Tree inference with factors selectively influencing processes in a processing tree

We show how to systematically construct a processing tree using data from an experiment in which two experimental factors are intended to selectively influence two different processes. Only two arrangements are possible for the two selectively influenced processes: ordered and unordered. We show that there are only two standard trees that need be considered, one for each arrangement. Necessary and sufficient conditions are given for each tree to be applicable. If the conditions do not hold, no tree is possible. If the selectively influenced processes are ordered, their order is sometimes determined by the data. We consider two factors that selectively influence two processes in every tree in a set of trees, such that on a given trial, a tree is selected from the set at random. We show that if the influenced processes are ordered in every tree or unordered in every tree, then the mixture of trees is equivalent to one of the two standard trees. To illustrate the method, a tree is constructed from simulated data from a model of Batchelder and Riefer Batchelder, W.H., Riefer, D.M. (1980). Separation of storage and retrieval factors in free recall of clusterable pairs. Psychological Review, 87, 375–397].