Connecting process models to response times through Bayesian hierarchical regression analysis

Process models specify a series of mental operations necessary to complete a task. We demonstrate how to use process models to analyze response-time data and obtain parameter estimates that have a clear psychological interpretation. A prerequisite for our analysis is a process model that generates a count of elementary information processing steps (EIP steps) for each trial of an experiment. We can estimate the duration of an EIP step by assuming that every EIP step is of random duration, modeled as draws from a gamma distribution. A natural effect of summing several random EIP steps is that the expected spread of the overall response time increases with a higher EIP step count. With modern probabilistic programming tools, it becomes relatively easy to fit Bayesian hierarchical models to data and thus estimate the duration of a step for each individual participant. We present two examples in this paper: The first example is children's performance on simple addition tasks, where the response time is often well predicted by the smaller of the two addends. The second example is response times in a Sudoku task. Here, the process model contains some random decisions and the EIP step count thus becomes latent. We show how our EIP regression model can be extended to such a case. We believe this approach can be used to bridge the gap between classical cognitive modeling and statistical inference and will be easily applicable to many use cases.