A comparison of presession and within-session reinforcement choice.

Single- and concurrent-operants procedures were used to evaluate the effects of two reinforcement conditions on the free-operant responding of 3 individuals with developmental disabilities and 1 with attention deficit disorder. In the presession choice condition, prior to each session the participant chose one item from an array of three different highly preferred stimuli. This item was delivered by the experimenter on each reinforcer delivery during that session. In the within-session choice condition, each reinforcer delivery consisted of placing an array of three different highly preferred stimuli in front of the participant, who was allowed to select one. Only one of the two reinforcement conditions was in effect for any particular session in single-operant phases. Buttons associated with each reinforcement condition were present, and the participant could allocate responses to one or the other in concurrent-operants phases. Data showed substantially more responding to the button associated with within-session choice than presession choice during concurrent-operants phases. This effect was not as apparent during single-operant phases, suggesting that a concurrent-operants procedure provided the more sensitive evaluation of within-session and presession reinforcer choice effects.     

A simple multivariate probabilistic model for preferential and triadic choices

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, wheren is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.     

Some implications of a relational principle of reinforcement

A formal statement of a relational principle of reinforcement is developed that makes contact with analyses of choice, interresponse-time distributions, and stimulus control. Some implications for current theoretical and empirical work in the various areas are examined.     

Self-control: teaching tolerance for delay in impulsive children.

We investigated a procedure to increase the selection of larger, more delayed reinforcers (i.e., more advantageous in the long run) over smaller immediate reinforcers, in an effort to increase a key aspect of self-control in children. Six preschoolers, including one comparison subject, identified by their teachers as impulsive, were preassessed and found consistently to select smaller immediate reinforcers over larger, more delayed ones. The teaching procedure consisted of gradually increasing the durations of the delay interval over many sessions. The follow-up assessments showed that 5 of these children increased the proportion of their choices of the delayed reinforcers. Before training, indifference points ranged from 1.7 to 51.7 s; following treatment, points rose to a range of 37.5 to at least 90 s, with 3 children preferring the larger reinforcer at all delay intervals tested. The results demonstrated the feasibility of teaching young children to make choices more advantageous to them in the long run.     

Choice: Effects of changeover schedules on concurrent performance

The components of concurrent schedules were separated temporally by placing interval schedules on the changeover key. The rates of responding on both the main and changeover keys were examined as a function of the reinforcement rates. In the first experiment, the sensitivity of main-key performance to changing reinforcement rates was inversely related to the temporal separation of components, and changeover performance was monotonically related to the ratio of the reinforcement rates. In the second experiment, when the ratio of the reinforcement rates was scheduled to remain constant while the frequency of reinforcement was varied, changeover performance did not remain constant. A “sampling” interpretation of changeover responding was proposed and subsequently tested in a third experiment where extinction was always scheduled in one component and the frequency of reinforcement was varied in the second component. It was concluded that changeover performance can be interpreted using molar measures of reinforcement and that animals sample activities available to them at rates which are controlled by relative reinforcement rates.     

Joint-space analysis of “pick-any” data: Analysis of choices from an unconstrained set of alternatives

Social and naturally occurring choice phenomena are often of the pick-any type in which the number of choices made by a subject as well as the set of alternatives from which they are chosen is unconstrained. These data present a special analytical problem because the meaning of non-choice among pick-any choice data is always ambiguous: A non-chosen alternative may be either unacceptable, or acceptable but not considered, or acceptable and considered but not chosen. A model and scaling method for these data are introduced, allowing for this ambiguity of non-choice. Subjects are represented as points whose coordinates are proportional to the centroids of the points representing their choices. Alternatives are represented at points whose coordinates are proportional to the centroids of the points representing subjects who have chosen them. This centroid scaling technique estimates multidimensional joint spaces from the pick-any data.I am indebted to John Baird, Clyde Coombs, David Eames, John Hunter, Michael J. Levine, Elliot Noma, Robert Z. Norman, William S. Roy, Joseph Schwartz, Daniel Velleman, the editor, and anonymous reviewers for ideas and suggestions that have been incorporated into this work. Conferences organized by Hans J. Hummel for the Deutsche Forschungsgemeinschaft (1977) and by Samuel Leinhardt for the National Science Foundation (1975) were instrumental in the development of this work.     

Uncertainty reduction, conditioned reinforcement, and observing

In a concurrent-chains procedure, pigeons chose between equivalent mixed and multiple fixed-interval schedules of reinforcement. In the first experiment, preference for the multiple schedule was higher when the probability of the shorter fixed interval was less than .50 than for complementary points, an outcome consistent with the delay-reduction hypothesis of conditioned reinforcement and observing, but inconsistent with the uncertainty-reduction hypothesis which requires symmetrical preferences with a maximum when the two intervals are equiprobable. A second experiment assessed preference for equivalent mixed and multiple schedules when each choice outcome resulted in two reinforcements, one on the longer and one on the shorter fixed interval. The order of the two fixed intervals was determined probabilistically. Pigeons again preferred multiple to mixed schedules, although multiple-schedule preference did not vary systematically with the likelihood of the shorter fixed interval occurring first. The results from these choice procedures are consistent with those from the observing-response literature in suggesting that the strength of a stimulus cannot be well described as a function of the degree of uncertainty reduction the stimulus provides about reinforcement.     

Economic concepts for the analysis of behavior

A review of the relationship between schedule of reinforcement, response rate, and choice suggests that certain unifying concepts from economics can contribute to a more complete science of behavior. Four points are made: 1) a behavioral experiment is an economic system and its characteristics—open or closed—can strongly determine the results; 2) reinforcers can be distinguished by a functional property called elasticity; 3) reinforcers may interact as complements as well as substitutes; 4) no simple choice rule, such as strict matching, can account for all choice behavior.     

THE RELATION BETWEEN CHOOSING AND WORKING PREVOCATIONAL TASKS IN TWO SEVERELY RETARDED YOUNG ADULTS

This study investigated the relation between prevocational preference, as measured by the client's selection of a task object, and the work that followed that choice. After selecting a task object, the clients worked a task previously assessed to be more or less preferred than the one indicated by the object. The results indicated that when the selection represented a task that was less preferred than the one actually worked, choices for that object increased on subsequent trials. Conversely, when the selection represented a task that was more preferred than the task subject actually worked, choices for the object decreased on subsequent trials. The work that followed object choices reinforced or punished subsequent selections. These findings indicated that the clients' object choices were valid indicators of their preference for working different tasks. They were also consistent with Premack's principle that one class of responses may reinforce or punish a different class of responses for the same individual.     

Estimation of covariance structure models with parameters subject to functional restraints

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.The author is indebted to several anonymous reviewers for creative suggestions for improvement of this paper. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.