The Harvard Pigeon Lab under Herrnstein

The history of the Harvard Pigeon Lab is a history of two periods of remarkable productivity, the first under Skinner's leadership and the second under Herrnstein's. In each period, graduate students flocked to the leader and then began stimulating one another. Chance favored Herrnstein's leadership, too, because an unusually large number of graduate students were admitted in the fall of 1962. In each period, productivity declined as the leader lost interest in the laboratory and withdrew. Directly and indirectly, the laboratory finally died as a result of the cognitive "revolution." Skinner and his students saw the possibility of a natural science of behavior and set about establishing that science based on concepts such as response rate, stimulus control, and schedules of reinforcement. Herrnstein and his students saw that the science could be quantitative and set about making it so, with relative response rate, the matching law, and the psychophysics of choice (analogous to S. S. Stevens' psychophysics). The history might provide a golden research opportunity for someone interested in the impact of such self-organizing research groups on the progress of science.     

Noncontingent reinforcement, alternative reinforcement, and the matching law: a laboratory demonstration

Basic researchers, but not most applied researchers, have assumed that the behavior-decelerating effects of noncontingent reinforcement result at least partly from adventitious reinforcement of competing behaviors. The literature contains only sketchy evidence of these effects because few noncontingent reinforcement studies measure alternative behaviors. A laboratory model is presented in which concurrent schedules of contingent reinforcement were used to establish a "target" and an "alternative" behavior. Imposing noncontingent reinforcement decreased target behavior rates and increased alternative behavior rates, outcomes that were well described by the standard quantitative account of alternative reinforcement, the generalized matching law. These results suggest that adventitious reinforcement of alternative behaviors can occur during noncontingent reinforcement interventions, although the range of conditions under which this occurs remains to be determined in future studies. As an adjunct to applied studies, laboratory models permit easy measurement of alternative behaviors and parametric manipulations needed to answer many research questions.     

Stimuli, reinforcers, and behavior: an integration

We propose that a fundamental unit of behavior is the concurrent discriminated operant, and we discuss in detail a quantitative model of the concurrent three-term contingency that is based on the notion that an animal's behavior is controlled to differing extents by both stimulus—behavior and behavior—reinforcer relations. We show how this model can describe performance in a variety of experimental procedures: conditional discrimination and matching to sample, both with and without reinforcement for responses that are traditionally identified as errors; conditional discrimination with more than two stimuli and choice alternatives; delayed matching to sample and delayed reinforcement in matching to sample; second-order and complex conditional discrimination; and multiple and concurrent schedules. Although the model is incomplete in its coverage, and may be incorrect, we believe that this conceptual approach will bear fruit in the development of behavior theory.     

Stimuli, reinforcers, and private events

Radical behaviorism considers private events to be a part of ongoing observable behavior and to share the properties of public events. Although private events cannot be measured directly, their roles in overt action can be inferred from mathematical models that relate private responses to external stimuli and reinforcers according to the same quantitative relations that characterize public operant behavior. This approach is illustrated by a model of attending to stimuli and to anticipated reinforcers in delayed matching to sample, in which the probabilities of attending are related to reinforcer rates by an expression derived from research on behavioral momentum.     

The Matching Law And Amount-dependent Exponential Discounting As Accounts Of Self-control Choice

Studies with humans have found evidence for amount-dependent temporal discounting, that is, that the sensitivity of choice to reinforcer delay varies inversely with reinforcer magnitude. To test whether similar results could be obtained with nonhumans, pigeons were trained on a two-component concurrent-chains procedure in which the durations of food reinforcement in the terminal links were equal within components but unequal between components. Terminal-link schedules were varied over four conditions to allow separate estimates of sensitivity to delay to be obtained for the large and small reinforcer-magnitude components. Although sensitivity to delay was greater in the small-magnitude component for all subjects, the effect was quite small. The difference in sensitivity was generally less than one standard error, and t tests on parameter differences failed to reach significance. Several models for temporal discounting, including an amount-dependent exponential function, were fitted to the data from the first four conditions. The resulting parameter estimates were used to make predictions for a self-control condition in which one terminal link arranged a smaller, less delayed reinforcer and the other arranged a larger, more delayed reinforcer. For all models, predictions were considerably more accurate when sensitivity to delay was the same regardless of reinforcer magnitude. The results support the independence of delay and magnitude as required by a version of the matching law, and provide strong evidence against amount-dependent exponential discounting as an account of self-control choice. A new two-parameter discounting function, consistent with the matching law, is proposed that has wide empirical generality for both human and nonhuman data.     

