Parametric supplements to systems factorial analysis: Identifying interactive parallel processing using systems of accumulators

Systems Factorial Technology (SFT; Townsend and Nozawa (1995)) gains much of its power from finding tight nonparametric links between theory and data. But this power comes at a price: Applying SFT typically requires low error rates, many observations, and a guarantee of selective influence of experimental manipulations, conditions that cannot be satisfied in many fields of psychology. We present a set of parametric methods that, while lacking the full power of traditional SFT, allow its logic to be applied to situations that do not adhere to those conditions. These methods are based around building different parallel architectures from systems of Linear Ballistic Accumulators (Brown and Heathcote (2008)), including architectures that involve interactions between processes. The primary output of these methods is an estimate of the probabilities that a participant is best described by each of these architectures. In an example and set of simulations, we show that these methods are accurate and robust at identifying the processing architectures employed by a set of participants, may be estimated in maximum a posteriori or fully Bayesian fashion, and that hierarchical estimation allowing accurate identification with as few as three trials per participant per condition. We provide code that allows researchers to apply these methods to their own data at https://osf.io/m6ubq/.