Generalized Matching Law Research Articles

Reconciling Signal-Detection Models of Criterion Learning with the Generalized Matching Law

Reconciling Signal-Detection Models of Criterion Learning with the Generalized Matching Law

Influence of reinforcement and its omission on trial-by-trial changes of response bias in perceptual decision making.

Discrimination performance in perceptual choice tasks is known to reflect both sensory discriminability and nonsensory response bias. In the framework of signal detection theory, these aspects of discrimination performance are quantified through separate measures, sensitivity (d') for sensory discriminability and decision criterion (c) for response bias. However, it is unknown how response bias (i.e., criterion) changes at the single-trial level as a consequence of reinforcement history. We subjected rats to a two-stimulus two-response conditional discrimination task with auditory stimuli and induced response bias through unequal reinforcement probabilities for the two responses. We compared three signal-detection-theory-based criterion learning models with respect to their ability to fit experimentally observed fluctuations of response bias on a trial-by-trial level. These models shift the criterion by a fixed step (1) after each reinforced response or (2) after each nonreinforced response or (3) after both. We find that all three models fail to capture essential aspects of the data. Prompted by the observation that steady-state criterion values conformed well to a behavioral model of signal detection based on the generalized matching law, we constructed a trial-based version of this model and find that it provides a superior account of response bias fluctuations under changing reinforcement contingencies.

Choice dynamics in concurrent ratio schedules of reinforcement.

The generalized matching law predicts performance on concurrent schedules when variable-interval schedules are programmed but is trivially applicable when independent ratio schedules are used. Responding usually is exclusive to the schedule with the lowest response requirement. Determining a method to program concurrent ratio schedules such that matching analyses can be usefully employed would extend the generality of matching research and lead to new avenues of research. In the present experiments, ratio schedules were programmed dependently such that responses to either of the two options progressed the requirement on both schedules. Responding is not exclusive because the probability of reinforcement increases on both schedules as responses are allocated to either schedule. In Experiment 1, performance on concurrent variable-ratio schedules was assessed, and reinforcer ratios were varied across conditions to investigate changes in sensitivity. Additionally, the length of a changeover delay was manipulated. In Experiment 2, performance was compared under concurrently available, dependently programmed variable-ratio and fixed-ratio schedules. Performance was well described by the generalized matching law. Increases in the changeover delay decreased sensitivity, whereas sensitivity was higher when variable-ratio schedules were employed, compared with fixed-ratio schedules. Concurrent ratio schedules can be a viable approach to studying functional differences between ratio and interval schedules.

Choice and rate-amount independence in a titration procedure

The generalized matching law or Law of Allocation proposed by Baum (2018a, 2018b) potentially provides a broad conceptual framework within which to understand the allocation of time among activities. In its simplest form, the law incorporates power-function induction of activities by variables such as rate and amount of delivered inducers. Whether these variables affect allocation independently of one another is a central issue, because independence of the variables would allow simple multiplication of power functions and would make quantitative prediction simple too. The present experiment used a titration procedure to test the independence of rate and amount of food in determining pigeons’ allocation of pecking between two keys. Amount ratio was varied within sessions to engender different peck ratios. Rate ratio was varied across two series of conditions. The results conformed to the predictions of the simple version of the Law of Allocation by strongly supporting independence of rate and amount. The Law of Allocation may have broad application for understanding activities in natural settings and everyday life.

Good, Better, Best: How Evolution Optimizes Anatomy and Action

Good, Better, Best: How Evolution Optimizes Anatomy and Action

IMPULSIVE CHOICE IN SPONTANEOUSLY HYPERTENSIVE (SHR) AND LEWIS (LEW) RATS

The Spontaneously Hypertensive rat (SHR), the most widely accepted rodent-model of Attention Deficit/Hyperactivity disorder (ADHD), usually is compared with its normotensive control, the Wistar Kyoto (WKY) rat, seeking differences in impulsivity between strains. The utilization of the WKY as a control strain for the SHR, however, has been questioned. Dopamine deficits in nucleus accumbens may cause low tolerance to delayed consequences in the SHR. Locomotion and dopamine activities in the Lewis (LEW) rat are comparable to those in the SHR, suggesting that both strains will develop similar levels of impulsivity. This possibility was examined with SHRs and LEWs responding to concurrentchains procedures. Choice was measured in the initial link where two random interval schedules operating concurrently on two levers arranged entries to two terminal links, one delivering 1-food pellet immediately and the other 4-food pellets with several delays randomly presented during the session. Both strains learned to choose impulsively with training, but the SHRs developed faster changes in preference and more impulsive choices than the LEWs. The Hyperbolic-decay Model and the Generalized Matching Law described choice well. Positive correlations between estimates of discounting rate and sensitivity to the immediacy of reinforcement confirmed some consistencies between these models of choice.

