Stochastic cascade processes as a model of multi-stage concurrent information processing

McClelland's (Psychol. Rev. 86 (1979) 287) influential cascade model of reaction time (RT) is often seen as an important explicitly formulated alternative to strictly serial models because some of its basic notions fit in with known characteristics of neural activation processes. A disadvantage is that it is an essentially deterministic model to which noise is added by across-trials parameter variability that is unrelated to the concept of cascaded activation propagation per se. We propose and analyze a general stochastic cascade model based on neural counting processes; within this framework we present a new process-oriented interpretation of McClelland's cascade activation equation. We then theoretically explain and numerically explore conditions under which the stochastic cascade model predicts additive vs. interactive mean RT effects, and compare them to known properties of McClelland's model. Some of these properties remain valid even within a stochastic neural counting formulation, while others reflect assumptions which are essentially unrelated to the concept of cascaded activation.