Choice in a self-control paradigm: Quantification of experience-based differences

Previous quantitative models of choice in a self-control paradigm (choice between a larger, more-delayed reinforcer and a smaller, less-delayed reinforcer) have not described individual differences. Two experiments are reported that provide additional quantitative data on experience-based differences in choice between reinforcers of varying sizes and delays. In Experiment 1, seven pigeons in a self-control paradigm were exposed to a fading procedure that increased choices of the larger, more-delayed reinforcer through gradually decreasing the delay to the smaller of two equally delayed reinforcers. Three control subjects, exposed to each of the small-reinforcer delays to which the experimental subjects were exposed, but for fewer sessions, demonstrated that lengthy exposure to each of the conditions in the fading procedure may be necessary in order for the increase to occur. In Experiment 2, pigeons with and without fading-procedure exposure chose between reinforcers of varying sizes and delays scheduled according to a concurrent variable-interval variable-interval schedule. In both experiments, pigeons with fading-procedure exposure were more sensitive to variations in reinforcer size than reinforcer delay when compared with pigeons without this exposure. The data were described by the generalized matching law when the relative size of its exponents, representing subjects' relative sensitivity to reinforcer size and delay, were grouped according to subjects' experience.     

Dynamical concurrent schedules

Previous work on the matching law has predominantly focused on the molar effects of the contingency by examining only one reinforcer ratio for extended periods. Responses are distributed as a function of reinforcer ratios under these static conditions. But the outcome under a dynamic condition in which reinforcer ratios change continuously has not been determined. The present study implemented concurrent variable-interval schedules that changed continuously across a fixed 5-min trial. The schedules were reciprocally interlocked. The variable interval for one key changed continuously from a variable-interval 15-s to a variable-interval 480-s, while the schedule for the other key changed from a variable-interval 480-s to a variable-interval 15-s. This dynamical concurrent schedule shifted behavior in the direction of matching response ratios to reinforcer ratios. Sensitivities derived from the generalized matching law were approximately 0.62, the mean absolute bias was approximately 0.11, and r2s were approximately 0.86. It was concluded that choice behavior can come to adapt to reinforcer ratios that change continuously over a relatively short time and that this change does not require extensive experience with a fixed reinforcer ratio. The results were seen as supportive of the view that all behavior constitutes choice.     

Concurrent schedules: Interaction of reinforcer frequency and reinforcer duration

Six pigeons were trained on concurrent variable-interval schedules with unequal reinforcer durations for the two responses. The schedules arranged on the two keys were kept equal while they were varied in absolute size. As the overall reinforcer rate was increased, both response-allocation and time-allocation measures of choice showed a trend toward indifference, and measures of sensitivity to reinforcer-duration ratios significantly decreased. Recent reports have shown that the generalized matching law cannot describe the changes in behavior allocation under constant delay-, duration-, or rate-ratios when changes are made in the absolute levels of each of these variables. The present results complement these findings by demonstrating that the concatenated generalized matching law cannot describe the interactions of two reinforcer variables on behavior allocation.     

Multilevel analysis of matching behavior

Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within‐subject and between‐subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.     

Dynamic response-by-response models of matching behavior in rhesus monkeys

We studied the choice behavior of 2 monkeys in a discrete-trial task with reinforcement contingencies similar to those Herrnstein (1961) used when he described the matching law. In each session, the monkeys experienced blocks of discrete trials at different relative-reinforcer frequencies or magnitudes with unsignalled transitions between the blocks. Steady-state data following adjustment to each transition were well characterized by the generalized matching law; response ratios undermatched reinforcer frequency ratios but matched reinforcer magnitude ratios. We modelled response-by-response behavior with linear models that used past reinforcers as well as past choices to predict the monkeys' choices on each trial. We found that more recently obtained reinforcers more strongly influenced choice behavior. Perhaps surprisingly, we also found that the monkeys' actions were influenced by the pattern of their own past choices. It was necessary to incorporate both past reinforcers and past choices in order to accurately capture steady-state behavior as well as the fluctuations during block transitions and the response-by-response patterns of behavior. Our results suggest that simple reinforcement learning models must account for the effects of past choices to accurately characterize behavior in this task, and that models with these properties provide a conceptual tool for studying how both past reinforcers and past choices are integrated by the neural systems that generate behavior.     

Zebrafish choice behavior is sensitive to reinforcer rate,immediacy, and magnitude ratios

Behavioral flexibility has, in part, been defined by choice behavior changing as a function of changes in reinforcer payoffs. We examined whether the generalized matching law quantitatively described changes in choice behavior in zebrafish when relative reinforcer rates, delays/immediacy, and magnitudes changed between two alternatives across conditions. Choice was sensitive to each of the three reinforcer properties. Sensitivity estimates to changes in relative reinforcer rates were greater when 2 variable-interval schedules were arranged independently between alternatives (Experiment 1a) than when a single schedule pseudorandomly arranged reinforcers between alternatives (Experiment 1b). Sensitivity estimates for changes in relative reinforcer immediacy (Experiment 2) and magnitude (Experiment 3) were similar but lower than estimates for reinforcer rates. These differences in sensitivity estimates are consistent with studies examining other species, suggesting flexibility in zebrafish choice behavior in the face of changes in payoff as described by the generalized matching law.     

