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Grice-Representability of Response Time Distribution Families

Published online by Cambridge University Press:  01 January 2025

Ehtibar N. Dzhafarov
Ehtibar N. Dzhafarov*
Affiliation:
University of Illinois at Urbana-Champaign The Beckman Institute For Advanced Science and Technology
*
Requests for reprints should be sent to Ehtibar N. Dzhafarov, Department of Psychology, University of Illinois at Urbana-Champaign, 603 East Daniel Street, Champaign, IL 61820.
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Abstract

Any family of simple response time distributions that correspond to different values of stimulation variables can be modeled by a deterministic stimulation-dependent process that terminates when it crosses a randomly preset criterion. The criterion distribution function is stimulation-independent and can be chosen arbitrarily, provided it is continuous and strictly increasing. Any family of N-alternative choice response time distributions can be modeled by N such process-criterion pairs, with response choice and response time being determined by the process that reaches its criterion first. The joint distribution of the N criteria can be chosen arbitrarily, provided it satisfies certain unrestrictive conditions. In particular, the criteria can be chosen to be stochastically independent. This modeling scheme, therefore, is a descriptive theoretical language rather than an empirically falsifiable model. The only role of the criteria in this theoretical language is to numerically calibrate the ordinal-scale axes for the deterministic response processes.

Keywords

response timechoicecriteriondeterministic processstochastic process
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 2 , June 1993 , pp. 281 - 314
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

The author is indebted to Richard Schweickert, James Townsend, and Duncan Luce for valuable comments and criticism.

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