data countries;
input angola argent australi china cuba japan usa zimbab; datalines;
......
1.41 ......
1.00 1.00 ......
1.00 1.73 1.41 . . . . .
1.41 1.41 1.73 1.00 . . . .
1.41 1.41 1.00 1.00 1.41 . . .
1.73 1.00 1.41 1.41 1.00 1.00 . .
.71 1.41 1.00 1.00 1.41 1.41 1.73 .
......
1 ......
2 2 ......
3 3 2 . . . . .
1 1 3 1 . . . .
2 2 1 2 1 . . .
3 3 2 3 2 2 . .
1 1 3 1 3 3 1 .
......
1.41 ......
1.41 1 ......
1 1.41 1.41 . . . . .
1 1.41 1.41 1 . . . .
1.41 1 1 1.41 1.41 . . .
1.41 1 1 1.41 1.41 1 . .
1 1.41 1.41 1 1 1.41 1.41 .
......
1 ......
0 1 ......
1 0 1 . . . . .
1.41 1 1.41 1 . . . .
1 1.41 1 0 1 . . .
1.41 1 1.41 1 0 1 . .
0 1 0 1 1.41 1 1.41 .
;
proc mds pconfig pfinal pdata pfit pcoef dim=2 to 3 level=interval coef=diagonal
iter=250 random=123;
var angola argent australi china cuba japan usa zimbab;
run;
The SAS System 1
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Data Matrix
1 angola argent australi china cuba japan usa zimbab
angola . 1.41 1 1 1.41 1.41 1.73 0.71
argent 1.41 . 1 1.73 1.41 1.41 1 1.41
australi 1 1 . 1.41 1.73 1 1.41 1
china 1 1.73 1.41 . 1 1 1.41 1
cuba 1.41 1.41 1.73 1 . 1.41 1 1.41
japan 1.41 1.41 1 1 1.41 . 1 1.41
usa 1.73 1 1.41 1.41 1 1 . 1.73
zimbab 0.71 1.41 1 1 1.41 1.41 1.73 .
Data Matrix
2 angola argent australi china cuba japan usa zimbab
angola . 1 2 3 1 2 3 1
argent 1 . 2 3 1 2 3 1
australi 2 2 . 2 3 1 2 3
china 3 3 2 . 1 2 3 1
cuba 1 1 3 1 . 1 2 3
japan 2 2 1 2 1 . 2 3
usa 3 3 2 3 2 2 . 1
zimbab 1 1 3 1 3 3 1 .
Data Matrix
3 angola argent australi china cuba japan usa zimbab
angola . 1.41 1.41 1 1 1.41 1.41 1
argent 1.41 . 1 1.41 1.41 1 1 1.41
australi 1.41 1 . 1.41 1.41 1 1 1.41
china 1 1.41 1.41 . 1 1.41 1.41 1
cuba 1 1.41 1.41 1 . 1.41 1.41 1
japan 1.41 1 1 1.41 1.41 . 1 1.41
usa 1.41 1 1 1.41 1.41 1 . 1.41
zimbab 1 1.41 1.41 1 1 1.41 1.41 .
The SAS System 2
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Data Matrix
4 angola argent australi china cuba japan usa zimbab
angola . 1 0 1 1.41 1 1.41 0
argent 1 . 1 0 1 1.41 1 1
australi 0 1 . 1 1.41 1 1.41 0
china 1 0 1 . 1 0 1 1
cuba 1.41 1 1.41 1 . 1 0 1.41
japan 1 1.41 1 0 1 . 1 1
usa 1.41 1 1.41 1 0 1 . 1.41
zimbab 0 1 0 1 1.41 1 1.41 .
