Reward, performance, and the response strength method in self-stimulating rats: Validation and neuroleptics

Hamilton, Aimee L.; Stellar, James R.; Hart, Elizabeth B.

doi:10.1016/0031-9384(85)90257-4

Cited by 81 publications

(41 citation statements)

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“…Previous research has shown that k varies with differences in the force required to make a response (Belke & Heyman, 1994b; Hamilton et al, 1985;Heyman & Monaghan, 1987) and response topography (McSweeney, 1978). In the present study, neither of these factors should have played a role.…”

Section: Discussionmentioning

confidence: 47%

“…Specifically, Heyman and Monaghan (1987) noted that, in studies in which the experimenter manipulated an aspect of the response requirement, such as the force or form, the value of k changed, whereas the value ofR, remained stable (Belke & Heyman, 1994b;Bradshaw, Szabadi, & Ruddle, 1983;Hamilton, Stellar, & Hart, 1985;Heyman & Monaghan, 1987;McSweeney, 1978). In contrast, in studies in which the experimenter manipulated reinforcement quantity or deprivation for the arranged reinforcement, the value of R, changed, whereas the value of k re-(I) Herrnstein's (1961) matching law equation, which holds that relative rates ofresponse across alternatives will match the relative rates ofreinforcement obtained from those alternatives, has been an important principle guiding the investigation of choice for several decades.…”

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confidence: 99%

“…I e BELKE mained stable (Belke & Heyman, 1994b;Bradshaw, Ruddle, & Szabadi, 1981;Bradshaw, Szabadi, Ruddle, & Pears, 1983;Conrad & Sidman, 1956;Guttman, 1954;Hamilton, Stellar, & Hart, 1985;Heyman & Monaghan, 1987Kraeling, 1961;de Villiers & Herrnstein, 1976, analyzed results from studies prior to 1976). Numerous studies have investigated the effects of differences in reinforcement quantity, deprivation level, response force, or response manipulanda on the responsestrength equation parameters (Belke & Heyman, 1994b;Bradshaw et aI., 1981;Bradshaw, Szabadi, & Ruddle, 1983;Bradshaw, Szabadi, et aI., 1983;Conrad & Sidman, 1956;Guttman, 1954;Hamilton et aI., 1985;Heyman & Monaghan, 1987Kraeling, 1961;McSweeney, 1978).…”

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Qualitatively different reinforcers and parameters of Herrnstein’s (1970) response-strength equation

Belke

1998

Animal Learning & Behavior

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Previous research that compared the estimated parameters (i.e., k and R e ) from Herrnstein's (1970) hyperbolic matching law equation within the same individuals responding for qualitatively different consummatory reinforcers (i.e., water and sucrose solution) found similar asymptotic response rates (k). The present study compared these parameters within subjects responding on levers for consummatory and nonconsummatory reinforcers. Male Wistar rats responded on a lever in a running wheel on a series of tandem FR 1 VI schedules for either 0.1 ml of a 15%sucrose solution or the opportunity to run for 15 sec. Herrnstein's hyperbola was fit to response and reinforcement rates from each session. Results showed that k values were significantly higher for sucrose than for wheel-running reinforcement. On average, R; was lower for sucrose than for wheel-running reinforcement, though not significantly lower. The results of the present study appear to violate the assumption of the constancy of kin Herrnstein's matching law analysis.In Equation 2, B I is the response rate on the single alternative, R I is the reinforcement rate obtained from that alternative, and k and R; are estimated parameters. Specifically, k refers to the asymptotic rate ofresponding (i.e., the maximal response rate), whereas R; is the rate of rein- forcement associated with one halfthe asymptotic rate ofresponding. R, describes how quickly the response rate rises toward asymptote as the reinforcement rate increases, and, at one half the asymptotic response rate (k/2), the value of R; can be estimated because R I and R; are equivalent.Although there is only a single experimenter-arranged source of reinforcement, Herrnstein (1970Herrnstein ( ,1974 assumed that responding for this reinforcement represented the choice between responding for the arranged source and responding for all other sources of reinforcement in the context. In other words, responding on the arranged source ofreinforcement is a function ofthe rate of reinforcement from that alternative, relative to the rate of reinforcement for any behavior other than responding for the arranged reinforcement (e.g., sniffing, grooming, exploring). Accordingly, R; in Equation 1 represents the rate of reinforcement from all sources ofreinforcement in the context, other than that arranged by the experimenter. The parameter k represents both responding (B I) maintained by the arranged source of reinforcement (R I) and responding (Be) maintained by the uncontrolled (i.e., extraneous) sources of reinforcement in the context (R e ) .

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Qualitatively different reinforcers and parameters of Herrnstein’s (1970) response-strength equation

Belke

1998

Animal Learning & Behavior

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“…This within-session procedure has produced 66 BACKGROUND REINFORCEMENT reliable results in previous studies of environmental (Bradshaw, Szabadi, & Bevan, 1976Heyman & Monaghan, 1987;Petry & Heyman, 1994) and pharmacological (Hamilton, Stellar, & Hart, 1985;Heyman, 1983Heyman, , 1992Heyman, Kinzie, & Seiden, 1986) manipulations of reinforcement efficacy.…”

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Increasing and Signaling Background Reinforcement: Effect on the Foreground Response—reinforcer Relation

