Skip to main content
Journal of the Experimental Analysis of Behavior logoLink to Journal of the Experimental Analysis of Behavior
. 1985 Jan;43(1):61–73. doi: 10.1901/jeab.1985.43-61

Confirmation of linear system theory prediction: Rate of change of Herrnstein's κ as a function of response-force requirement

J J McDowell, Helena M Wood
PMCID: PMC1348095  PMID: 16812408

Abstract

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes (¢/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's κ were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) κ increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of κ was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of κ was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's κ.

Keywords: linear system theory, Herrnstein's equation, reinforcer value, reinforcer magnitude, response force, variable-interval schedules, lever press, humans

Full text

PDF
63

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bradshaw C. M., Szabadi E., Bevan P. Behavior of humans in variable-interval schedules of reinforcement. J Exp Anal Behav. 1976 Sep;26(2):135–141. doi: 10.1901/jeab.1976.26-135. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bradshaw C. M., Szabadi E., Bevan P. Relationship between response rate and reinforcement frequency in variable-interval schedules: the effect of the concentration of sucrose reinforcement. J Exp Anal Behav. 1978 May;29(3):447–452. doi: 10.1901/jeab.1978.29-447. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. CHUNG S. H. EFFECTS OF EFFORT ON RESPONSE RATE. J Exp Anal Behav. 1965 Jan;8:1–7. doi: 10.1901/jeab.1965.8-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Catania A. C. Self-inhibiting effects of reinforcement. J Exp Anal Behav. 1973 May;19(3):517–526. doi: 10.1901/jeab.1973.19-517. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. FLESHLER M., HOFFMAN H. S. A progression for generating variable-interval schedules. J Exp Anal Behav. 1962 Oct;5:529–530. doi: 10.1901/jeab.1962.5-529. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. GUTTMAN N. Equal-reinforcement values for sucrose and glucose solutions compared with equal-sweetness values. J Comp Physiol Psychol. 1954 Oct;47(5):358–361. doi: 10.1037/h0062710. [DOI] [PubMed] [Google Scholar]
  7. Herrnstein R. J. Formal properties of the matching law. J Exp Anal Behav. 1974 Jan;21(1):159–164. doi: 10.1901/jeab.1974.21-159. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Herrnstein R. J. On the law of effect. J Exp Anal Behav. 1970 Mar;13(2):243–266. doi: 10.1901/jeab.1970.13-243. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. KRAELING D. Analysis of amount of reward as a variable in learning. J Comp Physiol Psychol. 1961 Oct;54:560–565. doi: 10.1037/h0040833. [DOI] [PubMed] [Google Scholar]
  10. McDowell J. J. An analytic comparison of Herrnstein's equations and a multivariate rate equation. J Exp Anal Behav. 1980 May;33(3):397–408. doi: 10.1901/jeab.1980.33-397. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. McDowell J. J., Kessel R. A multivariate rate equation for variable-interval performance. J Exp Anal Behav. 1979 Mar;31(2):267–283. doi: 10.1901/jeab.1979.31-267. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. McDowell J. J., Sulzen H. M. Dynamic equilibrium on a cyclic-interval schedule with a ramp. J Exp Anal Behav. 1981 Jul;36(1):9–19. doi: 10.1901/jeab.1981.36-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. McDowell J. J. Wilkinson's method of estimating the parameters of Herrnstein's hyperbola. J Exp Anal Behav. 1981 May;35(3):413–414. doi: 10.1901/jeab.1981.35-413. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. McDowell J. J., Wood H. M. Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude. J Exp Anal Behav. 1984 Mar;41(2):183–192. doi: 10.1901/jeab.1984.41-183. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. NOTTERMAN J. M., BLOCK A. H. Note on response differentiation during a simple discrimination. J Exp Anal Behav. 1960 Oct;3:289–291. doi: 10.1901/jeab.1960.3-289. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. NOTTERMAN J. M. Force emission during bar pressing. J Exp Psychol. 1959 Nov;58:341–347. doi: 10.1037/h0042801. [DOI] [PubMed] [Google Scholar]
  17. NOTTERMAN J. M., MINTZ D. E. Exteroceptive cueing of response force. Science. 1962 Mar 23;135(3508):1070–1071. doi: 10.1126/science.135.3508.1070. [DOI] [PubMed] [Google Scholar]
  18. Rachlin H. A molar theory of reinforcement schedules. J Exp Anal Behav. 1978 Nov;30(3):345–360. doi: 10.1901/jeab.1978.30-345. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. SEWARD J. P., SHEA R. A., UYEDA A. A., RASKIN D. C. Shock strength, shock reduction and running speed. J Exp Psychol. 1960 Oct;60:250–254. doi: 10.1037/h0041637. [DOI] [PubMed] [Google Scholar]
  20. Staddon J. E. On Herrnstein's equation and related forms. J Exp Anal Behav. 1977 Sep;28(2):163–170. doi: 10.1901/jeab.1977.28-163. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Tryon W. W. A simplified time-series analysis for evaluating treatment interventions. J Appl Behav Anal. 1982 Fall;15(3):423–429. doi: 10.1901/jaba.1982.15-423. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Journal of the Experimental Analysis of Behavior are provided here courtesy of Society for the Experimental Analysis of Behavior

RESOURCES