The SAS System 3
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Gconverge=0.01 Maxiter=350 Over=1 Ridge=0.0001
Badness-
of-Fit Change in Convergence
Iteration Type Criterion Criterion Measure
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0 Initial 0.3411 . 1.0000
1 Lev-Mar 0.3336 0.007475 0.2598
2 Gau-New 0.3292 0.004457 0.1990
3 Gau-New 0.3244 0.004766 0.1523
4 Lev-Mar 0.3240 0.000348 0.1480
5 Lev-Mar 0.3230 0.001055 0.1402
6 Gau-New 0.3211 0.001842 0.1739
7 Lev-Mar 0.3211 0.0000675 0.1855
8 Gau-New 0.3166 0.004495 0.1707
9 Gau-New 0.3110 0.005601 0.1177
10 Gau-New 0.3092 0.001761 0.1173
11 Lev-Mar 0.3087 0.000558 0.0553
12 Lev-Mar 0.3086 0.0000716 0.0571
13 Lev-Mar 0.3085 0.0000518 0.0491
14 Lev-Mar 0.3084 0.0000963 0.0483
15 Lev-Mar 0.3084 0.0000475 0.0401
16 Lev-Mar 0.3084 0.0000139 0.0392
17 Lev-Mar 0.3084 1.9193E-6 0.0441
18 Lev-Mar 0.3084 3.6988E-6 0.0410
19 Lev-Mar 0.3084 2.0447E-6 0.0419
20 Lev-Mar 0.3084 9.3621E-7 0.0436
21 Lev-Mar 0.3084 2.2043E-7 0.0408
...
344 Lev-Mar 0.3084 1.656E-12 0.0263
345 Lev-Mar 0.3084 7.37E-12 0.0251
346 Lev-Mar 0.3084 1.656E-12 0.0263
347 Lev-Mar 0.3084 7.37E-12 0.0251
348 Lev-Mar 0.3084 1.656E-12 0.0263
349 Lev-Mar 0.3084 7.37E-12 0.0251
350 Lev-Mar 0.3084 1.656E-12 0.0263
WARNING: Iteration limit reached without convergence. Results
may be inaccurate.
The SAS System 4
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Configuration
Dim1 Dim2
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
angola -0.86 0.33
argent 1.22 0.33
australi 0.74 -1.10
china -0.96 1.42
cuba -1.24 0.31
japan 0.78 -0.75
usa 1.18 -1.64
zimbab -0.86 1.09
Dimension Coefficients
_MATRIX_ 1 2
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 1.41 0.00
2 0.00 1.41
3 1.34 0.45
4 0.00 0.00
The SAS System 5
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Number of Badness-of- Uncorrected
Nonmissing Fit Distance Distance
_MATRIX_ Data Weight Criterion Correlation Correlation
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 28 0.25 0.18 0.56 0.98
2 28 0.25 0.33 0.51 0.94
3 28 0.25 0.04 0.96 1.00
4 28 0.25 0.49 0.00 0.87
- All - 112 1.00 0.31 0.67 0.95
The SAS System 6
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Data Matrix
1 angola argent australi china cuba japan usa zimbab
angola . 1.41 1 1 1.41 1.41 1.73 0.71
argent 1.41 . 1 1.73 1.41 1.41 1 1.41
australi 1 1 . 1.41 1.73 1 1.41 1
china 1 1.73 1.41 . 1 1 1.41 1
cuba 1.41 1.41 1.73 1 . 1.41 1 1.41
japan 1.41 1.41 1 1 1.41 . 1 1.41
usa 1.73 1 1.41 1.41 1 1 . 1.73
zimbab 0.71 1.41 1 1 1.41 1.41 1.73 .
Data Matrix
2 angola argent australi china cuba japan usa zimbab
angola . 1 2 3 1 2 3 1
argent 1 . 2 3 1 2 3 1
australi 2 2 . 2 3 1 2 3
china 3 3 2 . 1 2 3 1
cuba 1 1 3 1 . 1 2 3
japan 2 2 1 2 1 . 2 3
usa 3 3 2 3 2 2 . 1
zimbab 1 1 3 1 3 3 1 .
Data Matrix
3 angola argent australi china cuba japan usa zimbab
angola . 1.41 1.41 1 1 1.41 1.41 1
argent 1.41 . 1 1.41 1.41 1 1 1.41
australi 1.41 1 . 1.41 1.41 1 1 1.41
china 1 1.41 1.41 . 1 1.41 1.41 1
cuba 1 1.41 1.41 1 . 1.41 1.41 1
japan 1.41 1 1 1.41 1.41 . 1 1.41
usa 1.41 1 1 1.41 1.41 1 . 1.41
zimbab 1 1.41 1.41 1 1 1.41 1.41 .
