Theoretical Relationships Among Some Measures of Conditioning

Mueller, Conrad G.

doi:10.1073/pnas.36.2.123

Cited by 34 publications

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“…Anger (1956) recommended the use of the interresponsetimes-per-opportunity dependent variable for interrelated empirical and theoretical reasons. Stated briefly, these reasons were that both he and Mueller (1950) obtained flat interresponsetimes-per-opportunity curves early in training with rats on interval schedules of reinforcement, and that such empirical curves follow immediately from the intuitively plausible theoretical assumption that a subject chooses, every brief period of time, whether or not to respond. This way of responding sometimes is described as "go, no-go" behavior.…”

Section: Dependent Variablesmentioning

confidence: 99%

SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹

Shimp

1973

J Exper Analysis Behavior

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Three pigeons pecked for food on a synthetic variable-interval schedule of reinforcement that had two independent parts: a variable-interval schedule that arranged a distribution of interreinforcement intervals, and a device that randomly assigned each reinforcement to one of 10 classes of interresponse times. The frequencies of reinforcement for the 10 classes of interresponse times were systematically varied, while the overall frequency of reinforcement was held within a comparatively narrow range. The 10 classes extended either from 0.1 to 0.6 sec in 0.05-sec intervals, or from 1.0 to 6.0 sec in 0.5-sec intervals. In the former case, some control by reinforcement was obtained, but it was weak and no simple relationships were discernible. In the latter case, the relative frequency of an interresponse time was a generally increasing function of its relative frequency of reinforcement, and two simple controlling relationships were found. First, the function relating interresponse times per opportunity to reinforcements per opportunity was, over a restricted range, approximately linear with a slope of unity. Second, when all 10 classes of interresponse times were reinforced equally often, the relative frequency of an interresponse time approximately equalled the relative reciprocal of its length.A long-range goal of the experimental analysis of behavior is the development of methods that precisely control the probability with which a response occurs at a specific moment in time. The attempt to reach this goal has led to the use of response rate and interresponsetime distributions as measures of the probability of occurrence of that response. Unfortunately, classical schedules of reinforcement do not control all of the contingencies that are believed to determine response rate and interresponse-time distributions (Anger, 1956;Blough and Blough, 1968;Jenkins, 1970;Morse, 1966 which interresponse times are emitted depends on wlhich interresponse times are reinforced, and at the same time, which interresponse times are reinforced depends on which interresponse times are emitted, i.e., they depend on the organism. This interaction vastly complicates the search for functional relationships between response rate and frequencies of occurrence of interresponse times on the one hand, and reinforcement parameters on the other hand, in variable-interval schedules. Anger (1954)

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Section: Dependent Variablesmentioning

confidence: 99%

SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹

Shimp

1973

J Exper Analysis Behavior

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“…Another experiment described by Skinner (4, p. 306) indicates that the 3 Interval reinforcement refers to a schedule that reinforces the first response of the chosen class after certain events specified by a timer. In fixed-interval reinforcement (FI) these events are separated by fixed time-intervals; in variable-interval reinforcement (VI) the intervals are variable.…”

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“…Mueller's study (3) of the IRT distribution during 3-min. FI indicated that there is no definite difference in the response probability at different times after the last response.…”

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The dependence of interresponse times upon the relative reinforcement of different interresponse times.

Anger

1956

Journal of Experimental Psychology

344

280

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The literature contains indications that the time intervals between responses, i.e., the interresponse times (IRTs), made by rats depend on which IRTs have been followed more often by food reinforcements. In the present study evidence on the occurrence and nature of this dependence was obtained by comparing IRT distributions with reinforced-IRT distributions, and by altering the allocation of reinforcements to IRTs (reinforcement of an IRT refers to reinforcement of the terminal response of that IRT).The first indication that the IRT distribution is affected by the relative reinforcement of IRTs of different lengths came from the observation of Skinner (4) that fixed interval rein-1 This article is based on a thesis submitted in partial fulfillment of the requirements for the Ph.D. degree at Harvard University, 1955.

