An analytic form for the interresponse time analysis of Shull, Gaynor, and Grimes with applications and extensions

Shull, Gaynor and Grimes advanced a model for interresponse time distribution using probabilistic cycling between a higher-rate and a lower-rate response process. Both response processes are assumed to be random in time with a constant rate. The cycling between the two processes is assumed to have a constant transition probability that is independent of bout length. This report develops an analytic form of the model which has a natural parametrization for a higher-rate within-bout responding and a lower-rate visit-initiation responding. The analytic form provides a convenient basis for both a nonlinear least-squares data reduction technique to estimate the model's parameters and Monte Carlo simulations of the model. In addition, the analytic formulation is extended to both a refractory period for the rats' behavior and, separately, the strongly-banded behavior seen with pigeons.