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James E Mazur

Publications and source records attributed to James E Mazur.

8 recordsLinked to original sources

Mathematical models and the experimental analysis of behavior.

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists.

Humans↗

Choice between single and multiple reinforcers in concurrent-chains schedules.

Pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links. One terminal link delivered a single reinforcer after a fixed delay, and the other terminal link delivered either three or five reinforcers, each preceded by a fixed delay. Some conditions included a postreinforcer delay after the single reinforcer to equate the total durations of the two terminal links, but other conditions did not include such a postreinforcer delay. With short initial links, preference for the single-reinforcer alternative decreased when a postreinforcer delay was present, but with long initial links, the postreinforcer delays had no significant effect on preference. In conditions with a postreinforcer delay, preference for the single-reinforcer alternative frequently switched from above 50% to below 50% as the initial links were lengthened. This pattern of results was consistent with delay-reduction theory (Squires & Fantino, 1971), but not with the contextual-choice model (Grace, 1994) or the hyperbolic value-added model (Mazur, 2001) as they have usually been applied. However, the hyperbolic value-added model could account for the results if its calculations were expanded to include reinforcers delivered in later terminal links. The implications of these findings for models of concurrent-chains performance are discussed.

Animals↗

Heuristics and general principles of learning.

This research on decision-making heuristics is similar to research on animal learning in at least two ways. First, optimality modeling has not proven to be very useful for either research area. Second, both of these research areas seek to find general principles (or heuristics) that are applicable to different species in different settings. However, the basic principles of classical and operant conditioning seem to be more uniform across species and situations, whereas decision-making heuristics can vary for different species and different situations, even for tasks with very similar characteristics.

Algorithms↗

Exploring a concurrent-chains paradox: decreasing preference as an initial link is shortened.

Experiments with pigeons and rats on concurrent-chains schedules examined a paradoxical effect reported by R. A. Preston and E. Fantino (1991). One schedule in the concurrent chain had a variable-interval (VI) 60-s initial link, and its terminal link was a 10-s delay to food. The other schedule had an initial link that ranged from VI 60 s to VI 2 s, and its terminal link was a 20-s delay to food. The paradoxical effect--a decrease in preference for the 20-s delay as its initial link was shortened--was found in some conditions but not in others. An analysis of response-reinforcer delays suggested that the paradoxical effect occurred in conditions in which responding on the short VI schedule almost always led to the 20-s delay, eliminating the possibility of switching to the alternative with the shorter delay.

Animals↗

Effects of reinforcer probability, delay, and response requirements on the choices of rats and pigeons: possible species differences.

In Experiment 1 with rats, a left lever press led to a 5-s delay and then a possible reinforcer. A right lever press led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials to estimate an indifference point, or a delay at which the two alternatives were chosen about equally often. Indifference points increased as the probability of reinforcement for the left lever decreased. In some conditions with a 20% chance of food, a light above the left lever was lit during the 5-s delay on all trials, but in other conditions, the light was only lit on those trials that ended with food. Unlike previous results with pigeons, the presence or absence of the delay light on no-food trials had no effect on the rats' indifference points. In other conditions, the rats showed less preference for the 20% alternative when the time between trials was longer. In Experiment 2 with rats, fixed-interval schedules were used instead of simple delays, and the presence or absence of the fixed-interval requirement on no-food trials had no effect on the indifference points. In Experiment 3 with rats and Experiment 4 with pigeons, the animals chose between a fixed-ratio 8 schedule that led to food on 33% of the trials and an adjusting-ratio schedule with food on 100% of the trials. Surprisingly, the rats showed less preference for the 33% alternative in conditions in which the ratio requirement was omitted on no-food trials. For the pigeons, the presence or absence of the ratio requirement on no-food trials had little effect. The results suggest that there may be differences between rats and pigeons in how they respond in choice situations involving delayed and probabilistic reinforcers.

Animals↗

Varying initial-link and terminal-link durations in concurrent-chains schedules: a comparison of three models.

In Experiment 1, pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links and fixed delays to food as terminal links. One terminal-link delay was always three times as long as the other. As terminal-link delays increased, response percentages on the key with the shorter terminal link increased according to a curvilinear function. This result supported the predictions of the hyperbolic value-added model and the contextual-choice theory but not delay-reduction theory. In Experiment 2, the terminal links were always delays of 2s and 12s, followed by food, and the durations of the initial links varied across conditions. As initial-link durations increased, pigeons' response percentages on the key with the shorter terminal link decreased, but toward an asymptote greater than 50%, indicating a continued preference for the shorter terminal link with very long initial links. This result was more consistent with the predictions of the hyperbolic-value added model than with those of the contextual-choice model or of delay-reduction theory.

Animals↗

Evidence against a constant-difference effect in concurrent-chains schedules.

Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect. Both experiments used equal variable-interval schedules as initial links. The terminal links were fixed delays to reinforcement in Experiment 1 and variable delays to reinforcement in Experiment 2. The durations of the terminal links were varied across conditions, but the difference between pairs of terminal links was always 10 s. In both experiments, preference for the shorter terminal link became less extreme as terminal-link durations increased, so a constant-difference effect was not found. It is argued, however, that this choice situation does not provide clear evidence for or against delay-reduction theory versus other theories of choice.

Animals↗

Concurrent-chain performance in transition: effects of terminal-link duration and individual reinforcers.

Pigeons responded on concurrent-chain schedules with variable-interval initial links and equal delays as terminal links. The terminal-link delays were 1 sec in some conditions and 20 sec in other conditions. The percentages of reinforcers delivered for responses on the left key were 10%, 30%, 70%, or 90%, and this percentage was switched every five to nine sessions. The rate of change in the pigeons' response percentages after a switch was the same whether the terminal-link delays were 1 sec or 20 sec. Analysis of the effects of individual reinforcers showed that after a response on one key had been reinforced, response percentages on that key were higher for at least the next 100 responses. Small effects of individual reinforcers were evident after eight or nine additional reinforcers had been delivered. The effects of individual reinforcers were about equally large during times of transition and during periods in which overall response percentages were relatively stable.

Animals↗