A theoretical study of process dependence for critical statistics in standard serial models and standard parallel models

Publication date: Available online 7 September 2019Source: Journal of Mathematical PsychologyAuthor(s): Ru Zhang, Yanjun Liu, James T. TownsendAbstractLong before the mathematical developments that led inexorably to the development of systems factorial technology, the somewhat arduous, but arguably requisite labors which precisely defined parallel and serial architectures had begun (e.g., Townsend, 1969, 1972). Both then and now, what are now referred to as standard serial models and standard parallel models not only play an important role in psychological science, they are often what non-mathematical psychologists are (sometimes in an unschooled fashion) referring to when they bring up architectural concepts. Interestingly, two strategic and critical properties, and therefore implicit predictions of the canonical serial and parallel models have witnessed little analysis. In this article, we address three issues: (1) Standard parallel models predict stochastically independent processing times and therefore total completion times. There is a partially valid intuition that standard serial models will predict positive dependence among totally completion times and standard serial models based on exponential processing time do predict this (Townsend and Ashby, 1983, p. 73). This also holds if only one order of processing is possible. However, if there is a mixture of processing orders, certain distributions can predict negative dependencies on this statistic. (2) Analogously, stan...
Source: Journal of Mathematical Psychology - Category: Psychiatry & Psychology Source Type: research