Matching, delay-reduction, and maximizing models for choice in concurrent-chains schedules.

Models of choice in concurrent-chains schedules are derived from melioration, generalized matching, and optimization. The resulting models are compared with those based on Fantino's (1969, 1981) delay-reduction hypothesis. It is found that all models involve the delay reduction factors (T - t2L) and (T - t2R), where T is the expected time to primary reinforcement and t2L, t2R are the durations of the terminal links. In particular, in the case of equal initial links, the model derived from melioration coincides with Fantino's original model for full (reliable) reinforcement and with the model proposed by Spetch and Dunn (1987) for percentage (unreliable) reinforcement. In the general case of unequal initial links, the model derived from melioration differs from the revised model advanced by Squires and Fantino (1971) only in the factors affecting the delay-reduction terms (T - t2L) and (T - t2R). The models of choice obtained by minimizing the expected time to reinforcement depend on the type of feedback functions used. In particular, if power feedback functions are used, the optimization model coincides with that obtained from melioration.     

Suboptimal choice in a percentage-reinforcement procedure: effects of signal condition and terminal-link length.

Pigeons' choice between reliable (100%) and unreliable (50%) reinforcement was studied using a concurrent-chains procedure. Initial links were fixed-ratio 1 schedules, and terminal links were equal fixed-time schedules. The duration of the terminal links was varied across conditions. The terminal link on the reliable side always ended in food; the terminal link on the unreliable side ended with food 50% of the time and otherwise with blackout. Different stimuli present during the 50% terminal links signaled food or blackout outcomes under signaled conditions but were uncorrelated with outcomes under unsignaled conditions. In signaled conditions, most pigeons displayed a nearly exclusive preference for the 100% alternative when terminal links were short (5 or 10 s), but with terminal links of 30 s or longer, preference for the 100% alternative was sharply reduced (often to below .5). In unsignaled conditions, most pigeons showed extreme preference for the 100% alternative with either short (5 s) or longer (30 s) terminal links. Thus, pigeons' choice between reliable and unreliable reinforcement is influenced by both the signal conditions on the unreliable alternative and the duration of the terminal-link delay. With a long delay and signaled outcomes, many pigeons display a suboptimal tendency to choose the unreliable side.     

MAINTENANCE OF THERAPEUTIC CHANGE BY MOMENTARY DRO

Differential reinforcement of other behavior (DRO) involves delivery of reinforcement at the end of an interval during which the target behavior has not occurred. Momentary DRO, however, is a procedure in which reinforcement is delivered if a response did not occur at the end of an interval. We examined the extent to which momentary DRO maintained suppression, following initial treatment with whole-interval DRO, of nine retarded students' maladaptive behavior. Results indicate that momentary DRO maintained response suppression comparable to that obtained by whole-interval DRO.     

MAINTENANCE FACTORS IN COERCIVE MOTHER-CHILD INTERACTIONS: THE COMPLIANCE AND PREDICTABILITY HYPOTHESES

Two stimulus control processes by which some parent-child dyads occasionally escalate their aversive exchanges into progressively more coercive interactions are described. The compliance hypothesis suggests that aversive actions have instructional properties for the dyad and that parent compliance with such child instructions maintains behavior chains of increasing aversiveness. The predictability hypothesis suggests that social interactions are most likely to function as aversive stimuli in the dyad when delivered in unpredictable fashion by either party and that responses instrumental in reducing dyadic unpredictability maintain aversive behavior chains. Expectations derived from both hypotheses are evaluated in a series of correlational analyses of mother-child interactions obtained in extended baseline observations of three dyads seeking psychological help for severe interactional problems. Results provide tentative support for the predictability hypothesis and suggest important avenues of further research.     

The economics of the law of effect.

A corollary of the law of effect predicts that the larger the reinforcement, the greater the rate of responding. However, an animal must eat more small portions than large portions to obtain the same daily intake, and one would predict, therefore, that when eating smaller portions an efficient animal would eat less (conserving time and energy) and/or respond faster (conserving time). The latter of these predictions was supported by the present experiments with free-feeding rats for which portion size (pellet size or duration of feeder presentation) and portion price within meals were varied. Response rate was a function of the unit price (responses/g) of food: Rats responded faster when portions were smaller or when prices were higher. Meal size and frequency were relatively unaffected by unit price, but were influenced by the price of meal initiation. The results are discussed in relation to the economic differences between traditional operant and free-feeding paradigms and to both traditional and more recent formulations of the law of effect.     

