Interactive Diagnostic Plots for Multidimensional Scaling with Applications in Psychosis Disorder Data Analysis

Abstract: Multidimensional scaling (MDS) represents objects as points in an Euclidean space so that the perceived distances between points can reflect similarity (or dissimilarity) between objects. To be practical, the dimension of the projected space usually is kept as low as possible. Thus, it is unavoidable that part of the information in the original proximity matrix will be lost in the MDS plot. To assess the overall quality of projection, classical MDS diagnostic indices and plots are available. However, these global-fitness methods do not address another issue: how well represented is a specified individual object or a pair of objects in the projected space? Here, via the concept of color-linkage, a dynamic graphical system is developed for revealing the subtle spatial lack-of-fit pattern for any specified individual object. The proposed method is illustrated by using a data set from a psychopathological research project.