A model of changeover behavior in two-alternative choice

Abstract

The amount of time that organisms spend on a variable-interval schedule of a concurrent pair before departing to the other one (i.e., the dwell time on the schedule) follows an exponential distribution, meaning that the probability of switching to the other schedule does not increase or decrease throughout the visit. This appears to reflect an innate behavioral pattern and implies that concurrent-schedule performance can be modeled using continuous-time Markov chains. In the two-alternative case, the behavior of a Markov chain is completely determined by the leaving rates from each alternative (i.e., the number of departures per unit of time), so finding expressions for these leaving rates should suffice to completely characterize changeover behavior in concurrent schedules. Such expressions can be derived from the matching law in combination with either the mathematical principles of reinforcement or Baum's laws of allocation, induction, and covariance. The resulting equations are assessed in the particular case of concurrent variable-interval schedules using a large data set from a published study that systematically manipulated both the relative and the overall rates of reinforcement, resulting in excellent fits. The performance of the model is also assessed against that of competing models, proving to be superior in most cases.