Response-reinforcer contingency and spatially defined operants: testing an invariance property of phi

A chamber containing 72 response keys defining the circumference of a circle 1 m in diameter was used to examine the relation between differentiation of response location and a measure of response-reinforcer contingency known as the phi coefficient. A different target key was specified in each successive phase, and response location was differentiated with respect to the target. Criterional and noncriterional responses (i.e., responses "near" and "far" from the target) were defined using targeted percentile schedules to control the overall probability of each response class. By manipulating criterional (and, hence, noncriterional) response probability and the reinforcement probabilities conditional on each, a mathematical invariance property peculiar to phi in contingency analysis was examined. Specifically, diagonally interchanging cell frequencies in a 2 x 2 table relating criterional/noncriterional responses to reinforcement/nonreinforcement leaves phi unchanged. Hence, the degree of response differentiation predicted by phi remains unchanged under the four permutations implied by the various diagonal interchanges. This predicted invariance was examined under values of phi equal to .33, .58, and .82. Increasing phi generally increased the stereotypy of response location. Three of the permutations generated almost interchangeable performance at different phi values. The remaining permutation, however, generated functions relating response concentration to phi with slopes shallower than those obtained under the other permutations. This resulted from relatively higher levels of differentiation, compared to the other permutations, at low phi values. These data strongly suggest boundary conditions on the ability of phi to reflect completely the local processes that are indexed by phi at a molar level.     

Theories of probabilistic reinforcement.

In three experiments, pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck at a red key led to a delay of 5 s and then a possible reinforcer. A peck at a green key led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In Experiments 1 and 2, the intertrial interval was varied across conditions, and these variations had no systematic effects on choice. In Experiment 3, the stimuli that followed a choice of the red key differed across conditions. In some conditions, a red houselight was presented for 5 s after each choice of the red key. In other conditions, the red houselight was present on reinforced trials but not on nonreinforced trials. Subjects exhibited greater preference for the red key in the latter case. The results were used to evaluate four different theories of probabilistic reinforcement. The results were most consistent with the view that the value or effectiveness of a probabilistic reinforcer is determined by the total time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. According to this view, probabilistic reinforcers are analogous to reinforcers that are delivered after variable delays.     

The development of adaptive choice in a self-control paradigm

Sixteen girls (ages 4, 6, 9, and 12) performed on concurrent-chain schedules of reinforcement. The initial links were variable-interval 10-s schedules, and the terminal links offered a long delay (20, 30, 40, or 50 s) followed by two tokens or a short delay (10 s) followed by one token. Tokens were used to buy toys and sweets. The effect of increasing the delay to the large reward differed significantly across age groups. Whereas 6- and 9-year-olds maintained a strong preference for the larger, more delayed reward under all delay conditions, half of the 4-year-olds and all the 12-year-olds showed increasing preference for the small reward as the delay to the large reward increased. The results suggest a two-stage account of the development of self-control. In the first stage, behavior is increasingly controlled by reward size, as children learn how to wait for delayed rewards, and in the second phase behavior is increasingly controlled by reward rate, as children learn when it is in fact profitable to wait.     

Using token reinforcement to increase walking for adults with intellectual disabilities

The purpose of this study was to evaluate the effectiveness of token reinforcement, using an ABAB reversal design, for increasing distance walked for adults with mild to moderate intellectual disabilities at an adult day‐training center. Five participants earned tokens for walking 50‐m laps and exchanged tokens for back‐up reinforcers that had been identified through preference assessments. Token reinforcement resulted in a substantial increase from baseline in laps walked for 4 participants.     

Contingencies promote delay tolerance

The effectiveness of functional communication training as treatment for problem behavior depends on the extent to which treatment can be extended to typical environments that include unavoidable and unpredictable reinforcement delays. Time‐based progressive delay (TBPD) often results in the loss of acquired communication responses and the resurgence of problem behavior, whereas contingency‐based progressive delay (CBPD) appears to be effective for increasing tolerance for delayed reinforcement. No direct comparison of TBPD and CBPD has, however, been conducted. We used single‐subject designs to compare the relative efficacy of TBPD and CBPD. Four individuals who engaged in problem behavior (e.g., aggression, vocal and motor disruptions, self‐injury) participated. Results were consistent across all participants, and showed lower rates of problem behavior and collateral responses during CBPD than during TBPD. The generality of CBPD treatment effects, including optimal rates of communication and compliance with demands, was demonstrated across a small but heterogeneous group of participants, reinforcement contingencies, and contexts.