A QUANTITATIVE ANALYSIS OF THE RESPONDING MAINTAINED BY INTERVAL SCHEDULES OF REINFORCEMENT1

A QUANTITATIVE ANALYSIS OF THE RESPONDING MAINTAINED BY INTERVAL SCHEDULES OF REINFORCEMENT1 A. Charles Catania G. S. Reynolds

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A QUANTITATIVE ANALYSIS OF THE RESPONDING MAINTAINED BY INTERVAL SCHEDULES OF REINFORCEMENT1 1968 Journal of the Experimental Analysis of Behavior 10.1901/jeab.1968.11-s327 catania1968-a-quantitative-analysis-of-the-res catania1968-a-quantitative-analysis-of-the-res.txt, the project's staged copy 3c3618c1f4c5362089492cb1e1184d9058b6187e open-access behaviour-analysis

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them mechanism Quotation withheld because this record is not cleared for redistribution. responding under interval schedules of reinforcement Quotation withheld because this record is not cleared for redistribution. behavioural-experiment behavioural-experiment Quotation withheld because this record is not cleared for redistribution. mechanisms The effect of a reinforcement spreads along the continuum of time since reinforcement, so responding at any moment is controlled by reinforcement probability smeared over a surrounding window rather than at that instant alone Quotation withheld because this record is not cleared for redistribution. mechanisms That temporal spread is interpreted as a gradient of temporal generalization around the moment of reinforcement Quotation withheld because this record is not cleared for redistribution. mechanisms Overall response rate is produced indirectly: reinforcement rate acts on local response rates at each time after reinforcement, and the overall rate is their weighted average Quotation withheld because this record is not cleared for redistribution. mechanisms Time since reinforcement acts as a discriminative stimulus dimension, so intervals reliably paired with nonreinforcement come to control low response rates just as other stimulus dimensions do Quotation withheld because this record is not cleared for redistribution. A function these authors published earlier was fitted to the group average rather than to any animal. what this limits: the earlier published power function: the authors state it was fitted Quotation withheld because this record is not cleared for redistribution. That earlier published function is stated not to fit the data of individual animals. what this limits: the earlier power function applied to any individual pigeon: the authors state it does not fit individual data Quotation withheld because this record is not cleared for redistribution. The choice between two candidate functional forms was made on a priori grounds rather than on which fitted the data better. what this limits: the published functional form as an empirical result: the authors state the choice rested on logical considerations rather than superiority of fit Quotation withheld because this record is not cleared for redistribution. Individual differences between animals are large enough that the authors say a unified quantitative analysis would not survive comparison across them. what this limits: pooling or comparing the quantitative results across pigeons: the authors state Quotation withheld because this record is not cleared for redistribution. Deriving a single function across all animals is stated to be complicated by the idiosyncratic character of each animal's data. what this limits: a single reinforcement-responding function covering all pigeons: the paper says the derivation is complicated by each pigeon's idiosyncratic data Quotation withheld because this record is not cleared for redistribution. Whether the variable-interval and fixed-interval functions share a form is stated to be undecidable from the data presented. what this limits: any claim that the VI and FI functions share a form: the paper states this cannot be decided from the figure presented Quotation withheld because this record is not cleared for redistribution. Several quantitative extensions are placed outside the paper's scope. what this limits: the quantitative details and their coordination across schedule types: the paper places these beyond its scope Quotation withheld because this record is not cleared for redistribution. AND THE AUTHORS LATER USE THAT ARBITRARINESS AGAINST THEIR OWN RESULT: `Quotation withheld`. A DEFINITIONAL CHOICE DECLARED ARBITRARY WHEN IT IS MADE AND THEN CITED AS A REASON TO DISCOUNT A FINDING THIRTY-FIVE THOUSAND CHARACTERS LATER. The same paper does it a third time near the end - `the computation of local rates of reinforcement is most arbitrary at early and late times after reinforcement` - so the qualification is tracked, not mentioned once and forgotten. Quotation withheld because this record is not cleared for redistribution. arithmetic