Time-evolving psychological processes over repeated decisions

Many psychological experiments have participants repeat a simple task. This repetition is often necessary in order to gain the statistical precision required to answer questions about quantitative theories of the psychological processes underlying performance. In such experiments, time-on-task can have sizable effects on performance, changing the psychological processes under investigation in interesting ways. These changes are often ignored, and the underlying process is treated as static. We propose modern statistical approaches that are based on recent advances in particle Markov chain Monte-Carlo (MCMC) to extend a static model of decision-making to account for time-varying changes in a psychologically plausible manner. Using data from three highly-cited experiments we show that there are changes in performance with time-on-task, and that these changes vary substantially over individuals. We find strong evidence in favor of a hidden Markov switching process as an explanation of time-varying effects. This embodies the psychological assumption that participants switch between different cognitive states, representing different modes of decision-making, and explains key long- and short-term dynamic effects in the data. The central idea of our approach can be applied quite generally to quantitative psychological theories, beyond the models and data sets that we investigate.