The Generalized Matching Law as a Description of Multiple‐schedule Responding

McSweeney, Frances K.; Farmer, Valeri A.; Dougan, James D.; Whipple, Jennifer

doi:10.1901/jeab.1986.45-83

Cited by 32 publications

(35 citation statements)

References 45 publications

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“…The exponent m of the power function given by Equation 1, relating ratios of responses (P1, P2) to the ratios of reinforcers obtained in the two components (R 1, R2) was used as a higher order measure of discrimination (White, 1985;White, Pipe, & McLean, 1983;White et al, 1984). The power function has proved useful in describing performance in successive discriminations because the sensitivity of response rates to changes in reinforcer ratios (m) can be determined separately from any constant bias (q) that may exist between the components (Lander & Irwin, 1968;McSweeney, Farmer, Dougan, & Whipple, 1986;Williams, 1983). The power function is P1/P2 = q(Rl/R2)m.…”

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Delayed and Current Stimulus Control in Successive Discriminations

1990

J Exper Analysis Behavior

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In a successive discrimination in which successively alternating red and green hues signaled component variable-interval schedules, sensitivity of the ratio of responses in the two components to variation in the component reinforcer ratio decreased systematically during the course of the component. This decrease in stimulus control or discrimination over the course of the component was shown to be the result of delayed control of responding during the component by the stimulus transition between components. When the red-green stimulus transition was altered by interpolating a white stimulus at the end of each 60-s component, discrimination at the beginning of the component (measured by the power-function exponent for sensitivity to reinforcement) was reduced. Conditions with the white stimulus inserted in other quarters of the component indicated that the current discriminative stimulus exerts control over responding throughout the component, whereas during about the first half of the component, response differentials are influenced by the transition between discriminative stimuli.

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Delayed and Current Stimulus Control in Successive Discriminations

1990

J Exper Analysis Behavior

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“…Early evidence (Shimp & Wheatley, 1971;Todorov, 1972) showed larger interactions with shorter components. Fits of Equation 1 by McSweeney, Farmer, Dougan, and Whipple (1986) to the subjects of Shimp and Wheatley (1971) yielded median values of a that ranged from .86 to .52 as component duration varied from 2 to 180 sec. Thus, a strong effect of component duration occurred, and values ofa with the shortest components were comparable to those typically obtained with concurrent schedules.…”

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“…Such effects are also important because they impinge strongly on the issue of how performance on different types of schedules should be conceptualized. As has been noted by McSweeney et al (1986), a concurrent schedule might be regarded as a multiple schedule with very short components. Accordingly, the fact that concurrent schedules typically produce larger interactions than multiple schedules do would be ascribed to the effects of component duration, with the implication that robust effects of component duration should be obtained when they are studied in multiple schedules directly.…”

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Component duration effects in multiple schedules

Williams

1989

Animal Learning & Behavior

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Previous research has produced conflicting results regarding the effects of component duration on interactions in multiple schedules. In Experiment 1, potential sources of this conflict were evaluated. Both the effects of absolute reinforcement rate and carry-over effects (hysteresis) from a preceding condition were isolated. When lO-sec components were used, the sensitivity of relative response rate to relative reinforcement rate was affected very little by hysteresis effects and absolute reinforcement rate, but it was systematically reduced as a function of the number of prior conditions. Sensitivity to relative reinforcement rate was also substantially higher with the 10-sec components than with 2-min components. In Experiment 2, this effect of component duration was decomposed into two separate effects. Contrast effects during presentation of a target component with a constant reinforcement rate were greater the shorter the target component was itself; but they were smaller the shorter the alternative component in which reinforcement rate was varied. The latter effect was smaller and more unreliable across subjects. The existence of these two separate effects demonstrates that the usual method of studying component duration-that is, holding all components equal in duration-systematically causes underestimation of the effects of the component duration, and obscures the different processes controlling the two effects.A major emphasis in free-operant research has been the development of quantitative descriptions of behavior. One of the most influential of such descriptions is the generalized matching law, given by Equation 1, which has been applied to schedules in which two components are available, either simultaneously or successively (B refers to the behavior in a component; R refers to the corresponding reinforcement rate; b refers to a bias independent of the reinforcement rates, and a to the sensitivity to relative reinforcement rate). The assumption underlying this application is that variation in the interactions between the components of the schedule can be captured adequately by the two parameters of the expression. For this assumption to be sustained, parameter variations that should have important effects on behavior should yield corresponding changes in either bias or sensitivity.(1)An important schedule parameter that seems to challenge the use of Equation 1 as a description of multiple schedule behavior is the duration of the schedule components. Given that contrast effects in one component of the schedule are an inverse function of the reinforcement rate during the alternative component (see Williams, 1983a, for a review), it seems intuitively plausible that the duration of the components should be an important determinant of the size of the contrast effects. When each component is long, responding at most points in the component is distant from the alternative reinforcement schedule; when each component is short, responding at any point is close to the alternative schedule. It seems plausible, ...

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“…It is well established that the relation between component response rates and component reinforcer rates in multiple schedules may be described by the generalized matching law (Charman & Davison, 1982;Lobb & Davison, 1977;McSweeney, Farmer, Dougan, & Whipple, 1986 log (B) = a log(R ) + log c. (1) The parameter a in the above equations is known as sensitivity to reinforcement (Lobb & Davison, 1975) and it measures the rate of change of the log behavior ratio with respect to changes in the log reinforcer ratio. (Baum & Rachlin, 1969) of responding on two, unequal, multipleschedule components were the same, then as access time was decreased, the relation between log response-allocation ratios and log reinforcer-rate ratios would become similar to the relation between log time-allocation ratios and log component reinforcer-rate ratios.…”

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On the Measurement of Time Allocation on Multiple Variable‐interval Schedules

Davison

Charman

1986

J Exper Analysis Behavior

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Six pigeons were trained on a modified multiple-schedule procedure. In a three-key chamber, the center key was lighted red or green, depending upon which component schedule was in effect. A response on this key transferred this color to each of two side keys, and responses on one of those keys produced reinforcers according to the component schedule. After 2 s, the side-key lights were extinguished, the center key was reilluminated, and a further center-key response was required to give access, as before, to the component schedules. Components alternated every 3 min. This limited-access procedure allowed both times spent switched into the side keys and time spent not switched in to be measured in the two components. Component reinforcer rates were varied over eight experimental conditions. Both component response rate and component time allocation were increasing functions of relative component reinforcer rate, and these functions were not significantly different. This finding implies that local response rates (responses divided by time switched in) were unaffected by changing component reinforcer rates on multiple schedules. Because a similar result was recently obtained for concurrent schedules, models of multiple and concurrent-schedule performance may need to consider only the time allocation of behavior emitted at equal tempo in the component schedules. of an experimental chamber with a pivoted floor. The components of the multiple schedule alternated between the two ends of the chamber, and White measured the time during which the floor at the appropriate end was depressed. In White's first experiment, responses on the manipulanda could produce reinforcers according to VI schedules. In his second experiment, responses were not required and reinforcers were delivered on vari- (1970, 1974) (NOVEMBER) 1986, 46, 353-362

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The Generalized Matching Law as a Description of Multiple‐schedule Responding

Cited by 32 publications

References 45 publications

Delayed and Current Stimulus Control in Successive Discriminations

Delayed and Current Stimulus Control in Successive Discriminations

Component duration effects in multiple schedules

On the Measurement of Time Allocation on Multiple Variable‐interval Schedules

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