Making speeded choices is one of the simplest yet most prevalent human cognitive activities. We decide whether a traffic light is green or red. We decide whether the mouse is closer to the cheese than the cat is to the mouse, or whether our plate contains more apples than oranges, or vice versa, in a seemingly effortless and rapid manner. We first explored how those decisions might be modeled with the simple random-walk model in Chapter 2. At the time, we already noted the importance of the modeler's decisions during the construction of a model, and we placed the random-walk idea into a broader context of sequential-sampling models – that is, models that stipulate that the cognitive system is sampling information from the displayed stimulus over time in order to reach a decision.

We resume our exploration of response-time models by revisiting the taxonomy of models proposed by Ratcliff et al. (2016), shown again in Figure 14.1. At the time of this writing, the random-walk model from Chapter 2 is primarily of historical and pedagogical interest. Contemporary research interest is instead focused on the remaining models, including in particular the diffusion model of Ratcliff and colleagues and the linear ballistic accumulator (LBA) of Brown, Heathcote, and colleagues. We focus on those two particularly popular models.

We first introduce the diffusion model and show how it can be applied to data using maximum likelihood estimation. We then explore how the power of this model derives from its ability to describe performance in a choice task across the main response measures, namely speed and accuracy, thereby resolving a long-standing dilemma concerning the relationship between accuracy and speed. We show that the model is nonetheless in principle falsifiable. We then turn to the LBA and show how it can provide an alternative account of the data.

Ratcliff's Diffusion Model

The first variant of the diffusion model in psychology was proposed nearly four decades ago (Ratcliff, 1978). Although it has evolved considerably since then (for a brief history, see Ratcliff et al., 2016), the fundamental premise of the model has proven resilient across that time.