Abstract
Wide use has been made of multidimensional scaling (MDS) techniques since the pioneering papers of Shepard and Kruskal. In the main, dissimilarities used in the various MDS techniques are derived for pairs of objects or stimuli. This is termed 2‐way, 1‐mode data, meaning pairs of objects within a single set are considered. Some MDS techniques are designed for 3‐way or even higher, and for 2‐mode, 3‐mode or more. One such example is the CANDECOMP model which can deal with n‐way, m‐mode data where 3≤n≤7 and 2≤m≤7. This model considers n‐tuples of objects at a time, selecting these from m different sets.To date there are no models which consider n‐way, 1‐mode data, where n≥3. An attempt is made in this paper to cater for this situation by an extension of the Shepard‐Kruskal approach to non‐metric multidimensional scaling which deals with dissimilarities defined for three or more objects. A computer program has been written using the new model to produce a configuration in Euclidean space to represent the objects. Some historical voting data and some artificial data are then analysed.
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