In addition to fulfilling the goals of detecting underlying structure and data reduction that is shares with other methods, multidimensional scaling (MDS) provides the researcher with a spatial representation of data that can facilitate interpretation and reveal relationships. Therefore, we can define MDS as "a set of multivariate statistical methods for estimating the parameters in and assessing the fit of various spatial distance models for proximity data" (Davison, 1983)
The spatial display of data provided by MDS is why it is also sometimes referred to as perceptual mapping.
As mentioned in the Introduction, MDS has much more flexibility about the types of data that can be used to generate the solution. Almost any measures of similarity and dissimilarity can be used, depending on what your statistical computer software will accept. (See cautions page for more information.)
In general, there are two types of MDS:
Metric MDS makes the assumption that the input data is either ratio or interval data, while the non-metric model requires simply that the data be in the form of ranks. Therefore, the non-metric model has more fewer restrictions than the metric model, but also less rigor. One technique to use if you are unsure whether your data is ordinal or can be considered interval is to try both metric and non-metric models. If the results are very close, the metric model may be used.
An advantage of the non-metric models is that they permit the researcher to categorize and examine preference data, such as the kind obtained in marketing studies or other areas where comparisons are useful.
Another technique, correspondance analysis, can work with categorical data, i.e., data at the nominal level of measurement, however that technique will not be described here.
We have already seen that MDS can accept more different measures of similarity and dissimilarity than factor analysis techniques can. In addition, there are some differences in terminology. These differences reflect the origin of MDS in the field of pyschology. The measure corresponding to factors are called alternatively dimensions or stimulus coordinates.
The output of MDS looks very similar to that of factor analysis and the determination of the optimal number of dimensions is handled in much the same way.
There are four basic steps in MDS:
Let us say that you have a matrix of distances between a number of major cities, such as you might find on the back of a road map. These distances can be used as the input data to derive an MDS solution. When the results are mapped in two dimensions, the solution will reproduce a conventional map, except that the MDS plot might need to be rotated so that the north-south and east-west dimensions conform to expectations. However, the once the rotation is completed, the configuration of the cities will be spatially correct.
Check out Trochim's concept mapping which also employs MDS in order to develop a visual representation of the structured conceptualization of a group of people.
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