The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.     

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.     

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.     

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.     

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.     

The dynamic programming matching analysis of handwriting movement in delayed vision

Abstract: Dynamic programming matching analysis of the velocity profile of handwriting was used to examine temporally invariant characteristics of handwriting. This was done by comparing the performance of 12 subjects in writing five words under various delayed visual feedback conditions. The rate of temporally invariant handwriting decreased when delay of visual feedback was introduced. That is, the mean number of fluctuations or hesitations increased as a function of the delay time. This indicates that subjects wrote words by segmenting their movements into submovements. The relative positions of the boundaries of submovements was shown using dynamic programming matching analysis by the distribution of fluctuations along a time axis of templates. The results suggest the development of a segmented "move-and-wait" strategy under conditions of delayed vision. It was shown that in the "move" phase, subjects performed appropriate submovements as smoothly as in the no delay condition and waited during the delay until visual feedback caught up. The increased errors were due to inadequate segmentation of movements.     

Concurrent-schedule performance in dairy cows: persistent undermatching.

Performance of dairy cows responding under concurrent variable-interval variable-interval schedules of food delivery was examined, with results analyzed in terms of the generalized matching equation. In Experiment 1, bias measures indicated that crushed barley was preferred over meatmeal when these foods were available under the alternative schedules. For whole-session data, substantial undermatching of response and time-allocation ratios to obtained reinforcement ratios was evident. Postreinforcement pause time ratios approximately matched obtained reinforcement rates. Subtracting these times from total time-allocation values yielded net time-allocation ratios that undermatched obtained reinforcement ratios to a greater degree than did whole-session time-allocation ratios. In Experiment 2, substantial undermatching was evident when the same foods (hay for 2 cows, crushed barley for 2 others) were available under the alternative schedules. Food-related activities and other defined behavior not related to food were quantified by direct observation, and were found to occupy a substantial proportion (roughly 40% to 80%) of experimental sessions. Subtracting the time spent in these activities from the time allocated to each component schedule did not reduce the degree of undermatching obtained. Across all conditions in both experiments, slopes of regression lines relating behavioral outputs to environmental inputs characteristically were below 0.6, which agrees with prior findings and suggests that, contrary to suggestions in the literature, undermatching in dairy cows is not the result of using different foods under alternative schedules or differential pausing under those schedules.     

Relative sensitivity to reinforcer amount and delay in a self-control choice situation.

Rats were exposed to concurrent-chains schedules in which a single variable-interval schedule arranged entry into one of two terminal-link delay periods (fixed-interval schedules). The shorter delay ended with the delivery of a single food pellet; the longer day ended with a larger number of food pellets (two under some conditions and six under others). In Experiment 1, the terminal-link delays were selected so that under all conditions the ratio of delays would exactly equal the ratio of the number of pellets. But the absolute duration of the delays differed across conditions. In one condition, for example, rats chose between one pellet delayed 5 s and six pellets delayed 30 s; in another condition rats chose between one pellet delayed 10 s and six pellets delayed 60 s. The generalized matching law predicts indifference between the two alternatives, assuming that the sensitivity parameters for amount and delay of reinforcement are equal. The rats' choices were, in fact, close to indifference except when the choice was between one pellet delayed 5 s and six pellets delayed 30 s. That deviation from indifference suggests that the sensitivities to amount and delay differ from each other depending on the durations of the delays. In Experiment 2, rats chose between one pellet following a 5-s delay and six pellets following a delay that was systematically increased over sessions to find a point of indifference. Indifference was achieved when the delay to the six pellets was approximately 55 s. These results are consistent with the possibility that the relative sensitivities to amount and delay differ as a function of the delays.     

A monotonically convergent algorithm for orthogonal congruence rotation

Brokken has proposed a method for orthogonal rotation of one matrix such that its columns have a maximal sum of congruences with the columns of a target matrix. This method employs an algorithm for which convergence from every starting point is not guaranteed. In the present paper, an iterative majorization algorithm is proposed which is guaranteed to converge from every starting point. Specifically, it is proven that the function value converges monotonically, and that the difference between subsequent iterates converges to zero. In addition to the better convergence properties, another advantage of the present algorithm over Brokken's one is that it is easier to program. The algorithms are compared on 80 simulated data sets, and it turned out that the new algorithm performed well in all cases, whereas Brokken's algorithm failed in almost half the cases. The derivation of the algorithm is given in full detail because it involves a series of inequalities that can be of use to derive similar algorithms in different contexts.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to Willem J. Heiser and Jos M. F. ten Berge for useful comments on an earlier version of this paper.     

Response bias and the discrimination of stimulus duration

Pigeons discriminated stimulus duration in a psychophysical choice situation. Following presentation of any duration from a set of short duration (11 to 15 sec), responses on a red key were reinforced intermittently. Following presentation of any duration from a set of long durations (16 to 22 sec), responses on a green key were reinforced intermittently. Relative reinforcement rates were manipulated for choice responses across conditions. As relative reinforcement rates were varied, psychometric functions showed shifts in green-key responses at all durations. A signal-detection analysis showed that sensitivity remained roughly constant across conditions while response bias changed as a function of changes in relative reinforcement rate. Relative error rates tended to match relative reinforcement rates.