The substitutability of reinforcers

Substitutability is a construct borrowed from microeconomics that describes a continuum of possible interactions among the reinforcers in a given situation. Highly substitutable reinforcers, which occupy one end of the continuum, are readily traded for each other due to their functional similarity. Complementary reinforcers, at the other end of the continuum, tend to be consumed jointly in fairly rigid proportion, and therefore cannot be traded for one another except to achieve that proportion. At the center of the continuum are reinforcers that are independent with respect to each other; consumption of one has no influence on consumption of another. Psychological research and analyses in terms of substitutability employ standard operant conditioning paradigms in which humans and nonhumans choose between alternative reinforcers. The range of reinforcer interactions found in these studies is more readily accommodated and predicted when behavior-analytic models of choice consider issues of substitutability. New insights are gained into such areas as eating and drinking, electrical brain stimulation, temporal separation of choice alternatives, behavior therapy, drug use, and addictions. Moreover, the generalized matching law (Baum, 1974) gains greater explanatory power and comprehensiveness when measures of substitutability are included.     

Delay reduction: current status.

Delay-reduction theory states that the effectiveness of a stimulus as a conditioned reinforcer may be predicted most accurately by the reduction in time to primary reinforcement correlated with its onset. We review support for the theory and then discuss two new types of experiments that assess it. One compares models of choice in situations wherein the less preferred outcome is made more accessible; the other investigates whether frequency of conditioned reinforcement affects choice beyond the effect exerted by frequency of primary reinforcement.     

Violations of transitivity: Implications for a theory of contextual choice

Violations of strong stochastic transitivity in concurrent-chains choice were first reported by Navarick and Fantino. In a series of articles, Navarick and Fantino concluded that neither a unidimensional model capable of predicting exact choice probabilities nor a fixed-variable equivalence rule was possible for the concurrent-chains procedure. I show that when choice is modeled contextually (i.e., when preference for a schedule is affected by factors other than the schedule itself, e.g., aspects of the alternative schedule), a unidimensional, exact-choice probability model is possible that both predicts the intransitivities reported by Navarick and Fantino and provides a fixed-variable equivalence rule for the concurrent-chains procedure. The contextual model is an extension of the generalized matching law and violates a key assumption underlying traditional choice models—simple scalability—because of (a) schedule interdependence and (b) bias from procedural contingencies. Therefore, strong stochastic transitivity cannot be expected to hold. Contextual scalability is analyzed to reveal a hierarchy of context effects in choice. Navarick and Fantino's intransitivities can be satisfactorily explained by bias. If attribute sensitivity is context dependent, however, and if there are similarity structures among choice alternatives, the contextual model is shown to be able to predict violations of ordinal preference. Therefore, it may be possible to formulate a deterministic, general psychophysical model of choice as a behavioral alternative to probabilistic, multidimensional choice theories.     

Unit price as a useful metric in analyzing effects of reinforcer magnitude.

In this paper, we applied the behavioral-economic concept of unit price to the study of reinforcer magnitude in an attempt to provide a consistent account of the effects of reinforcer magnitude on behavior. Recent research in the experimental analysis of behavior and in behavioral pharmacology suggests that reinforcer magnitude interacts with the schedule of reinforcement to determine response rate and total consumption. The utility of the unit-price concept thus stems from its ability to quantify this interaction as a cost-benefit ratio (i.e., unit price = characteristics of the schedule of reinforcement divided by magnitude of reinforcement). Research employing the unit-price concept has shown that as unit price increases, a positively decelerating function exists for consumption (i.e., a function with an increasingly negative slope, when plotted on log coordinates) and a bitonic function exists for response rate. Based on these findings, the present analysis applied the unit-price concept to those studies of reinforcer magnitude and drug self-administration that examined the effects of reinforcer magnitude on response rate using simple schedules of reinforcement (e.g., fixed-ratio schedule). This resulted in three findings: (a) Reinforcer-magnitude manipulations and schedule manipulations interact in a manner that can be quantified in terms of unit price as benefit and cost factors, respectively; (b) different reinforcer-magnitude manipulations are functionally interchangeable as benefit factors in the unit-price ratio; and (c) these conclusions appear warranted despite the differences in reinforcers (food or drug), species (dogs, monkeys, or rats), and schedules (interval or ratio), and despite the fact that these studies were not designed for a unit-price analysis. In methodological terms, these results provide further evidence that employing the unit-price concept is a parsimonious method for examining the effects of reinforcer magnitude. In theoretical terms, these results suggest that a single process may underlie the effect of combined reinforcer-magnitude and schedule manipulations.     

Schedule-induced defecation by rats during ratio and interval schedules of food reinforcement.

Lever pressing in rats was maintained by continuous and intermittent schedules of food while defecation was monitored. In Experiment 1, reinforcement densities were matched across variable-ratio and variable-interval schedules for three pairs of rats. Defecation occurred in all 3 rats on the variable-ratio schedule and in all 3 rats on the yoked variable-interval schedule. In Experiment 2, fixed-ratio and fixed-interval schedules with similar reinforcement densities maintained lever pressing. Defecation occurred in 3 of 4 rats on the fixed-ratio schedule and in 4 of 4 rats on the fixed-interval schedule. Almost no defecation occurred during continuous reinforcement in either experiment. These results demonstrate that defecation may occur during both ratio and interval schedules and that the inter-reinforcement interval is more important than the behavioral requirements of the schedule in generating schedule-induced defecation.     

