This chapter introduces the basic terms required to enter the world of modeling while at the same time providing an overview of the entire enterprise. For illustrative purposes, our discussion focuses on a simple model that was developed 50 years ago to describe how people make decisions in a speeded-choice task.
Response Times in Speeded-Choice Tasks
You are in the cognitive laboratory to participate in an experiment. A tight cluster of 300 lines at various orientations is projected onto the screen in front of you. Are they predominantly tilted to the left or to the right? The experimenter has instructed you to respond as quickly as possible by pressing one of two keys: “z” for “left” and “/” for “right.” There are many such trials and in addition to being speedy, you are also asked to be as accurate as possible. Because the orientations of individual lines within each stimulus cluster are drawn from a distribution with considerable variance, the task is quite difficult.
The procedure just summarized was from an experiment by Smith and Vickers (1988) and is representative of a “choice reaction time” task. Although the task sounds simple, the data from such experiments are strikingly rich and can provide a broad window into human cognition. There are two classes of responses (correct and incorrect), and each class is characterized by an entire distribution of response times across the numerous trials of each type. A complete account of human performance in this quintessential decision-making task would thus describe response accuracy and latency, and the relationship between the two, as a function of various experimental manipulations. For example, the mean orientation of the lines might be changed or participants might be instructed to emphasize speed over accuracy, or vice versa.
There currently exist a number of sophisticated models that can describe performance in choice reaction time tasks (Brown and Heathcote, 2008; Ratcliff, 1978;Wagenmakers et al., 2007), and we will explain some of those in detail later in Chapter 14. For present purposes, we step back in time by approximately 50 years and illustrate the theoretical challenges associated with modeling choice tasks by building a model from scratch.
We begin with the assumption that when a stimulus is presented, not all information is available to the decision maker instantaneously. Instead, people gradually build up the evidence required to make a decision.