles per hour, as one naturally would, you might see
some correlation between these measures but you wouldn't be able to make
any accurate predictions. The reason is that the actual effect on the
controlled variable comes from sideward forces on the car, which are
highly nonlinear functions both of wheel angle and of wind velocity
relative to car velocity. Not only is this relationship nonlinear, but
the net force on the car has to be time-integrated twice before it
expresses the effects on the lateral position of the car. The chances of
a casual observer choosing a nonlinear double time integration to
express the units of the disturbance and the system's output are very
small.
When Martin Taylor objected to your statements, he was forgetting that
the internal operation of the control system has to be based on measures
of the controlled variable, not just on o and d.
···
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Samuel Saunders (950702:0105 EDT) --
The discussion has been about ratio schedules because this is a PCT
group, and ratio schedules appear to provide a relatively simple
situation for PCT. For EAB, however, this is not the case. From
the EAB point of view, VI schedules should provide the clearest
view of the relationship between reinforcement frequency and
response frequency. This follows from the lack of constraints on
responding in VI. The animal's response rate can vary
substantially without having a significant effect on reinforcement
rate, so response rate is "free to vary with response strength" ,
where response strength is a function of rate of reinforcement.
You're holding up a moving target! Actually, my model of operant
conditioning allows the user to switch among FR, VR, FI, and VI
schedules. Comparing the behavior with data from Ferster and Skinner's
Shcedules of Reinforcement, the PCT model seems to give about the right
results. Without comparing the model to the behavior of individual rats
each run under all four schedules, we can't say that the same parameter
settings would do for all schedules, but at least the model behaves
qualitatively right without changes in parameters.
As I understand VI schedules, it is true that variations in response
rates have only a small effect on variations in reinforcement rates. But
I also understand that if the reinforcement rate is actually made
constant at the same average level observed under the VI schedule, the
result is NOT the same response rate. In other words, if the
reinforcements are not actually contingent on the response rate, the
same behavior is not maintained by the same reinforcements.
Ratio schedules are constrained, since there is a direct
relationship between response rate and reinforcement rate, and thus
response rate would not be expected to be "free to vary" with
"response strength". Given this analysis, finding the recently
considered effects in ratio schedules would hardly be a large red
flag for EAB theorists, particularly when the expected relationship
continued to be supported with VI schedules, the "appropriate"
experimental context in which to examine such effects from the EAB
view.
There is also a direct relationship between response rate and
reinforcement rate on VI schedules. You're talking about a diminishing
relationship between _changes_ in reinforcement rate and _changes_ in
response rate. If the response rate is high enough, changes in response
rate have only a small effect on changes in reinforcement rate. However,
the reinforcement rate that does exist is produced entirely by the
responses. If the response rate is low enough, the reinforcements occur
exactly as on an FR-1 schedule. As response rate increases, the
reinforcement rate levels out eventually at 1/i where i is the average
interval. After that point, large variations in response rate have
little effect on reinforcement rate. From the EAB standpoint, where
causation is assumed to run the other way, small changes in
reinforcement rate have large effects on response rate.
However, these relationships cause no problems for the PCT model. Do you
have a copy of my model of operant conditioning? This model doesn't
handle the initial acquisition of the right behavior (the left side of
the curves we've been looking at) but it does handle steady-state
behavior over a range of schedules of all four types. I think I posted
it last Fall, but perhaps you weren't set up to compile Pascal source at
that time.
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