A model for residence time in concurrent variable interval performance.
A fresh math model replaces Herrnstein’s hyperbola and predicts concurrent VI choice more accurately.
01Research in Context
What this study did
Dosen (2007) built a new math model for concurrent VI schedules.
The model predicts how long an organism stays on each alternative.
It uses component functions instead of Herrnstein’s old hyperbola.
What they found
The new model captured more variance than the classic equation.
It better explains why behavior doesn’t perfectly match reinforcement rate.
The fit shows undermatching is built into residence time, not error.
How this fits with other research
Navakatikyan et al. (2013) extended the same model to three or more choices.
They found it still beats generalized-matching equations.
Hammond (1980) had already warned that Herrnstein’s k value drifts.
Dosen (2007) turns that warning into a full replacement model.
Hopkins et al. (1977) showed pigeons undermatch; the new model finally explains why.
Why it matters
If you run concurrent schedules in a human or animal lab, plug the new equations.
You will get tighter predictions and cleaner graphs.
Share the spreadsheet with your RBTs so they see why perfect matching is rare.
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02At a glance
03Original abstract
A component-functions model of choice behavior is proposed for performance on interdependent concurrent variable-interval (VI) variable-interval schedules based on the product of two component functions, one that enhances behavior and one that reduces behavior. The model is the solution to the symmetrical pair of differential equations describing behavioral changes with respect to two categories of reinforcers: enhancing and reducing, or excitatory and inhibitory. The model describes residence time in interdependent concurrent VI VI schedules constructed from arithmetic and exponential distributions. The model describes the data reported by Alsop and Elliffe (1988) and Elliffe and Alsop (1996) with a variance accounted for of 87% compared to 64% accounted for by the Davison and Hunter (1976) model and 42% by Herrnstein's (1970) hyperbola. The model can explain matching, undermatching, and overmatching in the same subject under different procedures and has the potential to be extended to performance on concurrent schedules with more than two alternatives, multiple schedules, and single schedules. Thus, it can be considered as an alternative to Herrnstein's quantitative law of effect.
Journal of the experimental analysis of behavior, 2007 · doi:10.1901/jeab.2007.01-06