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.     

Positive conditioned suppression: an explanation in terms of multiple and concurrent schedules

Rats performed under a baseline variable-interval schedule of food presentation. A response-independent food schedule was then superimposed on the baseline schedule for different periods of time across different conditions. The response-independent schedule operated for the whole session in some conditions, intermittently for sixty second periods in some, and intermittently for ten-second periods in others. Under these latter two sets of conditions, the response-independent food schedule was stimulus correlated and alternated with the baseline schedule according to a multiple schedule. Response-independent food presentations always suppressed responding. The degree of suppression tended to increase the longer the period of response-independent food. Control conditions, in which the superimposed schedule was response-dependent, rather than response-independent, did not produce response suppression. The results fit an analysis of positive conditioned suppression phenomena in the context of multiple and concurrent schedule effects.     

Response rate and changeover performance on concurrent variable-interval schedules

Six pigeons were exposed to variable-interval schedules arranged on one, two, three, and four response keys. The reinforcement rate was also varied across conditions. Numbers of responses, the time spent responding, the number of reinforcements, and the number of changeovers between keys were recorded. Response rates on each key were an increasing function of reinforcement rate on that key and a decreasing function of the reinforcement rate on other keys. Response and time-allocation ratios under-matched ratios of obtained reinforcements. Three sets of equations were developed to express changeover rate as a function of response rate, time allocation, and reinforcement rate respectively. These functions were then applied to a broad range of experiments in the literature in order to test their generality. Further expressions were developed to account for changeover rates reported in experiments where changeover delays were varied.     

Matching in concurrent variable-interval avoidance schedules

After pretraining with multiple variable-interval avoidance schedules, two rats were exposed to a series of concurrent variable-interval avoidance schedules. Responses on two levers cancelled delivery of electric shocks arranged according to two independent variable-interval schedules. The ratio of responses and time spent on the two levers approximately matched the ratio of shocks avoided on each. Matching to the number of shocks received was not obtained. Concurrent variable-interval avoidance can therefore be added to the group of positive and negative reinforcement schedules that can be expressed in the quantitative framework of the matching law.     

An evaluation of the value of choice with preschool children

The current study examined the reinforcing effects of choosing among alternatives in a four-part evaluation. In the first study, initial-link responses in a concurrent-chains arrangement resulted in access to terminal links in which the completion of an academic task resulted in (a) the choice of a reinforcer (choice), (b) the delivery of an identical reinforcer (no choice), or (c) no material reinforcer (control). Three patterns of responding emerged: persistent preference for choice (3 participants); initial preference for choice, which did not persist (2 participants); and preference for no choice (1 participant). Additional evaluations determined if preference for choice could be enhanced (Study 2) or established (Study 3) by including more stimuli from which to choose. Choice-link selections systematically increased for all participants when more items were available from which to choose. Study 4 identified the precise value of the opportunity to choose by progressively increasing the response requirement during the choice terminal links for 3 children and determining the point at which these children stopped selecting the choice link. All children continued to select the choice link even when the work required in the choice link was much greater than that arranged in the no-choice link.     

The effectiveness of and preschoolers' preferences for variations of multiple-schedule arrangements

Multiple schedules of reinforcement have been used to teach children to recruit attention only when it is available, thereby minimizing disruptive requesting during instructional activities. This procedure involves alternating periods of continuous reinforcement (CRF) with periods of extinction and correlating each period with a distinct and continuous discriminative stimulus. The present study evaluated the effectiveness of and children's preferences for multiple schedules in which (a) two different stimuli, one correlated with reinforcement (S+) and another correlated with extinction (S-), were presented; (b) only an S+ was presented (i.e., no stimulus was correlated with extinction), and (c) neither an S+ nor an S- was presented (i.e., a mixed schedule). S+/S- and S+ arrangements were similarly effective for 7 children, but 3 preferred the S+/S- condition and 4 preferred the S+ condition. Correlational analyses suggested that children who responded more effectively given the S- (discrimination indexes were relatively high) preferred the S+/S- condition, whereas children who responded less effectively given the S- preferred the S+ condition. The implications of these findings for arranging multiple schedules for social responses are discussed.     

