Relative Reinforcement Rate Research Articles

Enduring problems for molecular accounts of operant behavior.

Although the Associative Learner (AL) theory advocated by Shimp, Childers, and Hightower (1990) can simulate several features of human and nonhuman performance in free-operant situations, it fails to account for many of the findings that are theoretically most powerful. It underestimates the sensitivity of behavior to relative reinforcement rate and totally omits any role for incentive variables such as amount and delay of reinforcement. At present, it is not sufficiently comprehensive to serve as an adequate alternative to Herrnstein's (1961, 1970) matching theory as a general account of behavior.

Component duration effects in multiple schedules

Previous research has produced conflicting results regarding the effects of component duration on interactions in multiple schedules. In Experiment 1, potential sources of this conflict were evaluated. Both the effects of absolute reinforcement rate and carry-over effects (hysteresis) from a preceding condition were isolated. When 10-sec components were used, the sensitivity of relative response rate to relative reinforcement rate was affected very little by hysteresis effects and absolute reinforcement rate, but it was systematically reduced as a function of the number of prior conditions. Sensitivity to relative reinforcement rate was also substantially higher with the 10-sec components than with 2-min components. In Experiment 2, this effect of component duration was decomposed into two separate effects. Contrast effects during presentation of a target component with a constant reinforcement rate were greater the shorter the target component was itself; but they were smaller the shorter the alternative component in which reinforcement rate was varied. The latter effect was smaller and more unreliable across subjects. The existence of these two separate effects demonstrates that the usual method of studying component duration—that is, holding all components equal in duration—systematically causes underestimation of the effects of the component duration, and obscures the different processes controlling the two effects.

The effects of response contingency and reinforcement identity on response suppression by alternative reinforcement

Rats were trained on a multiple schedule in which lever pressing was reinforced in one component and nose poking was reinforced in the other. The reinforcers contingent on the two responses were always different, either corn oil or Noyes pellets. A schedule of alternative reinforcement was superimposed in each component, either presenting the same reinforcer as that contingent on the lever/key, or the alternative reinforcer. When the alternative reinforcers were freely presented on a variable time (VT) schedule, their suppressive effects were substantially larger when the free reinforcer was the same as the reinforcer contingent on the lever/key than when it was different. But when the alternative reinforcers were presented according to a variable-interval schedule for a third response (rod pressing), the differences caused by the nature of reinforcement were greatly reduced and not statistically significant. Similar effects occurred when the alternative reinforcement was presented on a VT schedule but preceded by a signal. The results suggest that the effects of alternative reinforcement cannot be explained solely in terms of relative reinforcement rate.

The effects of stimulus similarity on different types of behavioral contrast

Pigeons were trained on multiple schedules with component stimuli of different degrees of similarity. In Experiment 1, a two-component schedule was used in which the two stimuli were either two line orientations or a line orientation versus a diffuse color. Reinforcement rate was varied in one component to determine the effects of stimulus similarity on different aspects of behavioral contrast. Contrast in terms of average response rates (molar contrast) was larger with less similar stimuli. Local contrast effects at the beginning of the component were larger for more similar stimuli, but these effects were more variable and did not attain statistical significance. Independent of the level of molar contrast, the local pattern of schedule interaction differed for the two levels of similarity: with more similar stimuli, the maximum degree of interaction occurred at the beginning of the components and then decreased; with less similar stimuli, the degree of interaction increased throughout the components and was at its maximum near their end. In Experiment 2, the same three stimuli were used while reinforcement rate in the middle component of a three-component sequence was varied; this isolated the effects of the preceding schedule from those of the following schedule. Contrast effects were generally greater in the target component preceding the variable schedule, and these were enhanced by less similar stimuli. Contrast in the target component following the variable schedule was manifested primarily in terms of the behavior at the beginning of the component, and these effects were inconsistently related to stimulus similarity. The functional separation of the effects of stimulus similarity on the different locations of contrast suggest that “anticipatory contrast” and “local contrast” depend upon different mechanisms, thus excluding any account of contrast solely in terms of relative rate of reinforcement.