Increased Behavioral Sensitivity to Repeated Experiences of Punishment in Children With ADHD: Experimental Studies Using the Matching Law

Background: Research on altered motivational processes in ADHD has focused on reward. The sensitivity of children with ADHD to punishment has received limited attention. We evaluated the effects of punishment on the behavioral allocation of children with and without ADHD from the United States, New Zealand, and Japan, applying the generalized matching law. Methods: Participants in two studies (Furukawa et al., 2017, 2019) were 210 English-speaking (145 ADHD) and 93 Japanese-speaking (34 ADHD) children. They completed an operant task in which they chose between playing two simultaneously available games. Rewards became available every 10 seconds on average, arranged equally across the two games. Responses on one game were punished four times as often as responses on the other. The asymmetrical punishment schedules should bias responding to the less punished alternative. Results: Compared with controls, children with ADHD from both samples allocated significantly more responses to the less frequently punished game, suggesting greater behavioral sensitivity to punishment. For these children, the bias toward the less punished alternative increased with time on task. Avoiding the more punished game resulted in missed reward opportunities and reduced earnings. English-speaking controls showed some preference for the less punished game. The behavior of Japanese controls was not significantly influenced by the frequency of punishment, despite slowed response times after punished trials and immediate shifts away from the punished game, indicating awareness of punishment. Conclusion: Punishment exerted greater control over the behavior of children with ADHD, regardless of their cultural background. This may be a common characteristic of the disorder. Avoidance of punishment led to poorer task performance. Caution is required in the use of punishment, especially with children with ADHD. The group difference in punishment sensitivity was more pronounced in the Japanese sample; this may create a negative halo effect for children with ADHD in this culture.

Evolutionary theory prediction: Response rate as a joint function of reinforcement rate and reinforcer magnitude.

Artificial organisms (AOs) animated by an evolutionary theory of behavior dynamics (ETBD) worked on concurrent interval schedules with a standard reinforcer magnitude on 1 alternative and a range of reinforcer magnitudes on the other. The reinforcer magnitudes on the second alternative were hedonically scaled using the generalized matching law. The AOs then worked on single interval schedules that arranged various combinations of the scaled reinforcer magnitudes and a range of nominal schedule values. This produced bivariate response rate data to which 5 candidate equations were fitted. One equation was found to provide the best description of the bivariate data in terms of percentage of variance accounted for, information criterion value, and residual profile. This equation consisted of 2 factors, 1 entailing the scaled magnitude, 1 entailing the obtained reinforcement rate, and both expressed in the form of exponentiated hyperbolas. The theory's prediction of the bivariate equation, along with additional predictions of the theory, were tested on data from an experiment in which rats pressed levers for various concentrations of sucrose pellets. The bivariate equation predicted by the theory was confirmed, as were all the additional predictions of the theory that could be tested on this data set.

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.

Applications of the matching law to observe shifts in problem behavior: A proof‐of‐concept study

AbstractWe used the matching law to quantify the relation between the relative likelihood of appropriate behavior and problem behavior and the relative likelihood of parent‐delivered reinforcement for those behaviors. First, we conducted an initial descriptive observation in the dyads' homes. Second, we assessed the problem behavior within a clinic where participants were receiving behavior‐analytic services. Third, using behavioral skills training (BST), we taught parents how to implement treatments based on differential reinforcement. Fourth, we conducted a second descriptive observation in the dyads' home. Last, we used the generalized matching law to quantify the relation between the child's response allocation and parent‐delivered reinforcement before and after BST. The relation between the effects of parent‐delivered reinforcement on the relative likelihood of appropriate and problem behavior was well described by the matching law.

Scaling N from 1 to 1,000,000: Application of the Generalized Matching Law to Big Data Contexts.

The generalized matching law (GML) has been used to describe the behavior of individual organisms in operant chambers, artificial environments, and nonlaboratory human settings. Most of these analyses have used a handful of participants to determine how well the GML describes choice in the experimental arrangement or how some experimental manipulation influences estimated matching parameters. Though the GML accounts very well for choice in a variety of contexts, the generality of the GML to all individuals in a population is unknown. That is, no known studies have used the GML to describe the individual behavior of all individuals in a population. This is likely because the data from every individual in the population has not historically been available or because time and computational constraints made population-level analyses prohibitive. In this study, we use open data on baseball pitches to provide an example of how big data methods can be combined with the GML to: (1) scale within-subjects designs to the population level; (2) track individual members of a population over time; (3) easily segment the population into subgroups for further analyses within and between groups; and (4) compare GML fits and estimated parameters to performance. These were accomplished for each of 2,374 individuals in a population using 8,467,473 observations of behavior-environment relationships spanning 11 years. In total, this study is a proof of concept for how behavior analysts can use data-science techniques to extend individual-level quantitative analyses of behavior to the population-level focused on domains of social relevance.

