Performances on ratio and interval schedules of reinforcement: Data and theory

Two differences between ratio and interval performance are well known: (a) Higher rates occur on ratio schedules, and (b) ratio schedules are unable to maintain responding at low rates of reinforcement (ratio “strain”). A third phenomenon, a downturn in response rate at the highest rates of reinforcement, is well documented for ratio schedules and is predicted for interval schedules. Pigeons were exposed to multiple variable-ratio variable-interval schedules in which the intervals generated in the variable-ratio component were programmed in the variable-interval component, thereby “yoking” or approximately matching reinforcement in the two components. The full range of ratio performances was studied, from strained to continuous reinforcement. In addition to the expected phenomena, a new phenomenon was observed: an upturn in variable-interval response rate in the midrange of rates of reinforcement that brought response rates on the two schedules to equality before the downturn at the highest rates of reinforcement. When the average response rate was corrected by eliminating pausing after reinforcement, the downturn in response rate vanished, leaving a strictly monotonic performance curve. This apparent functional independence of the postreinforcement pause and the qualitative shift in response implied by the upturn in variable-interval response rate suggest that theoretical accounts will require thinking of behavior as partitioned among at least three categories, and probably four: postreinforcement activity, other unprogrammed activity, ratio-typical operant behavior, and interval-typical operant behavior.     

The simultaneous maximization of congruence for two or more matrices under orthogonal rotation

While a rotation procedure currently exists to maximize simultaneously Tucker's coefficient of congruence between corresponding factors of two factor matrices under orthogonal rotation of one factor matrix, only approximate solutions are known for the generalized case where two or more matrices are rotated. A generalization and modification of the existing rotation procedure to simultaneously maximize the congruence is described. An example using four data matrices, comparing the generalized congruence maximization procedure with alternative rotation procedures, is presented. The results show a marked improvement of the obtained congruence using the generalized congruence maximization procedure compared to other procedures, without a significant loss of success with respect to the least squares criterion. A computer program written by the author to perform the rotations is briefly discussed.     

Transfer of relational stimulus control in conditional discriminations.

Four adults were trained, using instructions and a matching-to-sample procedure, to select Stimulus B1 in the presence of Stimulus A1, B2 in the presence of A2, and B3 in the presence of A3 (the AB relations). Analogous PQ relations were trained. Afterwards, one stimulus in Set A and another stimulus in Set B appeared together as a sample, and novel Stimuli X1 and X2 were the comparisons. Responses to X1 were reinforced if the two stimuli in the sample had been related in the previous training (e.g., A1 and B1), and responses to X2 were reinforced if the two samples had not been related (e.g., A1 and B2). These were the ABX relations. In a test in which a stimulus of Set P and another of Set Q were the samples and X1 and X2 were the comparisons, 2 subjects selected X1 when the samples were P1 and Q1, P2 and Q2, and P3 and Q3, and selected X2 in the presence of the other six sample combinations (P1Q2, P1Q3, P2Q1, P2Q3, P3Q1, and P3Q2). Another subject showed the same responding after additional training. In the second experiment, 3 adults and an 11-year-old child were trained on AB, PQ, and ABX relations, and they showed the symmetrical relations BA and QP upon testing. Then all 4 of these subjects responded accurately to the PQX test. Results of Experiments 1 and 2 showed novel, consistent comparison selection based on the previously established relation between the two stimuli in the sample. In a third experiment, 3 of the subjects who had shown PQX relations were trained on EFX relations, with pairs of E and F stimuli as samples and X stimuli as comparisons. When the EF relations were tested, all 3 subjects consistently selected F1 in the presence of E1, F2 in the presence of E2, and F3 in the presence of E3 from the first trial. The results of Experiment 3 showed novel stimulus relations after training with a more complex conditional discrimination format.     

Use of an ambiguous-sample procedure to establish a cue to forget in pigeons

Pigeons were trained on a variation of the matching-to-sample task in which on double-sample trials two samples, one associated with each of the comparison stimuli, were presented successively. Responding to the comparison associated with the first sample was reinforced on half the double-sample trials, and responding to the comparison associated with the second sample was reinforced on the remaining half. One of two postsample stimuli was presented following the termination of each colored sample. A vertical line was presented after a correct or target sample, and a horizontal line was presented after an incorrect or interfering sample. With extended training, each bird demonstrated above-chance accuracy on double-sample trials, providing prima facie evidence that one or both of the postsample stimuli exerted control over matching behavior. Experiment 2 provided evidence that the horizontal line functioned as a cue to forget the code activated by the preceding sample stimulus. It was concluded that a condition sufficient to establish a postsample stimulus as a cue to forget is that the postsample immediately follow presentation of a sample that, if it were to control test responding, would lead to nonreinforcement.     

