MCA
library(ca)
data("wg93")
head(wg93)
## A B C D sex age edu
## 1 2 3 4 3 2 2 3
## 2 3 4 2 3 1 3 4
## 3 2 3 2 4 2 3 2
## 4 2 2 2 2 1 2 3
## 5 3 3 3 3 1 5 2
## 6 3 4 4 5 1 3 2
## 'data.frame': 871 obs. of 7 variables:
## $ A : Factor w/ 5 levels "1","2","3","4",..: 2 3 2 2 3 3 3 3 3 3 ...
## $ B : Factor w/ 5 levels "1","2","3","4",..: 3 4 3 2 3 4 4 4 2 3 ...
## $ C : Factor w/ 5 levels "1","2","3","4",..: 4 2 2 2 3 4 2 4 2 2 ...
## $ D : Factor w/ 5 levels "1","2","3","4",..: 3 3 4 2 3 5 4 2 1 2 ...
## $ sex: Factor w/ 2 levels "1","2": 2 1 2 1 1 1 2 1 1 1 ...
## $ age: Factor w/ 6 levels "1","2","3","4",..: 2 3 3 2 5 3 5 3 3 3 ...
## $ edu: Factor w/ 6 levels "1","2","3","4",..: 3 4 2 3 2 2 2 3 2 2 ...
mj= mjca(wg93) ### by default 'adjusted'
print(mj)
##
## Eigenvalues:
## 1 2 3 4 5 6 7
## Value 0.028924 0.017038 0.005828 0.004047 0.002142 0.000845 0.000676
## Percentage 36.55% 21.53% 7.36% 5.11% 2.71% 1.07% 0.85%
## 8 9 10 11 12
## Value 0.000383 0.000283 8.8e-05 2.9e-05 1e-06
## Percentage 0.48% 0.36% 0.11% 0.04% 0%
##
##
## Columns:
## A:1 A:2 A:3 A:4 A:5 B:1 B:2
## Mass 0.019518 0.052813 0.033459 0.029195 0.007873 0.011645 0.028539
## ChiDist 1.023569 0.518107 0.726500 0.798611 1.696104 1.412284 0.795195
## Inertia 0.020449 0.014177 0.017660 0.018620 0.022648 0.023227 0.018046
## Dim. 1 1.800225 0.792994 -0.335771 -1.430754 -3.049984 2.728791 1.181908
## Dim. 2 1.630097 -0.141322 -1.672746 0.451071 2.343200 2.754734 -0.663293
## B:3 B:4 B:5 C:1 C:2 C:3 C:4
## Mass 0.033623 0.046088 0.022962 0.024930 0.051829 0.032311 0.025258
## ChiDist 0.708551 0.581371 0.989433 0.947690 0.526559 0.745559 0.879602
## Inertia 0.016880 0.015577 0.022479 0.022390 0.014370 0.017960 0.019542
## Dim. 1 0.614157 -0.844770 -2.056557 2.104639 0.546124 -0.548248 -1.673899
## Dim. 2 -1.020932 -0.507231 1.940356 1.990773 -0.722204 -1.445168 0.359315
## C:5 D:1 D:2 D:3 D:4 D:5 sex:1
## Mass 0.008529 0.009841 0.038052 0.033131 0.037067 0.024766 0.070034
## ChiDist 1.629019 1.454722 0.649295 0.730987 0.653807 0.869302 0.401091
## Inertia 0.022633 0.020825 0.016042 0.017703 0.015845 0.018716 0.011267
## Dim. 1 -2.436440 0.993395 -0.124440 -0.088532 -0.183119 0.188971 -0.499006
## Dim. 2 2.980438 2.578626 -0.370493 -1.449258 -0.208603 1.795570 -0.323403
## sex:2 age:1 age:2 age:3 age:4 age:5 age:6
## Mass 0.072823 0.014925 0.034443 0.025914 0.023946 0.020338 0.023290
## ChiDist 0.385734 1.177718 0.694911 0.820879 0.857816 0.949948 0.905899
## Inertia 0.010835 0.020702 0.016633 0.017462 0.017621 0.018353 0.019113
## Dim. 1 0.479900 -0.814329 -0.613569 -0.252714 -0.104129 0.403346 1.465283
## Dim. 2 0.311020 0.272877 0.436093 -0.041419 -0.456510 -0.445403 0.084602
## edu:1 edu:2 edu:3 edu:4 edu:5 edu:6
## Mass 0.006233 0.061998 0.039692 0.015417 0.008037 0.011481
## ChiDist 1.835104 0.468936 0.626113 1.167358 1.578564 1.315351
## Inertia 0.020989 0.013633 0.015560 0.021010 0.020026 0.019864
## Dim. 1 0.770367 0.868600 -0.315998 -1.395753 -1.198734 -1.302775
## Dim. 2 0.163902 -0.259166 -0.438837 1.225141 0.797539 0.624175
##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.028924 36.5 36.5 ************
