A hidden Markov switching process captures dynamic effects of time-on-task in decision making.

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 important and 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 -- both in magnitude and direction. Model-based analysis reveals how different cognitive processes contribute to the observed changes. We find strong evidence in favor of a Markov switching process for the time-based evolution of individual subjects' model parameters. This embodies the psychological theory that participants switch in and out of different cognitive states during the experiment. The central idea of our approach can be applied quite generally to quantitative psychological theories, beyond the model that we investigate and the experimental data that we use.