Dallery, J., Soto, P. L., & McDowell, J. J (2005).
A test of the formal and modern theories of matching.
Journal of the Experimental Analysis of Behavior, 84, 129-
145.
The present study tested a formal, or purely mathematical, theory of matching,
and a modern account derived by McDowell (1986) that incorporates deviations
from strict matching–bias and sensitivity. Six humans pressed a lever for
monetary reinforcers on five concurrent variable interval (VI) schedules of
reinforcement. All schedules were presented during each session. The magnitude
on one alternative remained constant, and five magnitudes were presented across
sessions on the other alternative. To test the formal account, two absolute
response rate equations were fitted to the response and reinforcement rates at
each alternative at each magnitude. Although the equations accounted for a high
percentage of variance, there was a significant negative correlation between the
standardized residuals and the predicted response rates. To test the modern
account, an ensemble of four equations was fitted to the data. The equations
predicted relative and absolute responding, and the independent variables in
each equation were adjusted for bias and sensitivity. The equations accounted
for a high percentage of variance, and the standardized residuals were not
correlated with the predicted response rates. The values of the parameters were
consistent with empirical findings and theoretical predictions, including the
prediction that k should remain constant across changes in reinforcer magnitude.
The results suggest that the formal theory of matching does not describe the
data, and that the modern theory may provide an accurate and coherent
description of concurrent and single-alternative responding.
Key words: matching theory, concurrent schedules, reinforcer magnitude,
variable-interval schedules, lever press, humans