Concurrent-schedule performance: Effects of relative and overall reinforcer rate

Six pigeons were trained to respond on two keys, each of which provided reinforcers on an arithmetic variable-interval schedule. These concurrent schedules ran nonindependently with a 2-s changeover delay. Six sets of conditions were conducted. Within each set of conditions the ratio of reinforcers available on the two alternatives was varied, but the arranged overall reinforcer rate remained constant. Each set of conditions used a different overall reinforcer rate, ranging from 0.22 reinforcers per minute to 10 reinforcers per minute. The generalized matching law fit the data from each set of conditions, but sensitivity to reinforcer frequency (a) decreased as the overall reinforcer rate decreased for both time allocation and response allocation based analyses of the data. Overall response rates did not vary with changes in relative reinforcer rate, but decreased with decreases in overall reinforcer rate. Changeover rates varied as a function of both relative and overall reinforcer rates. However, as explanations based on changeover rate seem unable to deal with the changes in generalized matching sensitivity, discrimination accounts of choice may offer a more promising interpretation.     

Effects of alternative reinforcement sources: A reevaluation

The effects of two alternative sources of food delivery on the key-peck responding of pigeons were examined. Pecking was maintained by a variable-interval 3-min schedule. In the presence of this schedule in different conditions, either a variable-time 3-min schedule delivering food independently of responding or an equivalent schedule that required a minimum 2-s pause between a key peck and food delivery (a differential-reinforcement-of-other-behavior schedule) was added. The differential-reinforcement-of-other-behavior schedule reduced response rates more than did the variable-time schedule in most instances. The delay between a key peck and the next reinforcer consistently was longer under the differential-reinforcement-of-other-behavior schedule than under the variable-time schedule. Response rates and median delay between responses and reinforcers were negatively correlated. These results contradict earlier conclusions about the behavioral effects of alternative reinforcement. They suggest that an interpretation in terms of response–reinforcer contiguity is consistent with the data.     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Probability and delay of reinforcement as factors in discrete-trial choice.

Pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck on the red key always produced a delay of 5 s and then a possible reinforcer. The probability of reinforcement for responding on this key varied from .05 to 1.0 in different conditions. A response on the green key produced a delay of adjustable duration and then a possible reinforcer, with the probability of reinforcement ranging from .25 to 1.0 in different conditions. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices. The purpose of these adjustments was to estimate an indifference point, or a delay that resulted in a subject's choosing each alternative about equally often. In conditions where the probability of reinforcement was five times higher on the green key, the green-key delay averaged about 12 s at the indifference point. In conditions where the probability of reinforcement was twice as high on the green key, the green-key delay at the indifference point was about 8 s with high probabilities and about 6 s with low probabilities. An analysis based on these results and those from studies on delay of reinforcement suggests that pigeons' choices are relatively insensitive to variations in the probability of reinforcement between .2 and 1.0, but quite sensitive to variations in probability between .2 and 0.     

Effects of ratio reinforcement schedules on discrimination performance by Japanese monkeys

In Experiment 1, Japanese monkeys were trained on three conditional position-discrimination problems with colors as the conditional cues. Within each session, each problem was presented for two blocks of ten reinforcements; correct responses were reinforced under continuous-reinforcement, fixed-ratio 5, and variable-ratio 5 schedules, each assigned to one of the three problems. The assignment of schedules to problems was rotated a total of three times (15 sessions per assignment) after 30 sessions of acquisition training. Accuracy of discrimination increased to a moderate level with fewer trials under CRF than under ratio schedules. In contrast, the two ratio schedules, fixed and variable, were more effective in maintaining accurate discrimination than was CRF. With further training, as asymptotes were reached, accuracy was less affected by the schedule differences. These results demonstrated an interaction between the effects of reinforcement schedules and the level of acquisition. In Experiment 2, ratio sizes were gradually increased to 30. Discrimination accuracy was maintained until the ratio reached 20; ratio 30 strained the performance. Under FR conditions, accuracy increased as correct choice responses cumulated after reinforcement.     

Temporal proximity and reinforcement sensitivity in multiple schedules

Distributions of reinforcers between two components of multiple variable-interval schedules were varied over a number of conditions. Sensitivity to reinforcement, measured by the exponent of the power function relating ratios of responses in the two components to ratios of reinforcers obtained in the components, did not differ between conditions with 15-s or 60-s component durations. The failure to demonstrate the “short-component effect,” where sensitivity is high for short components, was consistent with reanalysis of previous data. With 60-s components, sensitivity to reinforcement decreased systematically with time since component alternation, and was higher in the first 15-s subinterval of the 60-s component than for the component whose total duration was 15 s. Varying component duration and sampling behavior at different times since component transition may not be equivalent ways of examining the effects of average temporal distance between components.     

Choice between reliable and unreliable outcomes: mixed percentage-reinforcement in concurrent chains.

Pigeons' choices between alternatives that provided different percentages of reinforcement in mixed schedules were studied using the concurrent-chains procedure. In Experiment 1, the alternatives were terminal-link schedules that were equal in delay and magnitude of reinforcement, but that provided different percentages of reinforcement, with one schedule providing, reinforcement twice as reliably as the other. All pigeons preferred the more reliable schedule, and their level of preference was not systematically affected by variation in the absolute percentage values, or in the magnitude of reinforcement. In Experiment 2, preference for a schedule providing 100% reinforcement over one providing 33% reinforcement increased systematically with increases in the duration of the terminal links. In contrast, preference decreased systematically with increases in the duration of the initial links. Experiment 3 examined choice with equal percentages of reinforcement but unequal delays to reinforcement. Preference for the shorter delay to reinforcement was not systematically affected by variation in the absolute percentage of reinforcement. The overall pattern of results supported predictions based on an extension of the delay-reduction hypothesis to choice procedures involving mixed schedules of percentage reinforcement.     

Variable-interval schedules of timeout from avoidance

Rats were trained on concurrent schedules in which pressing one lever postponed shock and pressing the other occasionally produced a 2-min timeout during which the shock-postponement schedule was suspended and its correlated stimuli were removed. Throughout, the shock-postponement schedule maintained proficient levels of avoidance. Nevertheless, in Experiment 1 responding on the timeout lever was established rapidly, was maintained at stable levels on variable-interval schedules, was extinguished by withholding timeout, was reestablished when timeout was reintroduced, and was brought under discriminative control with a multiple variable-interval extinction schedule of timeout. These results are in contrast with Verhave's (1962) conclusion that timeout is an ineffective reinforcer when presented to rats on intermittent schedules. In Experiment 2 the consequence of responding on the timeout lever was altered so that the shock-postponement schedule remained in effect even though the stimulus conditions associated with timeout were produced for 2 min. Responding extinguished, indicating that suspension of the shock-postponement schedule, not stimulus change, was the source of reinforcement. By establishing the reinforcing efficacy of timeout with standard variable-interval schedules, these experiments illustrate a procedure for studying negative reinforcement in the same way as positive reinforcement.