A model of timing in simple anticipatory decisions

Response time models are typically applied to make predictions about when participants will react to a stimulus. However, many of the choices we make require us to proactively plan when to act: when to leave home to arrive somewhere on time, when to swing at a ball to hit it (tennis, baseball, cricket), and so on. These anticipatory responses can also be modeled as an evidence accumulation process, where we form joint expectations of both object and time. To understand these dynamic representations, participants were asked to make decisions about two anticipated events. In an initial experiment, they were asked to decide when a moving, partially occluded ball will hit a wall. In a second experiment, participants were asked to infer the ball’s position at a particular time after it became occluded behind the wall. We manipulated the speed at which the ball travels, its distance from the wall, and the time for which the ball is occluded, forcing the decision-maker to mentally represent and calculate the object’s dynamic position and motion as they form judgements about eventual locations or timing. We model response times using the extended Wald accumulator model to draw parallels between the changes in speed, distance, and length with the corresponding changes in the model’s parameters: drift, threshold, and non-decision time. The results from both tasks suggest that response times in anticipatory decisions are right-skewed -- mostly too slow -- and the estimated parameters of the Wald model successfully predicted individual response times by condition.