A moving average model for sequenced reaction-time data

Reaction times are often collected in order to study the durations of hypothesized subprocesses. In many important cases, reaction times are collected for a sequence of tasks in which the processing for one task is a subset of the processing required for the next in the sequence. Data of this sort have been analyzed by multiple-regression methods. Here we propose a more sophisticated moving average model for such data. We show that ordinary multiple-regression methods produce estimates that are consistent, but not efficient, and that the usual R² statistic may provide a misleading impression of goodness of fit. One consequence of the suggested statistical model is that it allows the same quantity of data to be used to fit a psychological model to a larger range of tasks.