The SAS System 7
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Data Matrix
4 angola argent australi china cuba japan usa zimbab
angola . 1 0 1 1.41 1 1.41 0
argent 1 . 1 0 1 1.41 1 1
australi 0 1 . 1 1.41 1 1.41 0
china 1 0 1 . 1 0 1 1
cuba 1.41 1 1.41 1 . 1 0 1.41
japan 1 1.41 1 0 1 . 1 1
usa 1.41 1 1.41 1 0 1 . 1.41
zimbab 0 1 0 1 1.41 1 1.41 .
The SAS System 8
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Gconverge=0.01 Maxiter=350 Over=1 Ridge=0.0001
Badness-
of-Fit Change in Convergence
Iteration Type Criterion Criterion Measure
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0 Initial 0.3411 . 1.0000
1 Lev-Mar 0.3336 0.007475 0.2598
2 Gau-New 0.3292 0.004457 0.1990
3 Gau-New 0.3244 0.004766 0.1523
4 Lev-Mar 0.3240 0.000348 0.1480
5 Lev-Mar 0.3230 0.001055 0.1402
6 Gau-New 0.3211 0.001842 0.1739
7 Lev-Mar 0.3211 0.0000675 0.1855
8 Gau-New 0.3166 0.004495 0.1707
9 Gau-New 0.3110 0.005601 0.1177
10 Gau-New 0.3092 0.001761 0.1173
...
345 Lev-Mar 0.3084 7.37E-12 0.0251
346 Lev-Mar 0.3084 1.656E-12 0.0263
347 Lev-Mar 0.3084 7.37E-12 0.0251
348 Lev-Mar 0.3084 1.656E-12 0.0263
349 Lev-Mar 0.3084 7.37E-12 0.0251
350 Lev-Mar 0.3084 1.656E-12 0.0263
WARNING: Iteration limit reached without convergence. Results
may be inaccurate.
The SAS System 9
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Configuration
Dim1 Dim2
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
angola -0.86 0.33
argent 1.22 0.33
australi 0.74 -1.10
china -0.96 1.42
cuba -1.24 0.31
japan 0.78 -0.75
usa 1.18 -1.64
zimbab -0.86 1.09
Dimension Coefficients
_MATRIX_ 1 2
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 1.41 0.00
2 0.00 1.41
3 1.34 0.45
4 0.00 0.00
The SAS System 10
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=2 Formula=1 Fit=1
Number of Badness-of- Uncorrected
Nonmissing Fit Distance Distance
_MATRIX_ Data Weight Criterion Correlation Correlation
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 28 0.25 0.18 0.56 0.98
2 28 0.25 0.33 0.51 0.94
3 28 0.25 0.04 0.96 1.00
4 28 0.25 0.49 0.00 0.87
- All - 112 1.00 0.31 0.67 0.95
The SAS System 11
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=3 Formula=1 Fit=1
Gconverge=0.01 Maxiter=350 Over=1 Ridge=0.0001
Badness-
of-Fit Change in Convergence
Iteration Type Criterion Criterion Measure
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0 Initial 0.4931 . 0.7841
1 Lev-Mar 0.3601 0.1330 0.5867
2 Lev-Mar 0.3431 0.0170 0.5054
3 Gau-New 0.3347 0.008394 0.4506
4 Gau-New 0.3108 0.0239 0.2618
5 Gau-New 0.3038 0.007055 0.1392
6 Gau-New 0.3011 0.002632 0.1066
7 Lev-Mar 0.3008 0.000343 0.1207
8 Lev-Mar 0.3004 0.000421 0.0690
9 Lev-Mar 0.3001 0.000227 0.0947
10 Lev-Mar 0.3000 0.000104 0.0670
...
345 Lev-Mar 0.2998 8.448E-12 0.0718
346 Lev-Mar 0.2998 3.938E-11 0.0718
347 Lev-Mar 0.2998 2.882E-11 0.0724
348 Lev-Mar 0.2998 3.883E-12 0.0718
349 Lev-Mar 0.2998 3.934E-11 0.0718
350 Lev-Mar 0.2998 2.278E-11 0.0726
WARNING: Iteration limit reached without convergence. Results
may be inaccurate.
