A hierarchical Bayesian shifted Wald model with censoring

Modeling performance on cognitive tasks with accuracy at or near ceiling presents modelers with a difficult choice. One option is to use the full diffusion model, but high accuracy makes it difficult to obtain enough error trials to allow accurate estimation of the diffusion parameters. Another option is to use a single-boundary accumulator, such as the shifted Wald distribution. However, despite their conceptual similarity, the parameters of the shifted Wald distribution do not correspond uniquely to those of the diffusion model, and thus, the ability to interpret shifted Wald parameters in the context of a cognitive model is compromised. One way to "split the difference" is to introduce a censoring mechanism to the shifted Wald distribution, which allows the small number of error trials to be modeled as correct trials which have undergone censoring. Miller et al. (2018) showed that this censored shifted Wald model was able to successfully recover diffusion model parameters in high-accuracy contexts. In this talk, I will describe a hierarchical Bayesian version of the censored shifted Wald model. In addition, I will share some preliminary data from a parameter recovery study that shows its superior ability to accurately recover diffusion model parameters compared to classical maximum likelihood approaches. Finally, I will describe an application of the model to an open question in numerical cognition.