variable-interval schedules run with and without a 0-second interreinforcement interval, compared directly within the present experiment eliminates: the 0-second interval as the source of the local response-rate pattern - the two schedules are the same arithmetic VI otherwise · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. local rate of reinforcement local rate of reinforcement Quotation withheld because this record is not cleared for redistribution. overall rate of reinforcement overall rate of reinforcement Quotation withheld because this record is not cleared for redistribution. rate of responding rate of responding Quotation withheld because this record is not cleared for redistribution. interval schedule interval schedule Quotation withheld because this record is not cleared for redistribution. local rate of reinforcement local rate of reinforcement about this quote: PAGE FURNITURE IS SPLICED INTO THE QUOTE - the page number and the running head, '342 A. CHARLES CATANIA and G. S. REYNOLDS', between 'successive op-' and the rest of the word. The words on either side of it were never continuous on the page; read the quote with it deleted. Quotation withheld because this record is not cleared for redistribution. opportunity for reinforcement opportunity for reinforcement Quotation withheld because this record is not cleared for redistribution. Reinforcements per opportunity Reinforcements per opportunity Quotation withheld because this record is not cleared for redistribution. terminal rate of responding terminal rate of responding Quotation withheld because this record is not cleared for redistribution. temporal separation → time since reinforcement THE TWO CANNOT BE SEPARATED IN THIS STUDY - the DESIGN form / It bounds what the paper's own results can mean, and it lives in a methods paragraph where nothing downstream will find it. A 1968 methods sentence naming its own confound, in a paper nobody would search for it in. Quotation withheld because this record is not cleared for redistribution. rate of reinforcement - the overall rate a schedule provides, which the paper concludes is NOT what determines responding Quotation withheld because this record is not cleared for redistribution. rate of reinforcement - the local rate at a particular time within an interval, which the paper concludes is what responding tracks Quotation withheld because this record is not cleared for redistribution. rate of responding - a quantity that changes within a single interval, not a single value per schedule Quotation withheld because this record is not cleared for redistribution. 'local rate of reinforcement' - AN OPERATIONAL DEFINITION ITS OWN AUTHORS CALL ARBITRARY, WITH THE REJECTED ALTERNATIVES NAMED: other assignments of time to opportunities are 'possible, SUCH AS BISECTION ... using the geometric rather than the arithmetic mean, or the assignment to a given opportunity of the time since the last opportunity. The present technique, though arbitrary, seems to involve the simplest ad hoc assumptions.' The choice is defended on SIMPLICITY, not on correctness, and the competitors are printed so a reader can substitute one. This record already distinguishes the overall rate of reinforcement from the local one; this is the further fact that the local one is a construct with a dial on it. Quotation withheld because this record is not cleared for redistribution. `Reinforcements per opportunity` - A NAME SHAPED LIKE A RATE THAT DENOTES A PROBABILITY. `Quotation withheld` The `X per Y` form is how this literature writes rates (`reinforcements per hour` appears in the same paper), so the name invites the reader to expect a count over a denominator and delivers a bounded probability instead. The definition is explicit precisely because the name is misleading. Quotation withheld because this record is not cleared for redistribution. `opportunity for reinforcement` - THE DEFINITION IS A DISJUNCTION, AND THE TWO LIMBS ARE NOT THE SAME TEST. `a point on the continuum of time since reinforcement at which the probability of reinforcement is greater than zero, or at which at least one interval ends.` The first limb is a property of the schedule; the second is a property of the sample of intervals actually run. They coincide in the limit and can differ in a finite experiment. Quotation withheld because this record is not cleared for redistribution. qualifies → Reynolds and Catania (1961); Catania and Reynolds (1963) — the authors' own earlier publication differs in: WHETHER THE FUNCTION IS FITTED TO A GROUP OR TO AN ANIMAL, AND WHY THE FORM WAS CHOSEN. Two admissions in one passage: 'The choice between these two functions was based more on logical considerations ... than on the superiority of the fit of the power function to the data', and 'Quotation withheld' The published law was fitted to the group average, chosen on a priori grounds rather than fit, and fails on every individual - said by its own authors Quotation withheld because this record is not cleared for redistribution. qualifies → Reynolds and Catania (1962); Reynolds (1966); Stubbs (1968) differs in: CAPACITY VERSUS CONTROL. 