The implementation of a model of choice: the (truncated) linear ballistic accumulator

It is very common in cognitive science and psychology to use experimental tasks that involve making a fast choice among a restricted number of alternatives. While a class of choice models, the so-called sequential-sampling models, can give an accurate account of the relationship between the accuracy of the choice and the time it took to respond, it is fairly common to ignore the tradeoff between accuracy and response times and analyze them as if they were independent. The reason for this is that sequential-sampling models are mathematically and computationally difficult to apply. In this notebook, I focus on one influential and relatively simple model that belongs to the class of sequential-sampling models: the linear ballistic accumulator with a drift rate drawn from a normal distribution (restricted to positive values) (S. D. Brown and Heathcote 2008; Heathcote and Love 2012). Even though this model has been proved to be well-suited for tasks that elicit a speeded response (out of any number of possible choices), its hierarchical version is difficult to implement and fit. First, I discuss the motivation for fitting this model using the Stroop task (Stroop 1935) as a case study. Then, I discuss the challenges in the implementation of the model in (R)Stan (Stan Development Team 2017), which might also apply to other hierarchical models with complex likelihood functions. Finally, I show some results that exemplify how the linear ballistic accumulator can be used for examining individual differences.