Tree inference: Selective influence in multinomial processing trees with supplementary measures such as response time

Abstract

Multinomial Processing Trees are successful models of response probabilities for many phenomena. Empirical validation is often based on manipulating an experimental factor intended to selectively influence a process represented in a Multinomial Processing Tree, to see whether the factor indeed has an effect on and only on a parameter associated with that process. Response times are rarely included, but have great potential for increasing resolution. We consider Multinomial Processing Trees in which outcomes of processes represented by vertices occur with probabilities (as usual), and also take time. For response time itself, the method of selectively influencing processes is well developed. Established tests are based on response time means and distribution functions. We modify well established tests so they can be applied to Multinomial Processing Trees in which responses fall into two classes, say, correct and incorrect. The new tests are based on response time means and distribution functions, each multiplied by response probability. If two experimental factors selectively influence two different vertices in a two class Multinomial Processing Tree, the tree is equivalent to one of two simple trees. Patterns in response probabilities and times will indicate which of the two trees accounts for the data. In one of the two trees, the selectively influenced vertices are executed in order, in the other they are not. If there are more than two response classes, each class can be tested separately. If the patterns do not occur, no Multinomial Processing Tree exists in which the two experimental factors selectively influence two different vertices. We demonstrate the method with simulated data from a two factor experiment.