'the performances maintained by FI schedules do not appear to be as well under the control of time since reinforcement as the capacity of the pigeon to discriminate durations would suggest.' What an animal CAN discriminate and what its behaviour IS controlled by come apart, so a discrimination result does not license an inference about what governs performance Quotation withheld because this record is not cleared for redistribution. builds-on → Millenson (1966); Anger (1956) differs in: WHAT AN UNEXPECTED DIRECTION OF CHANGE IS TAKEN TO SHOW. Inter-response times shorten 'even in schedules of reinforcement in which long IRTs are differentially reinforced', i.e. against the contingency, and the literature's reading is a property of the reinforcement process itself - 'that short IRTs are more susceptible to reinforcement than long IRTs'. A behaviour that moves opposite to the arranged contingency is explained by postulating an asymmetry in what reinforcement can act on Quotation withheld because this record is not cleared for redistribution. EVIDENCE CORRECTED (RE-GROUNDED) · local rate of reinforcement —distinct-from→ overall rate of reinforcement local rate of reinforcement overall rate of reinforcement EVIDENCE CORRECTED: RE-GROUNDED. The old span stated a conclusion without naming either rate. This sentence names both AND DISTINGUISHES THEM BY EXPERIMENT: '…while the overall rate of reinforcement is held constant…' - one is held fixed while the other moves, which is the strongest form a distinction can take: not observed, but constructed. — strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. local rate of reinforcement —causes→ rate of responding local rate of reinforcement rate of responding strength of the relation: 0.9 Quotation withheld because this record is not cleared for redistribution. terminal rate of responding —part-of→ rate of responding terminal rate of responding rate of responding strength of the relation: 0.9 · note: The terminal rate is the local rate AT A PARTICULAR MOMENT - a restriction of the general measure, which is why 'part-of' and not 'is-a'. Quotation withheld because this record is not cleared for redistribution. overall rate of reinforcement —causes→ terminal rate of responding overall rate of reinforcement terminal rate of responding strength of the relation: 0.7 · note: DIRECTION CHECKED AGAINST THE SENTENCE, AND MY FIRST VERSION HAD IT BACKWARDS. 'INCREASED AS the overall…' - the reinforcement rate is what the SCHEDULE SETS and the responding is what the animal does, so the schedule variable is the cause. I wrote the edge the other way round while writing a note that said the reinforcement rate was the manipulated side; the dry run is where that was caught. Weight 0.7 records the paper's own hedge - in general, however - stated immediately after 'No systematic relationship…' for the FI rates. Quotation withheld because this record is not cleared for redistribution. mean mean Quotation withheld because this record is not cleared for redistribution. weighted average weighted average Quotation withheld because this record is not cleared for redistribution. conditional probability conditional probability Quotation withheld because this record is not cleared for redistribution. Across seven variable-interval schedules the overall rate of pigeons' key-pecking rose monotonically with the overall rate of reinforcement but with diminishing returns, over a span from 8.4 to 300 reinforcements per hour. Quotation withheld because this record is not cleared for redistribution. Within a single schedule, how fast the bird pecked at a given moment after reinforcement tracked the local rate of reinforcement at that moment, computed from the probability of reinforcement there and the nearness of reinforcement opportunities at other moments. Quotation withheld because this record is not cleared for redistribution. The paper's overall conclusion is that a schedule's overall response rate is not set by its overall reinforcement rate but is the sum of separate local reinforcement effects distributed across times within the interval. Quotation withheld because this record is not cleared for redistribution. A schedule engineered to hold the probability of reinforcement constant across time since reinforcement flattened the within-interval response gradient, keeping the local pecking rate roughly constant instead of rising. Quotation withheld because this record is not cleared for redistribution. The local