## 2 0.017038 21.5 58.1 *******
## 3 0.005828 7.4 65.4 **
## 4 0.004047 5.1 70.6 **
## 5 0.002142 2.7 73.3 *
## 6 0.000845 1.1 74.3
## 7 0.000676 0.9 75.2
## 8 0.000383 0.5 75.7
## 9 0.000283 0.4 76.0
## 10 8.8e-050 0.1 76.1
## 11 2.9e-050 0.0 76.2
## 12 1e-06000 0.0 76.2
## -------- -----
## Total: 0.079144
##
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | A:1 | 20 822 33 | 306 554 63 | 213 268 52 |
## 2 | A:2 | 53 639 23 | 135 627 33 | -18 12 1 |
## 3 | A:3 | 33 719 29 | -57 46 4 | -218 673 94 |
## 4 | A:4 | 29 658 30 | -243 622 60 | 59 36 6 |
## 5 | A:5 | 8 727 37 | -519 540 73 | 306 188 43 |
## 6 | B:1 | 12 768 38 | 464 480 87 | 360 288 88 |
## 7 | B:2 | 29 683 29 | 201 576 40 | -87 107 13 |
## 8 | B:3 | 34 648 27 | 104 247 13 | -133 401 35 |
## 9 | B:4 | 46 564 25 | -144 465 33 | -66 99 12 |
## 10 | B:5 | 23 686 36 | -350 450 97 | 253 236 86 |
## 11 | C:1 | 25 754 36 | 358 494 110 | 260 260 99 |
## 12 | C:2 | 52 569 23 | 93 281 15 | -94 289 27 |
## 13 | C:3 | 32 566 29 | -93 111 10 | -189 455 67 |
## 14 | C:4 | 25 657 32 | -285 640 71 | 47 17 3 |
## 15 | C:5 | 9 686 37 | -414 365 51 | 389 321 76 |
## 16 | D:1 | 10 656 34 | 169 132 10 | 337 524 65 |
## 17 | D:2 | 38 85 26 | -21 14 1 | -48 71 5 |
## 18 | D:3 | 33 504 29 | -15 3 0 | -189 501 70 |
## 19 | D:4 | 37 74 26 | -31 42 1 | -27 32 2 |
## 20 | D:5 | 25 644 30 | 32 12 1 | 234 632 80 |
## 21 | sex:1 | 70 625 18 | -85 501 17 | -42 124 7 |
## 22 | sex:2 | 73 625 18 | 82 501 17 | 41 124 7 |
## 23 | age:1 | 15 108 33 | -138 101 10 | 36 7 1 |
## 24 | age:2 | 34 364 27 | -104 281 13 | 57 84 7 |
## 25 | age:3 | 26 55 28 | -43 54 2 | -5 1 0 |
## 26 | age:4 | 24 125 28 | -18 10 0 | -60 115 5 |
## 27 | age:5 | 20 166 30 | 69 96 3 | -58 69 4 |
## 28 | age:6 | 23 611 31 | 249 610 50 | 11 1 0 |
## 29 | edu:1 | 6 64 34 | 131 62 4 | 21 2 0 |
## 30 | edu:2 | 62 586 22 | 148 557 47 | -34 29 4 |
## 31 | edu:3 | 40 255 25 | -54 120 4 | -57 136 8 |
## 32 | edu:4 | 15 386 34 | -237 266 30 | 160 121 23 |
## 33 | edu:5 | 8 471 32 | -204 374 12 | 104 97 5 |
## 34 | edu:6 | 11 500 32 | -222 441 19 | 81 60 4 |
MJCA
mj= mjca(wg93, lambda="JCA")
print(mj)
##
## Eigenvalues:
## 1 2 3 4 5 6 7
## Value 0.038461 0.022476 0.004907 0.003489 0.001748 0.000857 0.000698
## Percentage NA% NA% NA% NA% NA% NA% NA%
## 8 9 10 11 12
## Value 0.000664 0.000309 0.000161 9e-05 6.2e-05
## Percentage NA% NA% NA% NA% NA%
##
##
## Columns:
## A:1 A:2 A:3 A:4 A:5 B:1 B:2
## Mass 0.019518 0.052813 0.033459 0.029195 0.007873 0.011645 0.028539
## ChiDist 1.023569 0.518107 0.726500 0.798611 1.696104 1.412284 0.795195
## Inertia 0.020449 0.014177 0.017660 0.018620 0.022648 0.023227 0.018046
## Dim. 1 -1.782567 -0.759417 0.277099 1.431463 3.027691 -2.885516 -1.269201
## Dim. 2 -1.385122 0.169184 1.482822 -0.468861 -2.264293 -2.403163 0.793002
## B:3 B:4 B:5 C:1 C:2 C:3 C:4
## Mass 0.033623 0.046088 0.022962 0.024930 0.051829 0.032311 0.025258
## ChiDist 0.708551 0.581371 0.989433 0.947690 0.526559 0.745559 0.879602
## Inertia 0.016880 0.015577 0.022479 0.022390 0.014370 0.017960 0.019542
## Dim. 1 -0.740263 0.854859 2.408938 -2.439647 -0.506321 0.685860 1.756452
## Dim. 2 1.089168 