Connecting process models to response times through Bayesian hierarchical regression analysis

We propose a hierarchical Bayesian model that connects the counts of elementary processing steps from a process model with response times of individual participants in an experiment. We see our approach as bridging between the two fields of mathematical psychology and cognitive architectures. For models that are a bit simpler than GOMS (they need to be broken down into a count of one kind of processing step) we can make detailed response time analyses. We model each processing step as a draw from a Gamma distribution, so that for more elementary processing steps we expect both mean response time as well as variance to increase. We present two extensions of the basic model. We first extend the model to account for cases in which the number of processing steps is stochastic and unobserved. The second extension allows to work with several possible processing tactics and we don't know which tactics the participants use. From the distribution of response times it can thus be distinguished what kind of tactic was most likely used to which degree by each participant. We hope that our model will be a useful starting point for many similar analyses, allowing process models to be fit to and tested through detailed response time data.