Comparison of Variance and Covariance Patterns in Parallel and Serial Theories of Timing

Parallel and serial timing processes are analyzed for their account of the dynamics of intertrial responding in the peak procedure. A strictly serial model, such as the behavioral theory of timing (Killeen & Fetterman, 1988), does not fit the dynamic correlation pattern in the location and duration of the middle high-rate responding portion of peak trials. In contrast, the parallel scalar expectancy theory model, with a sample for memory and threshold, does fit this pattern. A modification of the serial model is presented that also accommodates the within-trial covariance pattern. The modification, which is formally equivalent to a model for human tapping (Wing & Kristofferson, 1973), entails the addition of concurrent processes operating in parallel with serial timing.