Multidimensional Scaling

Multidimensional scaling (MDS) will be explained at this point chiefly because it, too, is a form of proximity mea surement. It is a method for finding a configuration of points for individuals from information about the distance between the points. The usual metric is similarity or dissimilarity judgments, but correlation matrices, attribute ratings, or Euclidean distances can be used. The r x c matrix is generally not one of n x p but rather n x n. It has been stated that the strategy in MDS is to look for the solution with the smallest dimensionality in which the differences between the reconstructed distances and the original proximities are acceptably small (17). Smaller stress values indicate more satisfactory fit. Various programs for the analysis of proximity data have been described (18). It has been pointed out that MDS and correspondence analysis have some features in common with PCA (19). For MDS, if n > p, then a PCA should generally be preferred because it is easier to find the eigenvectors of a p x p matrix than the larger n x n matrix. The theory and methods of MDS have been published (20).

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