An extension of the shifted Wald model of human response times: Capturing the time dynamic properties of human cognition : Trial-varying Wald model.

Despite the ubiquitous nature of evidence accumulation models in cognitive and experimental psychology, there has been a comparatively limited uptake of such techniques in the applied literature. While quantifying latent cognitive processing properties has significant potential for applied domains such as adaptive work systems, accumulator models often fall short in practical applications. Two primary reasons for these shortcomings are the complexities and time needed for the application of cognitive models, and the failure of current models to capture systematic trial-to-trial variability in parameters. In this manuscript, we develop a novel, trial-varying extension of the shifted Wald model to address these concerns. By leveraging conjugate properties of the Wald distribution, we derive computationally efficient solutions for threshold and drift parameters which can be updated instantaneously with new data. The resulting model allows the quantification of systematic variation in latent cognitive parameters across trials and we demonstrate the utility of such analyses through simulations and an exemplar application to an existing data set. The analytic nature of our solutions opens the door for real-world applications, significantly extending the reach of computational models of behavioral responses.