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“…Anger pointed outthat if this correlation between IRT probability in time and IRT relative reinforcement rate was general, a procedure that maintained the latter constant over a given range might also maintain IRT probability constant over the same range. Verification of this suggestion has some interest because a constant IRT probability in time is one of the necessary properties of behavior for an organism to be responding randomly in time (Mueller, 1950). In order to investigate the generality of Anger's correlation and to see whether indeed a random responder might be maintained, rats were exposed to a procedure that appeared likely to generate equal reinforcement rates over a range of IRTs.…”

Section: Problemmentioning

confidence: 99%

A further investigation of the correlation between IRT frequency and IRT reinforcement distributions

Millenson

1964

Psychon Sci

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Forty sessions of a procedure that yielded a constant rate of reinforcement for lever pressing IRTs of rats over the range 0-25 sec. led to a distribution of IRT probabilities over that same range that contained a minimum at about 3-6 sec., and a continuous increase in this probability at longer times. This failure to find a one-to-one correspondence between relative reinforcement rate of IRTs and probability of occurrence of IRTs weakens any explanation of the distribution of the latter based on the distribution of the former. ProblemThe increase in response rate that occurs during initial exposure to variable or random interval reinforcement schedules after CRF (Ferster & Skinner, 1957;Millenson, 1963) is considered paradoxical because interval schedules in general provide ip.creased probabilities of reinforcement for slow, rather than rapid responding (Anger, 1956;Revusky, 1962). The observed increase in rate under interval contingencies is often described in terms of a distribution of inter-response times (IRTs), whose probabilities of occurrence in time gradually change from an initial time independence to an inverse function of time. Anger (1956) has theorized that such a latter temporal distribution of IRT probabilities can be explained by reference to the relative reinforcement rates associated with different IRT categories that VI produce. In one experiment with VI 5 min, he demonstrated that a rough correlation in the form of the relative reinforcement rates of different IRTs, and IRT probability in time did indeed develop. In a second experiment he showed that a complex procedure that modified the relative reinforcement rates at different IRTs, also correspondingly modified the IR T probability in time (Newman & Anger, 1954). Anger pointed outthat if this correlation between IRT probability in time and IRT relative reinforcement rate was general, a procedure that maintained the latter constant over a given range might also maintain IRT probability constant over the same range. Verification of this suggestion has some interest because a constant IRT probability in time is one of the necessary properties of behavior for an organism to be responding randomly in time (Mueller, 1950). In order to investigate the generality of Anger's correlation and to see whether indeed a random responder might be maintained, rats were exposed to a procedure that appeared likely to generate equal reinforcement rates over a range of IRTs.Pryclwn. Sci., 1964, Vol. I. Method d. R. Millenson CARNEGIE INSTITUTE OF TECHNOWCYThree hooded rats (66,67,68) lacking prior experimental history were trained to press a lever to obtain a drop of sweetened condensed milk in an apparatus described in detail elsewhere (Millenson & Hurwitz, 1961). Following training, approximately 750 reinforcements, distributed over 10 daily sessions, were obtained on CRF contingencies. On the following session the rats were exposed to an RI 2 min. schedule (period=4 sec.) for I hr. On following sessions a procedure known as Interval Selective (IS) ...

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Theoretical Relationships Among Some Measures of Conditioning

Cited by 34 publications

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SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹

SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹

The dependence of interresponse times upon the relative reinforcement of different interresponse times.

A further investigation of the correlation between IRT frequency and IRT reinforcement distributions

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Theoretical Relationships Among Some Measures of Conditioning

Cited by 34 publications

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SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT1

SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT1

The dependence of interresponse times upon the relative reinforcement of different interresponse times.

A further investigation of the correlation between IRT frequency and IRT reinforcement distributions

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SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹

SYNTHETIC VARIABLE‐INTERVAL SCHEDULES OF REINFORCEMENT¹