Collection time

[From Bruce Abbott (960123.1340 EST)]

Bill Powers (960121.0900 MST) --

The apparent behavior rate has to be corrected for factors that we know
can make the apparent rate different from the actual rate (during
successive bar presses). The main factor, as Bruce Abbott showed last
year, is the collection time. The animals must cease pressing in order
to collect the food pellets, and during this time the actual pressing
rate is zero. The recorded pressing rate, however, is calculated as
total presses divided by total elapsed time, which gives a low estimate
of actual pressing rate because part of the time no pressing is
occurring. Finding the true system function requires plotting the data
points using the true behavior rate instead of the apparent rate.

This comes under the heading of "everything old is new again." McDowell and
Wixted (1988) present a linear systems analysis of behavior on VR schedules
and have this to say about fitting their function to the data:

    Before discussing these studies it is necessary to consider what Baum
    (1981) has referred to as the obligatory postreinforcement pause. This
    pause consists of three (possibly overlapping) components, namely, the
    time required to move from the feeder to the operandum, the time after
    the end of the reinforcement cycle that may be required to finish
    ingesting the reinforcer, and the time that may be occupied by species-
    specific postprandial behavior like snout washing. According to Baum
    (1981), the cumulative obligatory pause time should be subtracted from
    the session time when calculating response rate. Failure to do so has
    little effect on the calculated response rate when reinforcers are
    delivered relatively infrequently, as on VR schedules with moderate to
    high mean ratio requirements and on most VI schedules. However, when
    reinforcers are delivered at very high rates, as on VR schedules with
    low mean ratio requirements, failure to subtract the cumulative
    obligatory pause time from the session time results in calculated
    response rates that are spuriously low.

    McDowell, J. J., & Wixted, J. T. (1988). The linear system theory's
        account of behavior maintained by variable-ratio schedules.
        _Journal of the Experimental Analysis of Behavior_, _49_, 143-169.

By the way, McDowell seems to have a good background in systems analysis and
can handle the required mathematics, including LaPlace transforms and the
like. In the above paper he extends what I take to be an open-loop analysis
of VI schedule behavior and extends it to the VR case by "closing the loop"
via the VR schedule feedback function: R(in) = [1/(Mean n)]*R(out). The
resulting equation for predicting response rate from Mean n cannot be solved
analytically, so they go the iterative route (Newton's method).

Unfortunately, this is just another equilibrium system; I looked in vain for
some mention of control theory.

Regards,

Bruce