Effects of qualitatively different reinforcers on the parameters of the response-strength equation.
Reinforcer type changes the Re parameter in Herrnstein’s equation, leaving the asymptote k untouched—yet reinforcer magnitude can later move k, so watch both.
01Research in Context
What this study did
The team tested how switching reinforcer types changes the numbers in Herrnstein response-strength equation.
Rats pressed a lever on variable-interval schedules. Sometimes drops of sucrose paid off. Other times plain water did.
The authors tracked which parameter moved when the tasty reinforcer replaced the bland one.
What they found
Only the Re parameter shifted. It rose with sucrose and fell with water.
The asymptote k stayed flat across both reinforcer types.
So, in the equation, reinforcer quality tweaks Re, not k.
How this fits with other research
Dougherty et al. (1994) ran a near twin study but varied sucrose concentration instead of type. They also saw Re move while k held steady, a clean conceptual replication.
Rose et al. (2000) later found k itself climbs with higher sucrose concentration, clashing with the constant-k claim here. The clash exposes a hole in matching theory: k may be fixed when you swap type yet flexible when you boost magnitude.
Earlier work by Wilkie et al. (1981) showed smaller reinforcer volumes push the response curve rightward, again shifting Re. Together the three papers map which manipulations tug each lever of the equation.
Why it matters
When you graph a client’s VI performance, treat Re as the sensitivity dial for reinforcer appeal. Swap stickers for snacks and watch Re, not the ceiling rate. If you later increase snack size, remember Rose et al. (2000) and check whether the ceiling itself inches up. Track both parameters and you will spot when motivation, not capacity, is driving low response rates.
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Join Free →Graph the last week of VI data, fit the hyperbola, and note Re; then swap to a high-preference edible and see if Re rises while k stays flat.
02At a glance
03Original abstract
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 Re. According to one theory, the k parameter is a measure of motor performance, and Re 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 Re was significantly larger in the sucrose-reinforcement condition. These results are consistent with the interpretation that k and Re 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.
Journal of the experimental analysis of behavior, 1994 · doi:10.1901/jeab.1994.61-97