SUCCESSIVE INDEPENDENCE OF MULTIPLE‐SCHEDULE COMPONENT PERFORMANCES

In three experiments, pigeons' responses were reinforced on two keys in each component of a series of multiple-schedule conditions. In each series, concurrent variable-interval schedules were constant in one component and were varied over conditions in the other component. In the first experiment both components arranged the same, constant total number of reinforcers, in the second the two components arranged constant but different totals, and in the third experiment the total was varied in one component and remained constant in the other. Relative reinforcer rate during the varied component was manipulated over conditions in all three experiments. In all these experiments, response and time allocation in the constant component were invariant when reinforcer ratios varied in the other component, demonstrating independence of behavior allocation in a multiple-schedule component from the relative reinforcer rate for the same alternatives in another component. In the two experiments which maintained constant reinforcer totals in components, sensitivity to reinforcement in the multiple schedules was the same as that in the concurrent schedules arranged during the varied component, with multiple-schedule bias in the experiment in which the totals were unequal.

CONCURRENT‐SCHEDULE PERFORMANCE: EFFECTS OF RELATIVE AND OVERALL REINFORCER RATE

Six pigeons were trained to respond on two keys, each of which provided reinforcers on an arithmetic variable-interval schedule. These concurrent schedules ran nonindependently with a 2-s changeover delay. Six sets of conditions were conducted. Within each set of conditions the ratio of reinforcers available on the two alternatives was varied, but the arranged overall reinforcer rate remained constant. Each set of conditions used a different overall reinforcer rate, ranging from 0.22 reinforcers per minute to 10 reinforcers per minute. The generalized matching law fit the data from each set of conditions, but sensitivity to reinforcer frequency (a) decreased as the overall reinforcer rate decreased for both time allocation and response allocation based analyses of the data. Overall response rates did not vary with changes in relative reinforcer rate, but decreased with decreases in overall reinforcer rate. Changeover rates varied as a function of both relative and overall reinforcer rates. However, as explanations based on changeover rate seem unable to deal with the changes in generalized matching sensitivity, discrimination accounts of choice may offer a more promising interpretation.

CHOOSING AMONG NATURAL STIMULI

Pigeons worked on concurrent variable-interval, variable-interval schedules with the alternatives signaled by slides either containing trees or not. The schedules were designed to hold both overall and relative rates of reinforcement within narrowly constrained limits, and slides were quasi-randomly ordered each day. Responding to the two alternatives was well described by the generalized matching equation with substantial undermatching. Using an adaptation of the matching law, we estimated that the subjects were correctly classifying 82% to 95% of exemplars. The matching performance transferred to new exemplars of trees and nontrees with only slight generalization decrement. The pigeons appeared to be discriminating among exemplars even when the alternatives provided equal rates of reinforcement and the average relative performances were close to 50%.

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.

CHOICE WITH A FIXED REQUIREMENT FOR FOOD, AND THE GENERALITY OF THE MATCHING RELATION

Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.

Choice behavior in a discrete-trial concurrent VI-VR: A test of maximizing theories of matching

Rats were trained on a discrete-trial procedure in which one alternative (VR) was correlated with a constant probability of reinforcement while the other was correlated with a VI schedule which ran during the intertrial intervals and held the scheduled reinforcer until they were obtained by the next VI response. Relative reinforcement rate was varied in series of conditions in which the VR schedule was varied and in series in which the VI was varied. Choice behavior was described well by the generalized matching law, although moderate undermatching occurred for all subjects. Contrary to the predictions of molar maximizing (optimality) theories, there was no consistent bias in favor of the ratio alternative, and the sensitivity to reinforcement allocation was not systematically affected by whether the ratio or interval schedule was varied. The results were also contrary to momentary maximizing accounts, as there was no correspondence between the probability of a changeover to the VI behavior and the time since the last response to the VI alternative. Neither variety of maximizing theory appears to provide a general explanation of matching in concurrent schedules.

