### Abstract

Matching theory and linear system theory make different predictions about how the y-asymptote, k, of Herrnstein's (1970) hyperbola varies with reinforcer value. The present experiment tested both these predictions and linear system theory's account of how reinforcement rate and reinforcer value jointly govern response rate. Eight rats served as subjects. In Phase 1, 3 sucrose pellets of different concentration (5%, 75%, and 95%) were alternately paired with a fourth concentration (50%) on concurrent VI VI schedules. By fitting linear system theory's equation for concurrent choice, measures of reinforcer value were assigned to each concentration for each subject. The reinforcer values for the 50%, 75%, and 95% were roughly equivalent, and the reinforcer values for the 5% concentration were lower. In Phase 2 subjects were exposed to a series of single-alternative VI schedules (8, 17, 55, 150, and 250 sec) and each sucrose concentration was studied separately, with a 25% pellet added. Herrnstein's equation was fitted to response rate as a function of reinforcement rate for each concentration. The asymptote, k, was roughly equivalent under the 50%, 75%, and 95% pellets, but was lower for the 5% and 25% pellets. The measures of reinforcer value from Phase 1 suggest that the equivalent ks in Phase 2 were the result of equivalent reinforcer values. Matching theory predicts that k should remain constant across changes in reinforcer value. The value of k varied with reinforcer value, and the form of variability in k supported linear system theory's prediction of a positively accelerating function. Linear system theory's prediction about how reinforcement rate and reinforcer value jointly govern response rate was also supported. The results contradict matching theory's account and support linear system theory's account of single-alternative responding.

Original language | English (US) |
---|---|

Pages (from-to) | 45-65 |

Number of pages | 21 |

Journal | Psychological Record |

Volume | 54 |

Issue number | 1 |

State | Published - Dec 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Psychology(all)

### Cite this

*Psychological Record*,

*54*(1), 45-65.

**The measurement and functional properties of reinforcer value in single-alternative responding : A test of linear system theory.** / Dallery, Jesse; McDowell, J. J.; Soto, Paul L.

Research output: Contribution to journal › Article

*Psychological Record*, vol. 54, no. 1, pp. 45-65.

}

TY - JOUR

T1 - The measurement and functional properties of reinforcer value in single-alternative responding

T2 - A test of linear system theory

AU - Dallery, Jesse

AU - McDowell, J. J.

AU - Soto, Paul L.

PY - 2004/12

Y1 - 2004/12

N2 - Matching theory and linear system theory make different predictions about how the y-asymptote, k, of Herrnstein's (1970) hyperbola varies with reinforcer value. The present experiment tested both these predictions and linear system theory's account of how reinforcement rate and reinforcer value jointly govern response rate. Eight rats served as subjects. In Phase 1, 3 sucrose pellets of different concentration (5%, 75%, and 95%) were alternately paired with a fourth concentration (50%) on concurrent VI VI schedules. By fitting linear system theory's equation for concurrent choice, measures of reinforcer value were assigned to each concentration for each subject. The reinforcer values for the 50%, 75%, and 95% were roughly equivalent, and the reinforcer values for the 5% concentration were lower. In Phase 2 subjects were exposed to a series of single-alternative VI schedules (8, 17, 55, 150, and 250 sec) and each sucrose concentration was studied separately, with a 25% pellet added. Herrnstein's equation was fitted to response rate as a function of reinforcement rate for each concentration. The asymptote, k, was roughly equivalent under the 50%, 75%, and 95% pellets, but was lower for the 5% and 25% pellets. The measures of reinforcer value from Phase 1 suggest that the equivalent ks in Phase 2 were the result of equivalent reinforcer values. Matching theory predicts that k should remain constant across changes in reinforcer value. The value of k varied with reinforcer value, and the form of variability in k supported linear system theory's prediction of a positively accelerating function. Linear system theory's prediction about how reinforcement rate and reinforcer value jointly govern response rate was also supported. The results contradict matching theory's account and support linear system theory's account of single-alternative responding.

AB - Matching theory and linear system theory make different predictions about how the y-asymptote, k, of Herrnstein's (1970) hyperbola varies with reinforcer value. The present experiment tested both these predictions and linear system theory's account of how reinforcement rate and reinforcer value jointly govern response rate. Eight rats served as subjects. In Phase 1, 3 sucrose pellets of different concentration (5%, 75%, and 95%) were alternately paired with a fourth concentration (50%) on concurrent VI VI schedules. By fitting linear system theory's equation for concurrent choice, measures of reinforcer value were assigned to each concentration for each subject. The reinforcer values for the 50%, 75%, and 95% were roughly equivalent, and the reinforcer values for the 5% concentration were lower. In Phase 2 subjects were exposed to a series of single-alternative VI schedules (8, 17, 55, 150, and 250 sec) and each sucrose concentration was studied separately, with a 25% pellet added. Herrnstein's equation was fitted to response rate as a function of reinforcement rate for each concentration. The asymptote, k, was roughly equivalent under the 50%, 75%, and 95% pellets, but was lower for the 5% and 25% pellets. The measures of reinforcer value from Phase 1 suggest that the equivalent ks in Phase 2 were the result of equivalent reinforcer values. Matching theory predicts that k should remain constant across changes in reinforcer value. The value of k varied with reinforcer value, and the form of variability in k supported linear system theory's prediction of a positively accelerating function. Linear system theory's prediction about how reinforcement rate and reinforcer value jointly govern response rate was also supported. The results contradict matching theory's account and support linear system theory's account of single-alternative responding.

UR - http://www.scopus.com/inward/record.url?scp=1542397168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542397168&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1542397168

VL - 54

SP - 45

EP - 65

JO - Psychological Record

JF - Psychological Record

SN - 0033-2933

IS - 1

ER -