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 responses are arranged in a tree structure. Evidence often indicates further that an experimental 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 examining 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 imposed on the trees considered: There were two classes of responses; parameters were probabilities, bounded above by 1; and factors were assumed to change parameters associated with children of a single vertex. More general results are derived here, removing these restrictions. Results on representation, uniqueness of parameters, uniqueness of tree structure, and mixtures of trees are presented.