Toward a Quantification of Anhedonia: Unified Matching Law and Signal Detection for Clinical Assessment and Drug Development.

Anhedonia, the loss of pleasure from previously rewarding activities, is a core symptom of several neuropsychiatric conditions, including major depressive disorder (MDD). Despite its transdiagnostic relevance, no effective therapeutics exist to treat anhedonia. This is due, in part, to inconsistent assays across clinical populations and laboratory animals, which hamper treatment development. To bridge this gap, recent work has capitalized on two long-standing research domains dedicated to quantifying responsivity to antecedents and consequences across species: the generalized matching law and signal detection theory. This review traces the integration of these quantitative frameworks, which yielded two empirically derived metrics: response bias (log b) and task discriminability (log d). These metrics serve as primary dependent variables in the Probabilistic Reward Task (PRT). In this computerized task, subjects make visual discriminations and probabilistic contingencies are arranged such that correct responses to one alternative are rewarded more often (rich) than correct responses to the other (lean). Under these conditions, healthy participants consistently develop a response bias in favor of the rich alternative, whereas participants with MDD exhibit blunted biases, which correlate with current and predict future anhedonia. Given the correspondence between anhedonic phenotypes and response bias, the PRT has been reverse-translated for rodents and nonhuman primates. Orderly log b and log d values have been observed across diverse clinical populations and laboratory animals. In addition, pharmacological challenges have produced similar outcomes across species. Taken together, this quantitative framework offers a highly translational approach to assaying reward responsiveness to accelerate treatment development for neuropsychiatric disorders involving anhedonia.

Methodological improvements to a Procedure for Rapidly Establishing Steady-State Behavior.

We performed three experiments to improve the quality and retention of data obtained from a Procedure for Rapidly Establishing Steady-State Behavior (PRESS-B; Klapes et al.,2020). In Experiment 1, 120 participants worked on nine concurrent random-interval random-interval (conc RI RI) schedules and were assigned to four conditions of varying changeover delay (COD) length. The 0.5-s COD condition group exhibited the fewest instances of exclusive reinforcer acquisition. Importantly, this group did not differ in generalized matching law (GML) fit quality from the other groups. In Experiment 2, 60 participants worked on nine conc RI RI schedules with a wider range of scheduled reinforcement rate ratios than was used in Experiment 1. Participants showed dramatic reductions in exclusive reinforcer acquisition. Experiment 3 entailed a replication of Experiment 2 wherein blackout periods were implemented between the schedule presentations and each schedule remained in operation until at least one reinforcer was acquired on each alternative. GML fit quality was slightly more consistent in Experiment 3 than in the previous experiments. Thus, these results suggest that future PRESS-B studies should implement a shorter COD, a wider and richer scheduled reinforcement rate ratio range, and brief blackouts between schedule presentations for optimal data quality and retention.

Analyzing the magnitude effect in spontaneously hypertensive (SHR) and wistar Kyoto (WKY) rats

We analyzed the magnitude effect in Spontaneously Hypertensive (SHR) and Wistar Kyoto (WKY) rats choosing between a smaller-sooner (SSF) and a larger-later food (LLF) in the initial link of a concurrent-chains procedure. The SSF was delivered immediately in one terminal link and the LLF delayed 0.01, 5, 10, 20, 40, or 80 s in the other terminal link. An ABABA design varied food amount, 1 vs. 4 and 3 vs. 8 food-pellets in conditions A and B, respectively. The SHRs made more impulsive choices than the WKYs. The hyperbolic-decay model and the Generalized Matching Law fitted the data well. Discounting rate (k) and the area under the discounting curve (AUC) for the choices made by the SHRs in conditions A, were like those in conditions B. For the choices that the individual WKYs made, k was slightly higher and AUC smaller in conditions B than in conditions A. For both strains sensitivity to the immediacy of the LLF (s) was slightly higher in conditions A than in conditions B. Thus, we found no conclusive, compelling evidence either supporting or discarding the magnitude effect in the SHRs and scarce evidence supporting an effect opposite to the magnitude effect in the WKYs.

