Multidimensional Scaling Overview
Multidimensional Scaling (MDS) can be considered to be an alternative to Factor Analysis. The goal of the analysis is to detect meaningful underlying dimensions that allow the researcher to explain observed similarities or dissimilarities of distances between the investigated objects. In factor analysis, the similarities between objects (example, 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
MDS attempts to arrange objects in a space with a particular number of dimensions to reproduce the observed distances. As a result, we can explain the distances in terms of underlying dimensions.
Orientation of axes in the plane or space is mostly the result of a subjective decision by the researcher, who chooses an orientation that can be most easily explained. In factor analysis, the actual orientation of axes in the final solution is arbitrary.
Computational Approach
Multidimensional Scaling is a way to rearrange objects in an efficient manner to arrive at a configuration that best approximates the observed distances. The program moves objects around in the space defined by the requested number of dimensions and checks how well the distances between objects can be reproduced by the new configuration.
How Many Dimensions to Specify?
If the number of dimensions we use in order to reproduce the distance matrix is more, we get a better fit of the reproduced matrix to the observed matrix. If we use as many dimensions as there are variables, then we can perfectly reproduce the observed distance matrix.
Interpreting the Dimensions
The interpretation of dimensions usually represents the final step of the analysis. The actual orientations of the axes from the Multidimensional Scaling analysis are arbitrary, and can be rotated in any direction.
Applications
You can analyze any kind of distance or similarity matrix. MDS methods enable the researcher to ask relatively unobtrusive questions and to derive from those questions underlying dimensions without the respondents ever knowing what is the researcher's real interest.
MDS and Factor Analysis
Even though there are similarities in the type of research questions to which these two procedures can be applied, Multidimensional Scaling and Factor Analysis are fundamentally different methods. Factor analysis requires that the underlying data are distributed as multivariate normal, and that the relationships are linear. MDS imposes no such restrictions. MDS methods are applicable to a wide variety of research designs because distance measures can be obtained in any number of ways.