The applied importance of research on the matching law

In this essay, we evaluate the applied implications of two articles related to the matching law and published in the Journal of the Experimental Analysis of Behavior, May 1994. Building on Mace's (1994) criteria for increasing the applied relevance of basic research, we evaluate the applied implications of basic research studies. Research by Elsmore and McBride (1994) and Savastano and Fantino (1994) involve an extension of the behavioral model of choice. Elsmore and McBride used rats as subjects, but arranged a multioperant environment that resembles some of the complex contingencies of human behavior. Savastino and Fantino used human subjects and extended the matching law to ratio and interval contingencies. These experiments contribute to a growing body of knowledge on the matching law and its relevance for human behavior.     

Optimization and the matching law as accounts of instrumental behavior

The interaction between instrumental behavior and environment can be conveniently described at a molar level as a feedback system. Two different possible theories, the matching law and optimization, differ primarily in the reference criterion they suggest for the system. Both offer accounts of most of the known phenomena of performance on concurrent and single variable-interval and variable-ratio schedules. The matching law appears stronger in describing concurrent performances, whereas optimization appears stronger in describing performance on single schedules.     

Choice, experience, and the generalized matching law

Five pigeons were exposed to different pairs of concurrent variable-interval, variable-interval schedules on nine experimental conditions of 30 sessions each. For every session, the parameters of the generalized matching equation were computed for the first five, six, seven, eight, and nine experimental conditions. The exponent a, both for response and time distribution, tended to decrease with increases in number of experimental conditions and to increase with number of sessions per condition, but values of k (bias) varied unsystematically. When the subjects were exposed to five new pairs of schedules, with 55 sessions per condition, the findings were confirmed. Data from the literature on the generalized matching law suggest that the variability of exponent values may be explained in part by the use of naive or experienced subjects in different investigations and by the variability in number of experimental conditions and in number of sessions per condition.     

Positive behavior support and applied behavior analysis

This article reviews the origins and characteristics of the positive behavior support (PBS) movement and examines those features in the context of the field of applied behavior analysis (ABA). We raise a number of concerns about PBS as an approach to delivery of behavioral services and its impact on how ABA is viewed by those in human services. We also consider the features of PBS that have facilitated its broad dissemination and how ABA might benefit from emulating certain practices of the PBS movement.     

The symmetrical law of effect and the matching relation in choice behavior

In a concurrent-chains procedure, pigeons chose between outcomes that differed in the rate of response-independent delivery of food and electric shocks. The application of functional measurement techniques confirmed the matching relation—between choice and rate of reinforcement value—for two of three pigeons. Scale values of the outcomes were extracted for the two birds that conformed to matching, and the value of a single occurrence of shock per minute—in terms of negative food units—was estimated. A second experiment with concurrent chains provided a test of these parameter estimates. The close correspondence between predicted and obtained choice behavior found in Experiment II indicated that the estimates of outcome value were indeed reliable. Both experiments together support the contention that the effects on choice behavior of positive and aversive stimuli appear to be equal, though opposite in sign.     

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.     

Concurrent reinforcement schedules for problem behavior and appropriate behavior: experimental applications of the matching law

This study evaluated how children who exhibited functionally equivalent problem and appropriate behavior allocate responding to experimentally arranged reinforcer rates. Relative reinforcer rates were arranged on concurrent variable-interval schedules and effects on relative response rates were interpreted using the generalized matching equation. Results showed that relative rates of responding approximated relative rates of reinforcement. Finally, interventions for problem behavior were evaluated and differential reinforcement of alternative behavior and extinction procedures were implemented to increase appropriate behavior and decrease problem behavior. Practical considerations for the application of the generalized matching equation specific to severe problem behavior are discussed, including difficulties associated with defining a reinforced response, and obtaining steady state responding in clinical settings.     

Women in applied behavior analysis

The status of women in applied behavior analysis was examined by comparing the participation of women in the Journal of Applied Behavior Analysis (JABA) to their participation in three similar journals. For all journals, the percentage of articles with at least one female author, the percentage of authors who are female, and the percentage of articles with a female first author increased from 1978 to 1997. Participation by women in JABA was equal to or greater than participation by women in the comparison journals. However, women appeared as authors on papers in special sections of Behavior Modification substantially more often when the editor was female than when the editor was male. In addition, female membership on the editorial boards of JABA, Behavior Modification, and Behaviour Research and Therapy failed to increase from 1978 to 1997. We conclude that a "glass ceiling" reduces the participation of women at the highest levels of applied behavior analysis and related fields.     

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.     

Recent reinforcement-schedule research and applied behavior analysis

Reinforcement schedules are considered in relation to applied behavior analysis by examining several recent laboratory experiments with humans and other animals. The experiments are drawn from three areas of contemporary schedule research: behavioral history effects on schedule performance, the role of instructions in schedule performance of humans, and dynamic schedules of reinforcement. All of the experiments are discussed in relation to the role of behavioral history in current schedule performance. The paper concludes by extracting from the experiments some more general issues concerning reinforcement schedules in applied research and practice.     

Concurrent random-interval schedules and the matching law

In Experiment I, a group of eight pigeons performed on concurrent random-interval schedules constructed by holding probability equal and varying cycle time to produce ratios of reinforcer densities of 1:1, 3:1, and 5:1 for key pecking. Schedules for a second group of seven were constructed with equal cycle times and unequal probabilities. Both groups deviated from simple matching, but the two forms of the schedules appeared to produce no consistent patterns of deviation. The data were found to be consistent with those obtained in concurrent variable-interval situations. The parameters of the matching equation in the form of Y=k X^a were estimated; the value of k was unity and a was 0.84. In Experiment II, six pigeons were exposed to two conc RI RI schedules in which one component increasingly approximated an FI schedule. The value of k was not 1.0. Concurrent RI RI schedules were shown to represent a continuum from conc FI VI to conc VI VI schedules. The use of the exponential equation in testing “matching laws” suggests that a<1 will continue to be observed, and this will set limits on the form of new laws and the assumed or rational values of the component variables in these laws.     

On differentiation in applied behavior analysis

Distinct types of activity in the field of applied behavior analysis are noted and discussed. Four metaphorical types of activity are considered: prospecting, farming, building, and guiding. Prospecting consists of time-limited exploration of a variety of beaviors, populations, or settings. Farming consists of producing new behaviors in the same setting using independent variables provided by the researchers or normally available in the setting. Building consists of combining procedural elements to create new programs or systems or to rehabilitate aspects of existing programs. Guiding involves pointing out connections between the principles of human behavior and the problems, populations, settings, and procedures with which researchers are (or could be) working. Advantages of each sphere are noted, and benefits of this division of labor to the field as a whole are discussed.     

Internet resources in applied behavior analysis

Internet communication is becoming an important tool for both academic and clinical areas in psychology and behavior analysis. The Internet, a confederation of thousands of computer systems covering the entire globe (Plaud, 1996b), can significantly enhance behavior analysis in at least three major areas: (a) information exchange and communication among behavior analysts through list servers, (b) dissemination of empirical data and commentary through on-line journals and information servers, and (c) promotion of programs and services in behavior analysis. This commentary provides specific examples in each of these areas and addresses the basics of connecting to the Internet.