Decomposing the Reaction Time Distribution: Pure insertion and Selective Influence Revisited1

This paper investigates the consequences of extending the assumptions of pure insertion and selective influence (popular in RT theorizing) to the level of the distribution. In the case of pure insertion and under the additional assumption that the additive random variable is exponentially distributed, a solution is obtained which not only allows estimation of the exponential-rate parameter but also provides a test of the assumptions. The result is shown to be applicable not only when processing is serial but also for certain parallel models. In addition, discrimination between self-terminating and exhaustive search strategies is provided, and in the case of either, both parameter estimation and tests of the model are possible. Extensions to nonexponential models are investigated and a general method of moments solution is outlined. In the case of selective influence a general non-parametric alternative to Sternberg’s additive factor method is developed. The problem of empirical estimation and application is then considered. Simulations which place bounds on the type I and II error are reported. Finally the first theorem is provided an illustrative application with data from a memory scanning experiment. The results provide some support for the double assumption of pure insertion and that the additiv