Multidimensional Scaling - Group C - Session 9,10

Multidimensional Scaling

Posted by Vijay Seelam (Roll No 14059, Group C, Operations)

Multidimensional scaling (MDS) can be considered to be an alternative to factor analysis. In general, the goal of the analysis is to detect meaningful underlying dimensions that allow the researcher to explain observed similarities or dissimilarities (distances) between the investigated objects. In factor analysis, the similarities between objects (e.g., variables) are expressed in the correlation matrix. With MDS, you can analyze any kind of similarity or dissimilarity matrix, in addition to correlation matrices.

Logic of MDS

Suppose we take a matrix of distances between major Indian cities from 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

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).

Applications

The "beauty" of MDS is that we can analyze any kind of distance or similarity matrix. These similarities can represent people's ratings of similarities between objects, the percent agreement between judges, the number of times a subjects fails to discriminate between stimuli, etc. For example, MDS methods used to be very popular in psychological research on person perception where similarities between trait descriptors were analyzed to uncover the underlying dimensionality of people's perceptions of traits. They are also very popular in marketing research, in order to detect the number and nature of dimensions underlying the perceptions of different brands or products.

In general, MDS methods allow the researcher to ask relatively unobtrusive questions ("how similar is brand A to brand B") and to derive from those questions underlying dimensions without the respondents ever knowing what is the researcher's real interest.