Multidimensional Scaling Introductory Overview - Logic of MDS

The following simple example may demonstrate the logic of a Multidimensional Scaling analysis. Suppose we take a matrix of distances between major US cities from a map. We then analyze this matrix, specifying that we want to reproduce the distances based on two dimensions. As a result of the MDS analysis, we would most likely obtain a two-dimensional representation of the locations of the cities, that is, we would basically obtain a two-dimensional map.

In general then, MDS attempts to arrange "objects" (major cities in this example) in a space with a particular number of dimensions (two-dimensional in this example) so as to reproduce the observed distances. As a result, we can "explain" the distances in terms of underlying dimensions; in our example, we could explain the distances in terms of the two geographical dimensions: north/south and east/west.

Orientation of axes
As in factor analysis, the actual orientation of axes in the final solution is arbitrary. To return to our example, we could rotate the map in any way we want, the distances between cities remain the same. Thus, the final orientation of axes in the plane or space is mostly the result of a subjective decision by the researcher, who will choose an orientation that can be most easily explained. To return to our example, we could have chosen an orientation of axes other than north/south and east/west; however, that orientation is most convenient because it "makes the most sense" (i.e., it is easily interpretable).