The SAS System 12
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=3 Formula=1 Fit=1
Configuration
Dim1 Dim2 Dim3
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
angola 0.61 -0.35 1.47
argent 1.30 -0.21 0.80
australi -1.61 0.11 0.83
china 0.42 0.80 -1.76
cuba 0.69 1.24 0.02
japan -0.96 1.25 0.25
usa -1.14 -1.44 -0.95
zimbab 0.69 -1.41 -0.66
Dimension Coefficients
_MATRIX_ 1 2 3
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 1.73 0.07 0.00
2 1.06 0.98 0.96
3 1.73 0.00 0.00
4 0.00 0.00 0.00
The SAS System 13
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=3 Formula=1 Fit=1
Number of Badness-of- Uncorrected
Nonmissing Fit Distance Distance
_MATRIX_ Data Weight Criterion Correlation Correlation
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 28 0.25 0.21 0.14 0.98
2 28 0.25 0.24 0.79 0.97
3 28 0.25 0.15 0.42 0.99
4 28 0.25 0.49 0.00 0.87
- All - 112 1.00 0.30 0.69 0.95
The SAS System 14
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=4 Formula=1 Fit=1
Gconverge=0.01 Maxiter=350 Over=1 Ridge=0.0001
Badness-
of-Fit Change in Convergence
Iteration Type Criterion Criterion Measure
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0 Initial 0.4299 . 1.0000
1 Lev-Mar 0.3859 0.0439 0.7907
2 Lev-Mar 0.3619 0.0241 0.7563
3 Lev-Mar 0.3374 0.0245 0.7081
4 Lev-Mar 0.3205 0.0169 0.6654
5 Lev-Mar 0.3026 0.0179 0.5994
6 Lev-Mar 0.2626 0.0400 0.4099
7 Gau-New 0.2568 0.005783 0.3218
8 Gau-New 0.2466 0.0103 0.3311
9 Gau-New 0.2456 0.000932 0.3145
10 Gau-New 0.2348 0.0109 0.3386
11 Lev-Mar 0.2325 0.002293 0.4124
12 Lev-Mar 0.2314 0.001035 0.4286
13 Gau-New 0.2142 0.0173 0.2139
14 Gau-New 0.2100 0.004158 0.1196
15 Gau-New 0.2088 0.001266 0.0850
16 Gau-New 0.2082 0.000586 0.0694
17 Gau-New 0.2078 0.000364 0.0486
18 Gau-New 0.2077 0.000146 0.0382
19 Gau-New 0.2076 0.0000790 0.0290
20 Gau-New 0.2075 0.0000395 0.0225
21 Gau-New 0.2075 0.0000224 0.0181
22 Gau-New 0.2075 0.0000167 0.0148
23 Gau-New 0.2075 0.0000148 0.0132
24 Gau-New 0.2075 0.0000174 0.0126
25 Gau-New 0.2075 0.0000226 0.0131
26 Gau-New 0.2074 0.0000300 0.0139
27 Gau-New 0.2074 0.0000375 0.0146
28 Gau-New 0.2073 0.0000415 0.0143
29 Gau-New 0.2073 0.0000395 0.0130
30 Gau-New 0.2073 0.0000313 0.0108
31 Gau-New 0.2073 0.0000212 0.008492
Convergence criterion is satisfied.
The SAS System 15
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=4 Formula=1 Fit=1
Configuration
Dim1 Dim2 Dim3 Dim4
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
angola -0.28 -0.50 1.03 1.19
argent 1.30 -0.45 -0.89 0.96
australi -0.96 1.38 0.90 0.94
china 1.52 1.22 -0.05 -0.36
cuba -0.89 0.27 -1.50 -0.86
japan 0.93 0.72 0.66 -1.28
usa -0.63 -1.50 -1.22 -1.31
zimbab -0.98 -1.14 1.08 0.73
Dimension Coefficients
_MATRIX_ 1 2 3 4
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 0.00 0.42 1.46 1.30
2 0.00 1.62 0.00 1.17
3 2.00 0.00 0.00 0.00
4 0.95 0.45 1.27 1.13
The SAS System 16
Multidimensional Scaling: Data=WORK.COUNTRIES.DATA
Shape=TRIANGLE Condition=MATRIX Level=INTERVAL
Coef=DIAGONAL Dimension=4 Formula=1 Fit=1
Number of Badness-of- Uncorrected
Nonmissing Fit Distance Distance
_MATRIX_ Data Weight Criterion Correlation Correlation
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 28 0.25 0.16 0.68 0.99
2 28 0.25 0.32 0.54 0.95
3 28 0.25 0.16 0.00 0.99
4 28 0.25 0.12 0.97 0.99
- All - 112 1.00 0.21 0.87 0.98