Generalizing survivor interaction contrast functions for coactive systems to the linear ballistic accumulator model, inhomogeneous Poisson processes, and presenting a novel ‘bare bones’ stochastic process

What the paper says

A typical redundant signals experiment assesses response time (RT) performance when either of two (or more) presented signals is sufficient to make a correct response against response time to respond to either of the signals alone. In some studies perception of both signals takes place faster than either alone and even faster than what a parallel system with independent, unlimited capacity channels can predict. This behavior is referred to as super capacity (Townsend & Nozawa, 1995). In fact, J. Miller’s earlier 1982 data was interpreted as exhibiting performance that was so super capacity that it violated an upper bound on performance through a statistic known in mathematics as the Poisson Inequality, and now referred to in the literature as the race model inequality (RMI). The most popular type of explanatory model assumes that information (treated as an activation random variable in each channel) from two parallel channels is summed into a subsequent single channel where the sum is compared with a criterion activation. Such a process is dubbed coactivation and several specific such models were shown to be able to make such predictions. Then, it was shown by Townsend & Nozawa (1995) that any arbitrary counter model (i.e., with arbitrary stochastic processes for the concurrent counters) perforce predicted violation of the RMI. Further, using the systems factorial technology statistical function named the survivor interaction contrast (SIC), they proved that standard Poisson counter models predict a specific distinctive function for coactive processing. However, other architectures (e.g., parallel and serial models) are entirely general rather than being confined to Poisson counters. Subsequently, Houpt & Townsend (2011) generalized the SIC prediction to the popular Ratcliff–Wiener drift–diffusion process. Our satisfied goal here was to further extend the classes of covered coactive systems to the popular Linear Ballistic Accumulator (e.g., Brown & Heathcote, 2008), the entire class of Inhomogeneous Poisson Processes, and a novel system we call the bare bones stochastic process. In addition, we adduce a set of sufficient conditions that any monotone distribution should meet to predict for their convolution to obey the canonical SIC form. • Demonstrated range of coactive models with canonical survivor interaction contrast. • Develop and explore a novel system, the bare bones stochastic process model. • Enumerate sufficient conditions to elicit the canonical SIC form.