Further application of the generalized matching law to multialternative sports contexts.

Cox et al. (2017) successfully applied the multialternative version of the generalized matching law (GML) to pitch selection among a sample of Major League Baseball (MLB) pitchers. The purpose of the present study was to replicate and extend these findings by fitting the multialternative GML to pitch data among a sample of MLB pitchers with varying levels of success in the major leagues. We also examined how matching parameters changed as a function of novel antecedent game contexts such as the infield shift, game location, and number of times the pitcher faced the batters in the batting order. These results replicate the findings from Cox et al. and suggest the multialternative GML is a robust descriptor of pitch selection among MLB pitchers. Together, these findings further extend the generality of the multialternative GML to naturalistic, nonlaboratory environments.

The appearance of matching

A computerized version of Houston and McNamara’s (1981) model of concurrent variable time schedules was used to generate large data sets consisting of behavior inputs and the corresponding reinforcement outputs. The data was analyzed to assess the hypothesis that matching behavior observed with CONCVTVT (or CONCVIVI) schedules is an inevitable product of the operation of the schedule. The results suggest that the generalized matching law does not provide the best description of the results obtained with CONCVTVT schedules; that the parameter value of schedule components determine the framework of the reinforcement efficiency maps of behavior choices; and that by random chance alone matching-like behavior is likely to appear if the reinforcement generation efficiency of the behavior is high.

A discriminated rapid-acquisition laboratory procedure for human continuous choice.

Previous continuous choice laboratory procedures for human participants are either prohibitively time-intensive or result in inadequate fits of the generalized matching law (GML). We developed a rapid-acquisition laboratory procedure (Procedure for Rapidly Establishing Steady-State Behavior, or PRESS-B) for studying human continuous choice that reduces participant burden and produces data that is well-described by the GML. To test the procedure, 27 human participants were exposed to 9 independent concurrent random-interval random-interval reinforcement schedules over the course of a single, 37-min session. Fits of the GML to the participants' data accounted for large proportions of variance (median R2 : 0.94), with parameter estimates that were similar to those previously found in human continuous choice studies [median a: 0.67; median log(b): -0.02]. In summary, PRESS-B generates human continuous choice behavior in the laboratory that conforms to the GML with limited experimental duration.

Application of the general matching law on the study of multi-coated radar absorbing materials

In this paper, the Generalized Matching Law of electromagnetic parameters was given for in the application of radar absorbing materials, and applied in the research of absorbing properties of multi -coated absorbing materials. We gave the power reflection formula, defined the constant of general matching law M, and discussed the relationship of general matching constant M with power reflectivity RP, thickness d, relative permittivity εr, relative permeability μr. We found that the enhancement of RP was not obvious at the ε″r was optimized, but the μ″r was primary. In short, this is consistent with panorama analysis method.

Application of the generalized matching law to chess openings: A gambit analysis.

During the opening moves of a chess game, a player (typically White) may offer a number of gambits, which involve sacrificing a chess piece for an opponent for capture to achieve long-term positional advantages. One of the most popular gambits is called the Queen's Gambit and involves White offering a pawn to Black, which will open a lane for White's Queen if accepted by Black. In the present study, the generalized matching law (GML) was applied to chess openings involving the Queen's Gambit using over 71,000 archived chess games. Overall, chess players' opening moves involving the Queen's Gambit exhibited orderly matching as predicted by the GML, and the GML accounted for more variance in players' chess decision making as their relative playing experience increased. This study provides support for the generality of the GML and its application to complex operant behavior outside of laboratory contexts.

Bayesian methods applied to the generalized matching law.

We demonstrate the usefulness of Bayesian methods in developing, evaluating, and using psychological models in the experimental analysis of behavior. We do this through a case study, involving new experimental data that measure the response count and time allocation behavior in pigeons under concurrent random-ratio random-interval schedules of reinforcement. To analyze these data, we implement a series of behavioral models, based on the generalized matching law, as graphical models, and use computational methods to perform fully Bayesian inference. We demonstrate how Bayesian methods, implemented in this way, make inferences about parameters representing psychological variables, how they test the descriptive adequacy of models as accounts of behavior, and how they compare multiple competing models. We also demonstrate how the Bayesian graphical modeling approach allows for more complicated modeling structures, including hierarchical, common cause, and latent mixture structures, to formalize more complicated behavioral models. As part of the case study, we demonstrate how the statistical properties of Bayesian methods allow them to provide more direct and intuitive tests of theories and hypotheses, and how they support the creative and exploratory development of new theories and models.