Linear Deterministic Accumulator Models of Simple Choice

We examine theories of simple choice as a race among evidence accumulation processes. We focus on the class of deterministic race models, which assume that the effects of fluctuations in the parameters of the accumulation processes between-choice trials (between-choice noise) dominate the effects of fluctuations occurring while making a choice (within-choice noise) in behavioral data (i.e., response times and choices). The latter deterministic approximation, when combined with the assumption that accumulation is linear, leads to a class of models that can be readily applied to simple-choice behavior because they are computationally tractable. We develop a new and mathematically simple exemplar within the class of linear deterministic models, the Lognormal race (LNR). We then examine how the LNR, and another widely applied linear deterministic model, Brown and Heathcote's (2008) LBA, account for a range of benchmark simple-choice effects in lexical-decision task data reported by Wagenmakers et al. (2008). Our results indicate that the LNR provides an accurate description of this data. Although the LBA model provides a slightly better account, both models support similar psychological conclusions.