IMPROVED CURVEBALL HITTING THROUGH THE ENHANCEMENT OF VISUAL CUES

This study investigated the effectiveness of using visual cues to highlight the seams of baseballs to improve the hitting of curveballs. Five undergraduate varsity baseball team candidates served as subjects. Behavior change was assessed through an alternating treatments design involving unmarked balls and two treatment conditions that included baseballs with 1/4-in. and 1/8-in. orange stripes marking the seams of the baseballs. Results indicated that subjects hit a greater percentage of marked than unmarked balls. These results suggest that the addition of visual cues may be a significant and beneficial technique to enhance hitting performance. Further research is suggested regarding the training procedures, effect of feedback, rate of fading cues, generalization to live pitching, and generalization to other types of pitches.     

Additional-delay schedules: A continuum of temporal contingencies by varying food delay

Pigeons performed on discrete-trial, temporally defined schedules in which the food delay (D) was adjusted according to the latency of the key peck (X) and two schedule parameters (t and A). The schedule function was D = A(t − X), where D is the experienced delay between a response and a reinforcer. The schedule parameter t is the maximum value below which the present contingencies occur. A is the additional delay to reinforcement for each second the response latency is shorter than the t value. When A = 0 s, the schedule is a continuous reinforcement schedule with immediate reinforcement. When A = 1 s, the schedule is a conjunctive fixed-ratio 1 fixed-time t-s schedule. When A approaches infinity, the schedule becomes a differential reinforcement of long latency schedule. The latencies for subjects with t = 10 s and t = 30 s were observed with the present schedules having seven values for A between 0 s and 11 s. In addition, the latencies for subjects for which t = 30 s were observed at an A value of 31 s to 41 s. As the A value increased, the latencies approached the t value for subjects for which t = 10 s. The latencies for 30-s-t subjects did not approach t, even when the A value was 41 s. The latencies for 10-s-t subjects at 11-s A value were longer than those under yoked conditions having exactly the same delays/interreinforcement intervals. These results demonstrated a continuum of latency related to the schedule continuum (value of A) at a small t value.     

Timeout from concurrent schedules.

Response-contingent timeouts of equal duration and frequency were added to both alternatives of unequal concurrent schedules of reinforcement. For each of 4 pigeons in Experiment 1, relative response rates generally became less extreme as the frequency of timeout increased. In Experiment 2, relative response rates consistently approached indifference as the duration of timeout was increased. Variation in time allocation was less consistent in both experiments. Absolute response rates did not vary with the timeout contingency in either experiment. In a third experiment, neither measure of choice varied systematically when the duration of a postreinforcement blackout was varied. In contrast to the present results, preference has been shown to vary directly with the parameters of shock delivery in related procedures. The pattern of results in the first two experiments follows that obtained with other manipulations of the overall rate of reinforcement in concurrent schedules. The results of the third experiment suggest that an intertrial interval following reinforcement is not a critical feature of the overall rate of reinforcement.     

Determinants of pigeons' waiting time: Effects of interreinforcement interval and food delay

Four pigeons performed on three types of schedules at short (i.e., 10, 30, or 60 s) interreinforcement intervals: (a) a delay-dependent schedule where interreinforcement interval was held constant (i.e., increases in waiting time decreased food delay), (b) an interreinforcement-interval-dependent schedule where food delay was held constant (i.e., increases in waiting time increased interreinforcement interval), and (c) a both-dependent schedule where increases in waiting time produced increases in interreinforcement interval but decreases in food delay. Waiting times were typically longer under the delay-dependent schedules than under the interreinforcement-interval-dependent schedules. Those under both-dependent schedules for 1 subject were intermediate between those under the other two schedule types, whereas for the other subjects waiting times under the both-dependent procedure were similar either to those under the delay-dependent schedule or to those under the interreinforcement-interval-dependent schedule, depending both on the subject and the interreinforcement interval. These results indicate that neither the interreinforcement interval nor food delay is the primary variable controlling waiting time, but rather that the two interact in a complex manner to determine waiting times.     

Inferential procedures for multifaceted coefficients of generalizability

A two-facet measurement model with broad application in the behavioral sciences is identified, and its coefficient of generalizability (CG) is examined. A normalizing transformation is proposed, and an asymptotic variance expression is derived. Three other multifaceted measurement models and CGs are identified, and variance expressions are presented. Next, an empirical investigation of the procedures follows, and it is shown that, in most cases, Type I error control in inferential applications is precise, and that the estimates are relatively efficient compared with the correlation coefficient. Implications for further research and for practice are noted. In an Appendix, four additional models, CGs, and variance expressions are presented.The research reported herein formed part of a doctoral dissertation conducted by Marsha Schroeder (Schroeder, 1986), under the direction of Ralph Hakstian, at the University of British Columbia. We acknowledge with thanks the contributions to this research of Todd Rogers and James Steiger. We are also very indebted to an mous reviewer who provided some important clarifications in connection with two of the models considered. Some support for this research was provided by a grant to Ralph Hakstian from the Natural Sciences and Engineering Research Council of Canada.