There are times when you want to do correspondence anlysis and the data have been collapsed into a summary with counts for each of the categories. For example, here is a dataset with the number of degrees given in 12 disciplines over eight different years.
discipline 1960 1965 1970 1971 1972 1973 1974 1975
Agri 414 576 803 900 855 853 830 904
Anth 69 82 217 240 260 324 381 385
Bio 1245 1963 3360 3633 3580 3636 3473 3498
Chem 1078 1444 2234 2204 2011 1849 1792 1762
Earth 253 375 511 550 580 577 570 556
Econ 341 538 826 791 863 907 833 867
Eng 794 2073 3432 3495 3475 3338 3144 2959
Math 291 685 1222 1236 1281 1222 1196 1149
Oth 314 502 1079 1392 1500 1609 1531 1550
Phy 530 1046 1655 1740 1635 1590 134 1293
Psych 772 954 1888 2116 2262 2444 2587 2749
Soc 162 239 504 583 638 599 645 680
We will begin by reading in the data.
data ca_summary;
input disc $ v60 v65 v70 v71 v72 v73 v74 v75;
datalines;
eng 794 2073 3432 3495 3475 3338 3144 2959
math 291 685 1222 1236 1281 1222 1196 1149
phy 530 1046 1655 1740 1635 1590 134 1293
chem 1078 1444 2234 2204 2011 1849 1792 1762
earth 253 375 511 550 580 577 570 556
bio 1245 1963 3360 3633 3580 3636 3473 3498
agri 414 576 803 900 855 853 830 904
psych 772 954 1888 2116 2262 2444 2587 2749
socio 162 239 504 583 638 599 645 680
econ 341 538 826 791 863 907 833 867
anthro 69 82 217 240 260 324 381 385
others 314 502 1079 1392 1500 1609 1531 1550
;
run;
Now we are ready to run the correspondence analysis and plot the results.
proc corresp data=ca_summary out=coord short;
var v60 v65 v70 v71 v72 v73 v74 v75;
id disc;
run;
The CORRESP Procedure
Inertia and Chi-Square Decomposition
Singular Principal Chi- Cumulative
Value Inertia Square Percent Percent 14 28 42 56 70
----+----+----+----+----+---
0.12662 0.01603 2031.34 68.55 68.55 ************************
0.06636 0.00440 557.91 18.83 87.38 *******
0.04960 0.00246 311.75 10.52 97.90 ****
0.01496 0.00022 28.36 0.96 98.86
0.01282 0.00016 20.81 0.70 99.56
0.00796 0.00006 8.04 0.27 99.83
0.00629 0.00004 5.01 0.17 100.00
Total 0.02339 2963.21 100.00
Degrees of Freedom = 77
Row Coordinates
Dim1 Dim2
eng 0.0151 -0.0248
math -0.0203 -0.0322
phy 0.3461 -0.1147
chem 0.1003 0.1269
earth 0.0002 0.0777
bio -0.0182 0.0135
agri 0.0204 0.0835
psych -0.1386 -0.0091
socio -0.1218 -0.0459
econ -0.0034 0.0432
anthro -0.2726 -0.0515
others -0.1475 -0.0918
Column Coordinates
Dim1 Dim2
v60 0.1142 0.2069
v65 0.1816 0.0676
v70 0.1048 0.0057
v71 0.0694 -0.0248
v72 0.0252 -0.0464
v73 -0.0114 -0.0631
v74 -0.2613 0.0695
v75 -0.0859 -0.0409
proc sgplot data = coord noautolegend;
xaxis min = -.4 max = .4 values=(-.3 to .3 by .1) valueshint;
yaxis min = -.3 max = .3;
scatter x = dim1 y = dim2 /group = _type_ MARKERCHAR = disc
markercharattrs=(size=10 weight=bold);
run;