Applied Behavior Analysis: New Directions from the Laboratory

Applied behavior analysis began when laboratory based principles were extended to humans inorder to change socially significant behavior. Recent laboratory findings may have applied relevance; however, the majority of basic researchers have not clearly communicated the practical implications of their work. The present paper samples some of the new findings and attempts to demonstrate their applied importance. Schedule-induced behavior which occurs as a by-product of contingencies of reinforcement is discussed. Possible difficulties in treatment and management of induced behaviors are considered. Next, the correlation-based law of effect and the implications of relative reinforcement are explored in terms of applied examples. Relative rate of reinforcement is then extended to the literature dealing with concurrent operants. Concurrent operant models may describe human behavior of applied importance, and several techniques for modification of problem behavior are suggested. As a final concern, the paper discusses several new paradigms. While the practical importance of these models is not clear at the moment, it may be that new practical advantages will soon arise. Thus, it is argued that basic research continues to be of theoretical and practical importance to applied behavior analysis.

Choice, Matching, and Human Behavior: A Review of the Literature

This review concerns human performance on concurrent schedules of reinforcement. Studies indicate that humans match relative behavior to relative rate of reinforcement. Herrnstein's proportional matching equation describes human performance but most studies do not evaluate the equation at the individual level. Baum's generalized matching equation has received strong support with humans as subjects. This equation permits the investigation of sources of deviation from ideal matching and a few studies have suggested variables which control such deviations in humans. While problems with instructional control are raised, the overall findings support the matching law as a principle of human choice.

ANOTHER LOOK AT CONTRAST IN MULTIPLE SCHEDULES

Recent research on multiple schedule interactions is reviewed. Contrary to formulations that view contrast as the result of elicited behavior controlled by the stimulus-reinforcer contingency (e.g., additivity theory), the major controlling variable is the relative rate of reinforcement, which cannot be reduced to some combination of stimulus-reinforcer and response-reinforcer effects. Other recent theoretical formulations are also reviewed and all are found to face serious counterevidence. The best description of the available data continues to be in terms of the "context of reinforcement," but Herrnstein's (1970) formulation of the basis of such context effects appears to be inadequate. An alternative conception is provided by Catania's concept of "inhibition by reinforcement," by which rate of responding is inversely related to the average rate of reinforcement in the situation. Such a conception is related to Gibbon's recent scalar-expectancy account of autoshaping and Fantino's delay-reduction model of conditioned reinforcement, suggesting that a common set of principles determines several diverse conditioning phenomena. However, the empirical status of such a description remains uncertain, because recent evidence shows that schedule interactions are temporally asymmetric, depending primarily upon the conditions of reinforcement that follow a schedule component.

AN INVARIANT RELATION BETWEEN CHANGING OVER AND REINFORCEMENT

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.

THE EFFECTS OF CONCURRENT RESPONDING AND REINFORCEMENT ON BEHAVIORAL OUTPUT

Four birds key pecked on concurrent variable-interval one-minute variable-interval four-minute schedules with a two-second changeover delay. Response rates to the variable-interval one-minute key were then reduced by signaling its reinforcer availability and later by providing its reinforcers independently of responding. Each manipulation increased response rates to the variable-interval four-minute key even though relative reinforcement rates were unchanged. In a final phase, eliminating the variable-interval one-minute key and its schedule produced the highest rates of all to the variable-interval four-minute key. These results show that both reinforcement and response rates to one schedule influence response rates to another schedule. These results join those of Guilkey, Shull, & Brownstein (1975) in failing to replicate Catania (1963). Moreover, they violate the predictions of the equation for simple action (de Villiers & Herrnstein, 1976). In terms of a median-rate measure (reciprocal of the median interresponse time), rates to the variable-interval four-minute key were high when responding was not reduced to the variable-interval one-minute key and were low when it was reduced. This rate difference suggests a process difference between concurrent-schedule procedures that maintain high concurrent response rates versus those that do not. This process difference jeopardizes attempts to integrate single- and concurrent-operant performances within a single formulation.