pecking rate at t sec depended on the probability of reinforcement at that time. Quotation withheld because this record is not cleared for redistribution. Including a 0-sec interval (first peck after reinforcement is reinforced) raised responding only in the first two or three time bins after reinforcement, not across the whole interval. Quotation withheld because this record is not cleared for redistribution. An early reinforcement probability of 0.05, unlike 0.50, was less able to maintain responding once the later, higher probability of reinforcement was removed. Quotation withheld because this record is not cleared for redistribution. At matched overall reinforcement rates, arithmetic variable-interval schedules sustained higher overall response rates than fixed-interval schedules for all but one pigeon. Quotation withheld because this record is not cleared for redistribution. Reinforcing a response immediately after a preceding reinforcement affected responding only over a short time since reinforcement. Quotation withheld because this record is not cleared for redistribution. reinforcements per opportunity (rft/op) reinforcements per opportunity (rft/op) Quotation withheld because this record is not cleared for redistribution. opportunity for reinforcement opportunity for reinforcement Quotation withheld because this record is not cleared for redistribution. local rate of reinforcement local rate of reinforcement Quotation withheld because this record is not cleared for redistribution. interval schedule interval schedule Quotation withheld because this record is not cleared for redistribution. fixed-interval schedule fixed-interval schedule Quotation withheld because this record is not cleared for redistribution. geometric VI schedule geometric VI schedule Quotation withheld because this record is not cleared for redistribution. Fibonacci VI schedule Fibonacci VI schedule Quotation withheld because this record is not cleared for redistribution. overall rate overall rate Quotation withheld because this record is not cleared for redistribution. local rate local rate Quotation withheld because this record is not cleared for redistribution. mean interval mean interval Quotation withheld because this record is not cleared for redistribution. relative durations relative durations Quotation withheld because this record is not cleared for redistribution. probability of reinforcement probability of reinforcement Quotation withheld because this record is not cleared for redistribution. overall rate of reinforcement overall rate of reinforcement Quotation withheld because this record is not cleared for redistribution. rate of key-pecking rate of key-pecking Quotation withheld because this record is not cleared for redistribution. body weight body weight Quotation withheld because this record is not cleared for redistribution. 8.4 to 300 reinforcements per hour — the span of overall reinforcement rates over which the response-rate function was measured in Experiment 1 Quotation withheld because this record is not cleared for redistribution. six — number of pigeons whose key-pecking was studied in Experiment 1, maintained at 80% of free-feeding weight Quotation withheld because this record is not cleared for redistribution. 0.10 + 0.02 — the reinforcement probability held nearly constant in the constant-probability schedule, over a span where the arithmetic schedule's probability rose from 0.07 to 0.33 Quotation withheld because this record is not cleared for redistribution. about 2 resp/min — the near-flat rise in local response rate across the constant-probability interval, about one-tenth of the rise seen in the arithmetic schedule Quotation withheld because this record is not cleared for redistribution. 63.7 and 63.2 resp/min ... 61.1 and 73.7 resp/min — overall response rates on the schedules without and with a 0-sec interval, for Pigeons 278 and 281 respectively Quotation withheld because this record is not cleared for redistribution. about 6% ... 50% to 90% — a tiny change in overall reinforcement rate produced a disproportionately large change in overall response rate, showing the distribution of intervals rather than the overall rate was responsible Quotation withheld because this record is not cleared for redistribution. a factor of almost 40 — the growth of local reinforcement rate from 10 to 140 sec after reinforcement in the arithmetic schedule, far larger than the accompanying growth in local response rate Quotation withheld because this record is not cleared for redistribution. about 12 resp/min — the rise in immediate post-reinforcement response rate that a single extra reinforced response would explain, against an observed increment roughly two and a half times larger Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1901/jeab.1968.11-s327.