, Volume 55, Issue 4, pp 617–632 | Cite as

Rasch-representable reaction time distributions

  • Dirk Vorberg
  • Wolfgang Schwarz


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.

Key words

Rasch test model serial model parallel model reaction time distributions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ashby, F. G. & Townsend, J. T. (1980). Decomposing the reaction time distribution: Pure insertion and selective influence revisited.Journal of Mathematical Psychology, 21, 93–123.Google Scholar
  2. Bamber, D. (1975). The area above the ordinal dominance graph and the below the Receiver Operating Characteristic graph.Journal of Mathematical Psychology, 12, 387–415.Google Scholar
  3. Colonius, H. (1984).Stochastische Theorien individuellen Wahlverhaltens [Stochastic theories of individual choice behavior]. Heidelberg: Springer.Google Scholar
  4. Donders, F. C. (1968). Die Schnelligkeit psychischer Processe [On the speed of mental processes],Archiv für Anatomie und Physiologie und Wissenschaftliche Medizin, 657–681.Google Scholar
  5. Donders, F. C. (1969). Over de snelhed van psychische processen [On the speed of mental processes]. In W. G. Koster (Ed.), Attention and Performance II,Acta Psychologica, 30, 412–431.Google Scholar
  6. Drösler, J. (1986). Figurale Wahrnehmung doch additiv? [Is figural perception additive?].Zeitschrift für experimentelle und angewandte Psychologie, 33, 351–359.Google Scholar
  7. Feller, W. (1966).An introduction to probability theory and its applications (Vol. II). New York: Wiley.Google Scholar
  8. Green, D. M., & Swets, J. A. (1966).Signal detection theory and psychophysics, New York: Wiley.Google Scholar
  9. Johnson, N. L. & Kotz, S. (1970).Distributions in statistics (Vol. II). Boston: Houghton Mifflin.Google Scholar
  10. Luce, R. D. (1959).Individual choice behavior. New York: Wiley.Google Scholar
  11. Luce, R. D. (1986).Response times. New York: Oxford University Press.Google Scholar
  12. McGill, W. J. (1963), Stochastic latency mechanisms. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of mathematical psychology (Vol. I, pp. 309–360). New York: Wiley.Google Scholar
  13. Meijers, L. M. M., & Eijkman, E. G. J. (1974). The motor system in simple reaction experiments.Acta Psychologica, 38, 367–377.Google Scholar
  14. Micko, H. C. (1969). A psychological scale for reaction time measurement. In W. G. Koster (Ed.), Attention and Performance II,Acta Psychologica, 30, 324–335.Google Scholar
  15. Micko, H. C. (1970). Eine Verallgemeinerung des Meβmodells von Reasch mit einer Anwendung auf die Psychophysik der Reaktionen [A generalization of Reash's measurement model with an application to the psychiphysics of reactions].Psychologische Beiträge, 12, 4–22.Google Scholar
  16. Rasch, G. (1966). An item analysis which takes individual differences into account.British Journal of Mathematical and Statistical Psychology, 19, 49–57.Google Scholar
  17. Ross, S. M. (1983).Stochastic processes. New York: Wiley.Google Scholar
  18. Sterngberg, S. (1969). The discovery of processing stages: Extensions of Donder's method. In W. G. Koster (Ed.), Attention and Performance II,Acta Psychologica, 30, 276–315.Google Scholar
  19. Townsend, J. T. & Ashby, F. G. (1983).The stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.Google Scholar
  20. Ulrich, R., & Stapf, K. (1984). A double-response paradigm to study stimulus intensity effects upon motor system in simple reaction time experiments.Perception & Psychophysics, 36, 545–558.Google Scholar
  21. Wilk, M. B. & Gnanadesikan, R. (1969). Probability plotting methods for the analysis of data.Biometrika, 55, 1–17.Google Scholar

Copyright information

© The Psychometric Society 1990

Authors and Affiliations

  • Dirk Vorberg
    • 1
  • Wolfgang Schwarz
    • 1
  1. 1.Fachbereich Psychnologie Philipps-Universität MarburgGermany

Personalised recommendations