USING MICROSOFT OFFICE EXCEL® 2007 TO CONDUCT GENERALIZED MATCHING ANALYSES

The generalized matching equation is a robust and empirically supported means of analyzing relations between reinforcement and behavior. Unfortunately, no simple task analysis is available to behavior analysts interested in using the matching equation to evaluate data in clinical or applied settings. This technical article presents a task analysis for the use of Microsoft Excel to analyze and plot the generalized matching equation. Using a data‐based case example and a step‐by‐step guide for completing the analysis, these instructions are intended to promote the use of quantitative analyses by researchers with little to no experience in quantitative analyses or the matching law.     

Local contrast in behavior allocation during multiple-schedule components

Allocation of responses between two keys was studied during two alternating multiple-schedule components. Responses were recorded in successive quarters of each component. Variable-interval reinforcer schedules on the two keys were constant throughout the experiment for one (constant) component and were varied over conditions on one key for the other, producing changes in reinforcer ratios for the varied component. Behavior allocation for the first quarter of the constant component was inversely related to varied-component reinforcer ratios, a form of local contrast, but this relationship was not observed later in the component. During the first quarter of the varied component, slopes of matching lines were high and decreased later in the component. It is argued that this form of local contrast cannot be explained in terms of reallocation of extraneous reinforcers between components, and that the matching law for concurrent operants does not capture some sources of control over behavior allocation. A simple extension of the matching law is offered that adequately describes behavior changes during both components. A version of this formulation can predict contrast effects in absolute response rates.     

An Empirical Analysis of Interspersal Research: Evidence, Implications, and Applications of the Discrete Task Completion Hypothesis

Because assignment completion is often reinforced, researchers have posited that when students work on assignments with many discrete tasks (e.g., 20 mathematics problems), that each completed discrete task may be a conditioned reinforcer (e.g., Skinner et al., 1999). If the discrete task completion hypothesis is accurate, then relative task completion rates should influence choice behavior in the same manner as relative rates of reinforcement. In the current study, previous interspersal research was combined across experiments and regression analysis revealed a linear relationship between relative problem completion rates (RPCR) and choice in accordance with the matching law (Herrnstein, 1961, 1970). These results support the discrete task completion hypothesis and suggest that interspersing additional brief tasks enhances interval schedules of reinforcement. Theoretical and applied implications of the current study and the discrete problem completion hypothesis are discussed and directions for future research are provided.     

IMPULSIVITY IN STUDENTS WITH SERIOUS EMOTIONAL DISTURBANCE: THE INTERACTIVE EFFECTS OF REINFORCER RATE,DELAY, AND QUALITY

We conducted two studies extending basic matching research on self-control and impulsivity to the investigation of choices of students diagnosed as seriously emotionally disturbed. In Study 1 we examined the interaction between unequal rates of reinforcement and equal versus unequal delays to reinforcer access on performance of concurrently available sets of math problems. The results of a reversal design showed that when delays to reinforcer access were the same for both response alternatives, the time allocated to each was approximately proportional to obtained reinforcement. When the delays to reinforcer access differed between the response alternatives, there was a bias toward the response alternative and schedule with the lower delays, suggesting impulsivity (i.e., immediate reinforcer access overrode the effects of rate of reinforcement). In Study 2 we examined the interactive effects of reinforcer rate, quality, and delay. Conditions involving delayed access to the high-quality reinforcers on the rich schedule (with immediate access to low-quality reinforcers earned on the lean schedule) were alternated with immediate access to low-quality reinforcers on the rich schedule (with delayed access to high-quality reinforcers on the lean schedule) using a reversal design. With 1 student, reinforcer quality overrode the effects of both reinforcer rate and delay to reinforcer access. The other student tended to respond exclusively to the alternative associated with immediate access to reinforcers. The studies demonstrate a methodology based on matching theory for determining influential dimensions of reinforcers governing individuals' choices.     

The watershed years of 1958-1962 in the Harvard Pigeon Lab

During the years 1958-1962, the final years of support by the National Science Foundation for B. F. Skinner's Pigeon Lab in Memorial Hall at Harvard University, 20 or so pigeon experiments (plus some with other organisms) ran concurrently 7 days a week. The research style emphasized experimental analyses, exploratory procedures, and the parametric exploration of variables. This reminiscence describes some features of the laboratory, the context within which it operated, and the activities of some of those who participated in it.     

The matching law

The matching law may be viewed either as an empirical generalization, and therby subject to disproof, or as part of a system of equations used to define the utility (“value”) of a reinforcer. In the latter case it is tautologous, and not subject to disproof within the defining context. A failure to obtain matching will most often be a signal that the independent variables have not been properly scaled. If, however, the proper transformations have been made on the independent variables, and matching is not obtained, the experimental paradigm may be outside the purview of the matching law. At that point, reinterpretations or revisions of the law are called for. The theoretical matching law is but one of many possible ways to define utility, and it may eventually be rejected in favor of a more useful definition.