  Many psychological experiments have subjects repeat a task to gain the
statistical precision required to test quantitative theories of psychological
performance. In such experiments, time-on-task can have sizable effects on
performance, changing the psychological processes under investigation. Most
research has either ignored these changes, treating the underlying process as
static, or sacrificed some psychological content of the models for statistical
simplicity. We use particle Markov chain Monte-Carlo methods to study
psychologically plausible time-varying changes in model parameters. Using data
from three highly-cited experiments we find strong evidence in favor of a
hidden Markov switching process as an explanation of time-varying effects. This
embodies the psychological assumption of "regime switching", with subjects
alternating between different cognitive states representing different modes of
decision-making. The switching model 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.
