GRICE-REPRESENTABILITY OF RESPONSE-TIME DISTRIBUTION FAMILIES

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.