Rasch-representable reaction time distributions

This article investigates properties of a representation based on the Rasch test model for reaction times (RT) that was proposed by Micko. Necessary and sufficient conditions for a set of RT distributions to be Rasch-representable are derived. It is shown that independent serial and independent parallel processing models cannot be reconciled with the representation. However, random extreme models compatible with the Reasch-representation exist that assume RT is determined by the longest or he shortest processing time of a random number of independent paraloel channels. Nonparametric properties of Rasch-representable distributions are derived that can be used for testing the model and for estimating its parameters. Conditions are presented for Rasch-representable distributions to form a scale family. Finally, Rasch-represent-able distributions are characterized interms of their hazard functions.For helpful discussions, we are grateful to Hans Irtel, Christoph Micko, Hartmann Scheiblechner, and Hans-Henning Schultz.