Constrained multidimensional unfolding of confusion matrices: Goal point and slide vector models

Two constrained multidimensional unfolding models, the goal point and slide vector models, are proposed for analyzing confusion matrices. In both models, the row and column stimuli are expressed as two sets of points in a low-dimensional space, where the difference vector connecting a column point to the corresponding row point indicates the change in the stimulus representation through a cognitive process. The difference vector is constrained by the hypothesis that the trend in the representational change is invariant across stimuli: the goal point model constrains all difference vectors to point toward a single point, and the slide vector model constrains all difference vectors to be parallel to each other. In both models the coordinates of points are estimated by the maximum-likelihood method. Examples illustrate that the two models allow us to examine hypotheses about invariant trends in representational changes and to grasp such trends from the resulting configurations.