The ex-Wald distribution as a descriptive model of response times

Abstract

We propose a new quantitative model of response times (RTs) that combines some advantages of substantive, process-oriented models and descriptive, statistically oriented accounts. The ex-Wald model assumes that RT may be represented as a convolution of an exponential and a Wald-distributed random variable. The model accounts well for the skew, shape, and hazard function of typical RT distributions. The model is based on two broad information-processing concepts: (1) a data-driven processing rate describing the speed of information accumulation, and (2) strategic response criterion setting. These concepts allow for principled expectations about how experimental factors such as stimulus saliency or re-sponse probability might influence RT on a distributional level. We present a factorial experiment involving mental digit comparisons to illustrate the application of the model, and to explain how substantive hypotheses about selective factor effects can be tested via likelihood ratio tests.