Belke

Heyman

1994

J Exper Analysis Behavior

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Herrnstein's (1970) hyperbolic matching equation describes the relationship between response rate and reinforcement rate. It has two estimated parameters, k and Re. According to one interpretation, k measures motor performance and Re measures the efficacy of the reinforcer maintaining responding relative to background sources of reinforcement. Experiment 1 tested this interpretation of the Re parameter by observing the effect of adding and removing an additional source of reinforcement to the context. Using a within-session procedure, estimates of Re were obtained from the responsereinforcer relation over a series of seven variable-interval schedules. A second, concurrently available variable-interval schedule of reinforcement was added and then removed from the context. Results showed that when the alternative was added to the context, the value of Re increased by 107 reinforcers per hour; this approximated the 91 reinforcers per hour obtained from this schedule. Experiment 2 investigated the effects of signaling background reinforcement on k and Re. The signal decreased Re, but did not have a systematic effect on k. In general, the results supported Herrnstein's interpretation that in settings with one experimenter-controlled reinforcement source, Re indexes the strength of the reinforcer maintaining responding relative to uncontrolled background sources of reinforcement.Key words: Herrnstein's hyperbola, matching law, background reinforcement, signaled reinforcement, lever press, rats Herrnstein (1970) formulated an elementary matching law equation for the case in which there is only a single measured source of reinforcement and a single measured response rate. The form of that equation is kRj BIRi+Re' (1) where B1 is response rate, R1 is reinforcement rate, and k and Re are fitted constants. The structural or curve-fitting definitions of the constants reveal the relationship between response rate and reinforcement rate implied by Equation 1. In the numerator, k is an estimate of the response-rate asymptote. For instance, as reinforcement rate increases, response rate approaches but does not exceed k. Thus, k is measured in the same units as the measured behavior (e.g., responses per minute). In the numerator, Re is equal to the rate of reinforcement that maintains a one-half asymp-The authors gratefully acknowledge the helpful comments of the reviewers and members of the Behavioral and Decision Analysis research seminar in the Department of Psychology at Harvard in the preparation of this manuscript. Correspondence regarding this article should be sent to Terry W. Belke, Department of Psychology, Biological Sciences Building, University of Alberta, Edmonton, Alberta T6G 2E9, Canada (E-mail: tbelke@cyber.psych.ualberta.ca).totic response rate. For example, when RI is equal to Re, response rate must be equal to k/2. Thus, Re is measured in the same units as the experimenter-controlled reinforcer (e.g., 0.10 mL sucrose servings per hour).On the basis of the matching law, Herrnstein (1970, 1974) provided em...

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“…By this account, k quantifies the topography of the reinforced response and Re measures the efficacy of the background reinforcers relative to the arranged reinforcer (Herrnstein, 1970(Herrnstein, , 1974. In studies in which estimates of Re have systematically decreased while k has remained constant (Bradshaw, Ruddle, & Szabadi, 1981;Bradshaw, Szabadi, & Bevan, 1978a;Brad-shaw, Szabadi, Ruddle, & Pears, 1983;Conrad & Sidman, 1956;Guttman, 1954;Hamilton, Stellar, & Hart, 1985;Heyman & Monaghan, 1987; Kraeling, 1961;Logan, 1960;see de Villiers & Herrnstein, 1976, for parameter estimations for studies published before 1976), the magnitude of the arranged reinforcer was increased (i.e., in volume or concentration, or as an increase in deprivation level). Likewise, studies that have demonstrated systematic changes in k and no alterations in Re have altered response requirements by, for example, adding weights to levers Hamilton et al, 1985;Heyman & Monaghan, 1987;McSweeney, 1978;Porter & Villanueva, 1989).…”

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Effects of Qualitatively Different Reinforcers on the Parameters of the Response‐strength Equation

Petry

Heyman

1994

J Exper Analysis Behavior

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This experiment examined the relationship between two qualitatively different reinforcers and the parameters of a quantitative model of reinforced responding, referred to as the response-strength equation or the Herrnstein equation. A group of rats was first food deprived and later water deprived. An 11.5% sucrose solution served as the reinforcer in the food-deprivation condition, and water was the reinforcer in the water-deprivation condition. Each experimental session consisted of a series of seven variable-interval schedules, providing reinforcement rates that varied between 20 and 1,200 reinforcers per hour. The response rates increased in a negatively accelerating function in a manner consistent with the response-strength equation. This equation has two fitted parameters, k and R,. According to one theory, the k parameter is a measure of motor performance, and R, is indicative of the relative reinforcement efficacy of the background uncontrollable sources of reinforcement in relation to the experimentally arranged reinforcer. In this study, k did not change as a result of the different reinforcers, but R, was significantly larger in the sucrose-reinforcement condition. These results are consistent with the interpretation that k and R, measure two independent and experimentally distinguishable parameters and provide further evidence that absolute response rate is a function of relative reinforcement rate, as implied by the derivation of the response-strength equation based on the matching law.Key words: response-strength equation, matching law, water deprivation, food deprivation, lever press, ratsThe matching law equation, introduced by Herrnstein (1 970), has generated considerable interest to researchers studying behavioral psychology, psychopharmacology, animal behavior, and economic theory. Nonetheless, a number of issues concerning this equation and its underlying assumptions remain to be addressed. In his paper, Herrnstein demonstrated that relative response rate is a function of relative reinforcement rate when two reinforcement sources are concurrently available. The equation for relative response rates is Bl/(Bl + B2) = RI/(Rj + R2), where B1 and RI are response and reinforcement rates, respectively, at Alternative 1. This equation has come to be known as the matching law. Herrnstein further demonstrated that, when only one source of reinforcement is available, absolute response rate is a hyperbolic

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Reward, performance, and the response strength method in self-stimulating rats: Validation and neuroleptics

Cited by 81 publications

References 19 publications

Qualitatively different reinforcers and parameters of Herrnstein’s (1970) response-strength equation

Qualitatively different reinforcers and parameters of Herrnstein’s (1970) response-strength equation

Increasing and Signaling Background Reinforcement: Effect on the Foreground Response—reinforcer Relation

Effects of Qualitatively Different Reinforcers on the Parameters of the Response‐strength Equation

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