Some Modified Inhibition Models for Response Time series

Abstract

A modification of the Inhibition model of Van der Ven and Smit (Van Breukelen, Jansen, Roskam, Van der Ven & Smit, 1987), is derived which contains four parameters and conceptually lies between the three-parameter Poisson-Erlang model of Pieters and Van der Ven (1982) and the five-parameter Inhibition model, which both appeared to be partly valid In an earlier study. These models were derived to describe response time (RT) series on simple overlearned mental tasks, such as concentration tests, and assume that for a given subject, type of item and condition, the processing time is a constant whereas RT variability is due to the random occurrence of short distractions. The modified model, called the IMAX model, predicts an RT trend much like the exponential trend predicted by the Inhibition model, but in contrast with it, predicts a zero autocorrelation between successive RTs, and under stationarity reduces to the Poisson-Erlang model. Parameter estimators are derived and the model is shown to fit empirical data acceptably. Because some data indicate variability of the processing time, the IMAX and the original Inhibition model are next both derived by replacing the assumption of a constant processing time by the less restrictive assumption that the processing time is a stochast with finite mean and variance and stationary probability density. It is shown that then the IMAX model almost and the Inhibition model exactly predicts the same RT trend as the original Inhibition model with constant processing time. It is further shown that the autocorrelation predicted by the Inhibition model approaches zero as the processing time variance increases. As a result, the IMAX and Inhibition model may become empirically equivalent with respect to trend and autocorrelation, for increasing processing time variance.