Adding a speed-accuracy trade-off to discrete-state models: A comment on Heck and Erdfelder (2016)

Heck and Erdfelder (2016) developed a model that extends discrete-state multinomial processing tree models to response time (RT) data. Their model is an important advance, but it does not have a mechanism to produce the speed-accuracy trade-off, the bedrock empirical observation that rushed decisions are less accurate. I present a similar model, the "discrete-race" model, with a simple mechanism for the speed-accuracy trade-off. In the model, information that supports detection of the stimulus type is available for some proportion of items and unavailable for others. Both the amount of time needed for detection to succeed and the amount of time that the decision maker waits before guessing are variable from trial to trial. Responses are based on detection when it is available and has a finishing time before the guess time for that trial. In other words, the decision maker sometimes loses opportunities to respond correctly on the basis of detection by first making a guess. These lost opportunities are more common when the guess-time distribution tends to have low wait times, which decreases accuracy. I report simulations showing that the model can accurately recover parameter values and is strongly constrained by the speed-accuracy trade-offs across conditions with different levels of response caution.