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.     

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.     

Three-term contingency patterns in mother-child verbal interactions during first-language acquisition

Selections from a large longitudinal data set of verbal interactions between a mother and her child are presented. Two sets of three-term contingency sequences that seemed to reflect maternal rewards and corrections were noted. Both the antecedents as well as the immediate consequences of maternal interventions are presented to explore training and learning processes. The observed frequencies of three-step sequences are compared to those expected based upon Markov-chain logic to substantiate the patterning of the interactions. Behavioral conceptualizations of the learning process are supported by these analyses, although their sufficiency is questioned. It is suggested that maternal rewards and corrections should be integrated with perceptual, cognitive, and social learning conceptualizations in a skill-learning approach to explain the complexity of language transmission and acquisition processes.     

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.     

Unification of models for choice between delayed reinforcers.

Two models for choice between delayed reinforcers, Fantino's delay-reduction theory and Killeen's incentive theory, are reviewed. Incentive theory is amended to incorporate the effects of arousal on alternate types of behavior that might block the reinforcement of the target behavior. This amended version is shown to differ from the delay-reduction theory in a term that is an exponential in incentive theory and a difference in delay-reduction theory. A power series approximation to the exponential generates a model that is formally identical with delay-reduction theory. Correlations between delay-reduction theory and the amended incentive theory show excellent congruence over a range of experimental conditions. Although the assumptions that gave rise to delay-reduction theory and incentive theory remain different and testable, the models deriving from the theories are unlikely to be discriminable by parametric experimental tests. This congruence of the models is recognized by naming the common model the delayed reinforcement model, which is then compared with other models of choice such as Killeen and Fetterman's (1988) behavioral theory of timing, Mazur's (1984) equivalence rule, and Vaughan's (1985) melioration theory.     

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.     

Enhancing Classroom Performance: A Review of Reinforcement Schedules

During the past decade the application of elementary principles of behavior have become a standard in the classroom teacher's repertoire of behavior change strategies. Unfortunately, the application of more advanced principles of behavior derived through basic behavioral research lies as an untapped resource for classroom teachers. Nowhere is this more apparent than in the use of systematic procedures to deliver reinforcers to enhance academic performance. In this paper we provide educators with information on the use of reinforcement schedules in academic settings. Various schedules of reinforcement are presented along with examples of their application in applied settings.     

EFFECTS OF REINFORCEMENT HISTORY AND INSTRUCTIONS ON THE PERSISTENCE OF STUDENT ENGAGEMENT

We examined the effects of three reinforcement histories on the persistence of task engagement by 2 fourth-grade students using a partially counterbalanced ABCDBCD design. In each condition, an experimenter made four student contacts during the first 2 min of each session (reinforcement baseline), followed by an 8-min extinction period. The reinforcement history that contained an instructional control component produced the greatest persistence in student engagement. The applied relevance of instructional control is discussed.     

BEHAVIORAL PERSISTENCE AND VARIABILITY DURING EXTINCTION OF SELF-INJURY MAINTAINED BY ESCAPE

The self-injurious escape behavior of a developmentally disabled adult was treated with extinction. Results of a reversal design showed substantial bursts of responding when extinction was introduced and reintroduced: self-injury remained at a variable and elevated rate for some time before stable, low rates were observed. Data on aggression, a nontarget behavior during both baseline and treatment, showed a pattern similar to that seen for self-injury during the extinction conditions.     

The paradox of preference for unreliable reinforcement: The role of context and conditioned reinforcement

We discuss Belke and Spetch's (1994) work on choice between reliable and unreliable reinforcement. The studies by Belke and Spetch extend a line of basic research demonstrating that under certain experimental conditions in a concurrent chains procedure, pigeons prefer an alternative that produces unreliable reinforcement. The authors describe the variables that influence preference for unreliable reinforcement, including the signaling and the duration of the reinforcement schedules, the context in which the signaling stimuli occur, and the effects of conditioned reinforcement. Hypothetical applied examples that address these variables are provided, and their influence on preference for unreliable reinforcement in humans is discussed. We conclude by suggesting a line of applied research to examine the relationship between these variables and a preference for unreliable reinforcement.