The MDS Procedure

Getting Started: MDS Procedure

The simplest application of PROC MDS is to reconstruct a map from a table of distances between points on the map (Kruskal and Wish 1978, pp. 7–9). For example, the following DATA step reads a table of flying mileages between 10 U.S. cities:

   data city;
      title 'Analysis of Flying Mileages between Ten U.S. Cities';
      input (Atlanta Chicago Denver Houston LosAngeles
             Miami NewYork SanFrancisco Seattle WashingtonDC) (5.)
             @56 City $15.;
      datalines;
       0                                                  Atlanta
     587    0                                             Chicago
    1212  920    0                                        Denver
     701  940  879    0                                   Houston
    1936 1745  831 1374    0                              Los Angeles
     604 1188 1726  968 2339    0                         Miami
     748  713 1631 1420 2451 1092    0                    New York
    2139 1858  949 1645  347 2594 2571    0               San Francisco
    2182 1737 1021 1891  959 2734 2408  678    0          Seattle
     543  597 1494 1220 2300  923  205 2442 2329    0     Washington D.C.
   ;

Since the flying mileages are very good approximations to Euclidean distance, no transformation is needed to convert distances from the model to data. The analysis can therefore be done at the absolute level of measurement, as displayed in the following PROC MDS step (LEVEL=ABSOLUTE). The following statements produce Figure 53.1 and Figure 53.2:

   ods graphics on;
   
   proc mds data=city level=absolute;
      id city;
   run;
   
   ods graphics off;

PROC MDS first displays the iteration history. In this example, only one iteration is required. The badness-of-fit criterion 0.001689 indicates that the data fit the model extremely well. You can also see that the fit is excellent in the fit plot in Figure 53.2.

Figure 53.1 Iteration History from PROC MDS

Analysis of Flying Mileages between Ten U.S. Cities

Multidimensional Scaling: Data=WORK.CITY.DATA

Shape=TRIANGLE Condition=MATRIX Level=ABSOLUTE

Coef=IDENTITY Dimension=2 Formula=1 Fit=1

Gconverge=0.01 Maxiter=100 Over=1 Ridge=0.0001

Iteration	Type	Badness- of-Fit Criterion	Change in Criterion	Convergence Measure
0	Initial	0.003273	.	0.8562
1	Lev-Mar	0.001689	0.001584	0.005128

Convergence criterion is satisfied.

While PROC MDS can recover the relative positions of the cities, it cannot determine absolute location or orientation. In this case, north is toward the bottom of the plot. (See the first plot in Figure 53.2.)

Figure 53.2 Plot of Estimated Configuration and Fit

Plot of Estimated Configuration and Fit, continued

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