Independence of stimulus discriminability from absolute rate of reinforcement in a signal-detection procedure.

Three experiments are reported in which two pigeons were trained to detect differences in stimulus duration under varying levels of absolute rate of reinforcement. Two red stimuli, differing in duration, were arranged probabilistically on the center key of a three-key chamber. On completion of the center-key duration, the center keylight was extinguished and the two side keys were illuminated white. Correct responses were left-key pecks following the shorter duration and right-key pecks following the longer duration. In Experiment 1, relative rate of reinforcement for correct responses was held constant and absolute rate of reinforcement was varied in seven conditions from continuous reinforcement to a variable-interval 90-second schedule. In Experiment 2, relative rate of reinforcement was manipulated across three different absolute rates of reinforcement (continuous reinforcement, variable-interval 15-second, and variable-interval 45-second). Stimulus discriminability was unaffected by changes in absolute or relative rates of reinforcement. Experiment 3 showed that discriminability was also unaffected by arranging the same consequences (three-second blackout) for unreinforced correct responses and errors.

Matching, maximizing, and the behavioral unit: concurrent reinforcement of response sequences.

Pigeons pecked two keys in a probability matching situation in which four two-peck sequences were intermittently reinforced: left-left, left-right, right-left and right-right. In Phase 1, relative reinforcement rate was varied with respect to the first response of a sequence: reinforcers were differentially assigned for left-left and left-right sequences as opposed to right-left and right-right sequences. The second response of reinforced sequences occurred equally on the left and right keys across conditions. In Phase II, relative reinforcement rate was varied for sequences that involve an alternation as opposed to those that did not. The relative outputs of the different sequences matched the relative reinforcement rates for the different sequences in both phases. Relative response rates for key pecks did not always match relative reinforcement rates. The intertrial interval separating responses was varied in both phases; increases in the intertrial interval affected the relative frequency of different sequences. The results demonstrate that response sequences acted as functional units influencing choice and thus support a structural account of choice. At the same time, the matching of relative sequence proportion and relative reinforcement rate supports a matching account.

THE ROLE OF DISCRIMINATIVE STIMULI IN CONCURRENT PERFORMANCES

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.

Choice and the conditional probability of alternation: Some new data

Three pigeons were exposed to two independent concurrent variable-interval schedules of reinforcement, with a changeover key procedure. Relative reinforcement rate and the fixed-ratio changeover requirement were varied. The effects of these manipulations were assessed with respect to the conditional probability of alternation as a function of successive responses on the same schedule. Previous experiments employing this measure have found essentially unchanging probabilities of alternation. However, we found the probability of alternation to be an increasing function of successive choices of the same schedule, especially with the schedule providing the higher relative reinforcement rate. These findings were discussed with respect to the pro­ cedural variables we employed.

THE FOLLOWING SCHEDULE OF REINFORCEMENT AS A FUNDAMENTAL DETERMINANT OF STEADY STATE CONTRAST IN MULTIPLE SCHEDULES

Two experiments investigated whether steady-state interactions in multiple schedules depend exclusively on the following schedule of reinforcement. Experiment 1 used a four-component multiple schedule in which two components were associated with the same constant schedule of reinforcement, and where rate of reinforcement was varied in the component that followed one of these. Contrast effects were reliable only in the component that preceded the point of reinforcement variation, although some contrast did occur otherwise. In those instances where contrast other than the following-schedule effect did occur, it was accounted for by the effect of the preceding schedule, an effect for which there were consistent individual differences among subjects, and which varied with component duration. Experiment 2 used a three-component schedule, in which reinforcement rate was varied in the middle component. The results were consistent with Experiment 1, as the following-schedule effect was the only consistent effect that occurred, although an effect of the preceding schedule did occur for some subjects under some conditions, and was especially evident early in training. The conclusion from both experiments is that there is no general effect of relative rate of reinforcement apart from the sum of the effects of the preceding and following schedules, and that the following-schedule effect is the fundamental cause of steady-state interactions.