An equation for behavioral contrast.

Pigeons were trained on a three-component multiple schedule in which the rates of reinforcement in the various components were systematically varied. Response rates were described by an equation that posits that the response-strengthening effects of reinforcement are inversely related to the context of reinforcement in which it occurs, and that the context is calculated as the weighted average of the various sources of reinforcement in the situation. The quality of fits was comparable to that found with previous quantitative analyses of concurrent schedules, especially for relative response rates, with over 90% of the variance accounted for in every case. As with previous research, reinforcements in the component that was to follow received greater weights in determining the context than did reinforcements in the preceding component.     

The generalized matching law as a description of multiple-schedule responding

The literature was examined to determine how well the generalized matching law (Baum, 1974) describes multiple-schedule responding. In general, it describes the data well, accounting for a median of 91% of the variance. The median size of the undermatching parameter was 0.46; the median bias parameter was 1.00. The size of the undermatching parameter, and the proportion of the variance accounted for by the equation, varied inversely with the number of schedules conducted, with the number of sessions conducted per schedule, and with the time within a component. The undermatching parameter also varied with the operanda used to produce reinforcers and with the reinforcer used. The undermatching parameter did not vary consistently with component duration or with several other variables. Bias was greater when fewer rather than more schedules were conducted, when two rather than one operanda were used, and when White Carneaux rather than homing pigeons served as subjects. These results imply that the generalized matching law may describe both concurrent and multiple-schedule responding, but that the same variables do not always influence the bias and undermatching parameters in the same way for the two types of schedules.     

Verbal self-reports of delayed matching to sample by humans

Undergraduates participated in two experiments to develop methods for the experimental analysis of self-reports about behavior. The target behavior was the choice response in a delayed-matching-to-sample task in which monetary reinforcement was contingent upon both speed and accuracy of the choice. In Experiment 1, the temporal portion of the contingency was manipulated within each session, and the presence and absence of feedback about reinforcement was manipulated across sessions. As the time limits became stricter, target response speeds increased, but accuracy and reinforcement rates decreased. When feedback was withheld, further reductions in speed and reinforcement occurred, but only at the strictest time limit. Thus, the procedures were successful in producing systematic variation in the speed, accuracy, and reinforcement of the target behavior. Experiment 2 was designed to assess the influence of these characteristics on self-reports. In self-report conditions, each target response was followed by a computer-generated query: “Did you earn points?” The subject reported by pressing “Yes” or “No” buttons, with the sole consequence of advancing the session. In some cases, feedback about reinforcement of the target response followed the reports; in other cases it was withheld. Self-reports were less accurate when the target responses occurred under greater time pressure. When feedback was withheld, the speed of the target response influenced reports, in that the probability of a “Yes” report increased directly with the speed of accurate target responses. In addition, imposing the self-report procedure disrupted target performance by reducing response speeds at the strictest time limit. These results allow investigation of issues in both behavioral and cognitive psychology. More important, the overall order in the data suggests promise for the experimental analysis of self-reports by human subjects.     

Behavioral stereotypy and the generalized matching equation

The development of behavioral stereotypy is a common result of exposure to both response-dependent and response-independent reinforcement procedures. The generalized matching equation and two dynamic versions of that equation, which take into account the time differential between reinforcements and their effect on behavior, predict this outcome of many procedures involving reinforcement. Following from the assumption that distinct response topographies, distinct response sequences, or orientations to distinct stimuli can be treated in the equations as distinct classes of behavior, the equations predict that-at least for matching and undermatching-the behavior class that is most biased relative to other behavior classes of the same type will tend to predominate to the exclusion or near exclusion of those behavior classes.     

Quantitative studies of reinforcement relativity

Three experiments examined an application of the matching law to the area of reinforcement relativity. In Experiment I, rats ran in a wheel and drank a sucrose solution. Equations derived from the matching law made fairly accurate predictions of the amounts of time spent running and drinking when licks and wheel revolutions had to occur in fixed proportions. In Experiment II, rats were required to spend four times as much time drinking as running, but the absolute durations of the cycles of drinking and running were varied. Except for the shortest cycle size tested, durations were close to those predicted. Experiments III investigated a tendency for obtained durations of running and drinking to be slightly longer than predicted. Simply shortening the periods when these behaviors were available increased their values. It was concluded that the matching law equations provided reasonably accurate predictions in some experiments, but changes in motivation set the limits of such accuracy.