Conflict tasks are one of the most widely studied paradigms within cognitive psychology, where participants are required to respond based on relevant sources of information while ignoring conflicting irrelevant sources of information. The flanker task, in particular, has been the focus of considerable modeling efforts, with only three models being able to provide a complete account of empirical choice response time distributions: the dual- stage two-phase model (DSTP), the shrinking spotlight model (SSP), and the diffusion model for conflict tasks (DMC). Although these models are grounded in different theoretical frameworks, can provide diverging measures of cognitive control, and are quantitatively distinguishable, no previous study has compared all three of these models in their ability to account for empirical data. Here, we perform a comparison of the precise quantitative predictions of these models through Bayes factors, using probability density approximation to generate a pseudo-likelihood estimate of the unknown probability density function, and thermodynamic integration via differential evolution to approximate the analytically intractable Bayes factors. We find that for every participant across three data sets from three separate research groups, DMC provides an inferior account of the data to DSTP and SSP, which has important theoretical implications regarding cognitive processes engaged in the flanker task, and practical implications for applying the models to flanker data. More generally, we argue that our combination of probability density approximation with marginal likelihood approximation – which we term pseudo-likelihood Bayes factors – provides a crucial step forward for the future of model comparison, where Bayes factors can be calculated between any models that can be simulated. We also discuss the limitations of simulation-based methods, such as the potential for approximation error, and suggest that researchers should use analytically or numerically computed likelihood functions when they are available and computationally tractable.
Parallel probability density approximation