0.420548 -2.205795 -2.315422 0.713852 1.639972 -0.218680
## C:5 D:1 D:2 D:3 D:4 D:5 sex:1
## Mass 0.008529 0.009841 0.038052 0.033131 0.037067 0.024766 0.070034
## ChiDist 1.629019 1.454722 0.649295 0.730987 0.653807 0.869302 0.401091
## Inertia 0.022633 0.020825 0.016042 0.017703 0.015845 0.018716 0.011267
## Dim. 1 2.407997 -0.837419 0.144092 0.139614 0.135887 -0.278787 0.383997
## Dim. 2 -3.135208 -2.593653 0.320436 1.468640 0.225561 -1.764000 0.221930
## sex:2 age:1 age:2 age:3 age:4 age:5 age:6
## Mass 0.072823 0.014925 0.034443 0.025914 0.023946 0.020338 0.023290
## ChiDist 0.385734 1.177718 0.694911 0.820879 0.857816 0.949948 0.905899
## Inertia 0.010835 0.020702 0.016633 0.017462 0.017621 0.018353 0.019113
## Dim. 1 -0.369294 0.585910 0.437420 0.174132 0.084674 -0.267665 -1.069443
## Dim. 2 -0.213433 -0.102002 -0.302311 -0.002521 0.280797 0.306286 -0.040914
## edu:1 edu:2 edu:3 edu:4 edu:5 edu:6
## Mass 0.006233 0.061998 0.039692 0.015417 0.008037 0.011481
## ChiDist 1.835104 0.468936 0.626113 1.167358 1.578564 1.315351
## Inertia 0.020989 0.013633 0.015560 0.021010 0.020026 0.019864
## Dim. 1 -0.588403 -0.660892 0.215749 1.052435 0.928278 1.079296
## Dim. 2 0.088569 0.221036 0.329008 -0.924384 -0.693470 -0.652358
##
## Principal inertias (eigenvalues):
##
## dim value
## 1 0.038461
## 2 0.022476
## 3 0.004907
## 4 0.003489
## 5 0.001748
## 6 0.000857
## 7 0.000698
## 8 0.000664
## 9 0.000309
## 10 0.000161
## 11 9e-05000
## 12 6.2e-050
## --------
## Total: 0.084311
##
## Diagonal inertia discounted from eigenvalues: 0.0164741
## Percentage explained by JCA in 2 dimensions: 65.5%
## (Eigenvalues are not nested)
## [Iterations in JCA: 31 , epsilon = 9.83e-05]
##
##
## Columns:
## name mass inr k=1 k=2 cor ctr
## 1 | A:1 | 20 33 | -350 -208 | 920 59 |
## 2 | A:2 | 53 23 | -149 25 | 706 21 |
## 3 | A:3 | 33 29 | 54 222 | 729 33 |
## 4 | A:4 | 29 30 | 281 -70 | 789 42 |
## 5 | A:5 | 8 37 | 594 -339 | 847 64 |
## 6 | B:1 | 12 38 | -566 -360 | 899 91 |
## 7 | B:2 | 29 29 | -249 119 | 791 31 |
## 8 | B:3 | 34 27 | -145 163 | 803 23 |
## 9 | B:4 | 46 25 | 168 63 | 620 24 |
## 10 | B:5 | 23 36 | 472 -331 | 890 107 |
## 11 | C:1 | 25 36 | -478 -347 | 952 119 |
## 12 | C:2 | 52 23 | -99 107 | 618 19 |
## 13 | C:3 | 32 29 | 135 246 | 706 34 |
## 14 | C:4 | 25 32 | 344 -33 | 784 48 |
## 15 | C:5 | 9 37 | 472 -470 | 843 65 |
## 16 | D:1 | 10 34 | -164 -389 | 750 31 |
## 17 | D:2 | 38 26 | 28 48 | 88 2 |
## 18 | D:3 | 33 29 | 27 220 | 621 28 |
## 19 | D:4 | 37 26 | 27 34 | 77 1 |
## 20 | D:5 | 25 30 | -55 -264 | 755 31 |
## 21 | sex:1 | 70 18 | 75 33 | 535 10 |
## 22 | sex:2 | 73 18 | -72 -32 | 535 10 |
## 23 | age:1 | 15 33 | 115 -15 | 79 4 |
## 24 | age:2 | 34 27 | 86 -45 | 272 7 |
## 25 | age:3 | 26 28 | 34 0 | 38 1 |
## 26 | age:4 | 24 28 | 17 42 | 77 1 |
## 27 | age:5 | 20 30 | -52 46 | 113 2 |
## 28 | age:6 | 23 31 | -210 -6 | 484 22 |
## 29 | edu:1 | 6 34 | -115 13 | 53 2 |
## 30 | edu:2 | 62 22 | -130 33 | 489 23 |
## 31 | edu:3 | 40 25 | 42 49 | 202 4 |
## 32 | edu:4 | 15 34 | 206 -139 | 310 20 |
## 33 | edu:5 | 8 32 | 182 -104 | 420 7 |
## 34 | edu:6 | 11 32 | 212 -98 | 519 13 |