Multidimensional Scaling (MDS) is a descriptive technique, to look for underlying dimensions or structure behind a set of objects. For a given set of objects, the similarity or dissimilarity between each pair must first be determined. This MDS overview document presents different ways of operationalizing similarity/dissimilarity. One ends up with a visual diagram, where more-similar objects end up physically close to each other. As with other techniques we've learned this semester (e.g., log-linear models, cluster analysis), there is no "official" way to determine which solution, of different possible ones, to accept. MDS provides different guidelines for how many dimensions to accept, one of which is the "stress" value (p. 13 of linked article).
The input to MDS in SPSS is either a similarity matrix (e.g., how similar is Object A to Object B? how similar is A to C? how similar is B to C?) or a dissimilarity/distance matrix. Zeroes are placed along the diagonal of the matrix, as it is not meaningful to talk about how similar A is to A, B is to B, etc.
A video on running MDS in SPSS can be accessed via the links column to the right. Once you select your visual solution, you get to name the dimensions, based on where the objects appear in the graph. The video illustrates the use of one particular MDS program called PROXSCAL, in which the numerical values in the input matrix can either represent similarities (i.e., higher numbers = greater similarity) or distances (i.e., higher numbers = greater dissimilarities).
However, the SPSS version we have in our computer lab does not provide access to PROXSCAL (not easily, at least) and only makes a program called ALSCAL readily available. In ALSCAL, higher numbers in the input matrix are read only as distances.
This is presumably where our initial analysis in last Thursday's class went awry. In trying to map the dimensions underlying our Texas Tech Human Development and Family Studies faculty members' research interests, we used the number of times each pair of faculty members had been co-authors on the same article as the measure of similarity. A high number of co-authorships would thus signify that the two faculty members in question had similar research interests. However, ALSCAL treats high numbers as indicative of greater distance (which I failed to catch at the time), thus messing up our analysis.
Once the numbers in the matrix are reverse-scored, so that a high number of co-authorships between a pair of faculty is converted to a low number for distance, then the MDS graph becomes more understandable. Below is an annotated screen-capture from SPSS, on which you can click to enlarge. (The graph does not show some of our newer faculty members, who would not have had much opportunity yet to publish with their faculty colleagues, or some of our faculty members who publish primarily with graduate students or with faculty from outside Texas Tech.)
The stress values shown in the output are somewhere between good and fair, according to the overview document linked above.
And now, our song for this topic...
Multidimensional Scaling is Fun
Lyrics by Alan Reifman
May be sung to the tune of “Minuano (Six Eight)” (Metheny/Mays)
YouTube video of performance here.
Multidimensional scaling, is fun,
Multidimensional scaling, is fun, to run, yeah,
Measure the objects’ similarities,
Or you can enter, as disparities, yes you can,
Multidimensional scaling, is fun,
SPSS is one place, that it’s done,
Submit your matrix in, and a spatial map, will come out,
Multidimensional scaling, is fun,
Multidimensional scaling, is fun,
Multidimensional scaling, is fun, to run, yeah,
Aim for a stress value, below point-ten,
Or you’ll have to run, your model again, yes you will,
Multidimensional scaling, is fun,
ALSCAL is one version, that you can run,
Submit your matrix in, and a spatial map, will come out,
Multidimensional scaling, is fun,
(Guitar improvisation 1:39-3:38, then piano and percussion interlude 3:38-4:55)
Multidimensional scaling, is fun,
Multidimensional scaling, is fun, to run, yeah,
Measure the objects’ similarities,
Or you can enter, as disparities, yes you can,
Multidimensional scaling, is fun,
SPSS is one place, that it’s done,
Submit your matrix in, and a spatial map, will come out,
Multidimensional scaling, is fun,
Multidimensional scaling, is fun,
Multidimensional scaling, is fun, to run, yeah,
Aim for a stress value, below point-ten,
Or you’ll have to run, your model again, yes you will,
Multidimensional scaling, is fun,
PROXSCAL’s another version, you can run,
Submit your matrix in, and a spatial map, will come out,
Multidimensional scaling, is fun,
Yes it’s fun,
Yes it’s fun,
Yes it’s fun,
Let it run!