Rapid acquisition in concurrent chains: evidence for a decision model

Pigeons' choice in concurrent chains can adapt to rapidly changing contingencies. Grace, Bragason, and McLean (2003) found that relative initial-link response rate was sensitive to the immediacy ratio in the current session when one of the terminal-link fixed-interval schedules was changed daily according to a pseudorandom binary sequence (e.g., Schofield & Davison, 1997). The present experiment tested whether the degree of variation in delays across sessions had any effect on acquisition rate in Grace et al.'s (2003) rapid-acquisition procedure. In one condition ("minimal variation"), the left terminal link was always fixed-interval 8 s and the right terminal link was either fixed-interval 4 s or fixed-interval 16 s. In the other condition ("maximal variation"), a unique pair of fixed-interval values was used in each session. Responding was sensitive to the current-session immediacy ratio in both conditions, but across subjects there was no systematic difference in sensitivity. These results challenge the view that initial-link responding in the rapid-acquisition procedure is determined by changes in the learned value of the terminal-link stimuli, and suggests instead that a process resembling categorical discrimination may control performance. A decision model based on the assumption that delays are categorized as short or long relative to the history of delays provided a good account of the data and shows promise in being able to explain other choice phenomena.     

Evaluation of pharmacological treatment of impulsivity in children with attention deficit hyperactivity disorder

We used an assessment that involved competing reinforcer dimensions in a concurrent-schedules arrangement to examine the effects of stimulant medication on impulsivity (i.e., sensitivity of choices to reinforcer immediacy relative to rate, quality, and effort) with 4 students with attention deficit hyperactivity disorder. The assessments were administered in the context of a double-blind, placebo-controlled, counterbalanced reversal design. Reinforcer immediacy was the most influential dimension for 3 of the students and the second most influential dimension for 1 of the students across placebo and medication conditions; medication did not affect these sensitivities.     

Behavioral assessment of impulsivity: a comparison of children with and without attention deficit hyperactivity disorder

We conducted a brief computer-based assessment involving choices of concurrently presented arithmetic problems associated with competing reinforcer dimensions to assess impulsivity (choices controlled primarily by reinforcer immediacy) as well as the relative influence of other dimensions (reinforcer rate, quality, and response effort), with 58 children. Results were compared for children with attention deficit hyperactivity disorder (ADHD) who were and were not receiving medication, and with typically developing children without ADHD. Within-subject and between-groups analyses of the ordinal influence of each of the reinforcer dimensions were conducted using both time- and response-allocation measures. In general, the choices of children with ADHD were most influenced by reinforcer immediacy and quality and least by rate and effort, suggesting impulsivity. The choices of children in the non-ADHD group were most influenced by reinforcer quality, and the influence of immediacy relative to the other dimensions was not statistically significant. Results are discussed with respect to the implications for assessment and treatment of ADHD.     

A TEST OF THE FORMAL AND MODERN THEORIES OF MATCHING

Pigeons' choosing between fixed-interval and random-interval schedules of reinforcement was investigated in three experiments using a discrete-trial procedure. In all three experiments, the random-interval schedule was generated by sampling a probability distribution at an interval (and in multiples of the interval) equal to that of the fixed-interval schedule. Thus the programmed delays to reinforcement on the random alternative were never shorter and were often longer than the fixed interval. Despite this feature, the fixed schedule was not strongly preferred. Increases in the probability used to generate the random interval resulted in decreased preferences for the fixed schedule. In addition, the number of consecutive choices on the preferred alternative varied directly with preference, whereas the consecutive number of choices on the nonpreferred alternative was fairly constant. The probability of choosing the random alternative was unaffected by the immediately prior interval encountered on that schedule, even when it was very long relative to the average value. The results loosely support conceptions of a "preference for variability" from foraging theory and the "utility of behavioral variability" from human decision-making literatures.