Multiplicatively Interacting Factors Selectively Influencing Parameters in Multiple Response Class Processing and Rate Trees

Evidence in many experiments indicates that the processes involved in producing re-sponses are arranged in a tree structure. Evidence often indicates further that an ex-perimental factor, such as item similarity, changes a single parameter, leaving others invariant. In typical studies, a few tree structures are hypothesized a priori, and tested by goodness of fit. With the method of Tree Inference, a tree is constructed by exam-ining the data to see if patterns occur that are predicted when two factors selectively influence different processes (Schweickert & Chen, 2008). The patterns can reveal, for example, whether selectively influenced processes are executed in order, and what the order is. If the patterns do not occur, one can conclude that no tree is possible in which the factors selectively influence processes. In earlier work, three restrictions were im-posed on the trees considered: There were two classes of responses; parameters were probabilities, bounded above by 1; and factors were assumed to change parameters as-sociated with children of a single vertex. More general results are derived here, remov-ing these restrictions. Results on representation, uniqueness of parameters, uniqueness of tree structure, and mixtures of trees are presented