ANLY 545- Homework #5
Priyanka Bodepudi
2018-09-23
Exercise 6.1 The JobSat data in vcdExtra gives a 4 × 4 table recording job satisfaction in relation to income.
library(vcdExtra)## Warning: package 'vcdExtra' was built under R version 3.4.4## Loading required package: vcd## Warning: package 'vcd' was built under R version 3.4.4## Loading required package: grid## Loading required package: gnm## Warning: package 'gnm' was built under R version 3.4.4data(JobSat)
JobSat## satisfaction
## income VeryD LittleD ModerateS VeryS
## < 15k 1 3 10 6
## 15-25k 2 3 10 7
## 25-40k 1 6 14 12
## > 40k 0 1 9 11(a) Carry out a simple correspondence analysis on this table. How much of the inertia is accounted for by a one-dimensional solution? How much by a two-dimensional solution?
data("JobSat", package="vcdExtra")
JobSat## satisfaction
## income VeryD LittleD ModerateS VeryS
## < 15k 1 3 10 6
## 15-25k 2 3 10 7
## 25-40k 1 6 14 12
## > 40k 0 1 9 11library(ca)## Warning: package 'ca' was built under R version 3.4.4JobSat.ca <- ca(JobSat)
summary(JobSat.ca)##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.047496 76.4 76.4 *******************
## 2 0.012248 19.7 96.1 *****
## 3 0.002397 3.9 100.0 *
## -------- -----
## Total: 0.062141 100.0
##
##
## Rows:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | 15k | 208 658 81 | -126 658 70 | 4 1 0 |
## 2 | 1525 | 229 977 247 | -208 647 209 | -148 329 412 |
## 3 | 2540 | 344 956 114 | -35 59 9 | 136 897 519 |
## 4 | 40k | 219 1000 558 | 393 976 712 | -62 24 69 |
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | VryD | 42 985 384 | -662 766 385 | -354 219 427 |
## 2 | LttD | 135 990 294 | -289 621 239 | 223 369 549 |
## 3 | MdrS | 448 334 31 | -31 233 9 | -21 101 16 |
## 4 | VryS | 375 967 292 | 216 961 367 | -16 6 8 |It can be seen that 96.1% of the ??2 for this model is accounted for in the first two dimensions. The scree plot display above shows that the association between job satisfaction and income is one-dimensional,the dimension in the analysis has inertia (0.0474)
(b) Plot the 2D CA solution. Explain the first dimension of the plot? Are the points ordered? What does it show? Do you see any association? If yes, where? If no, what is the reason?
plot(JobSat.ca)
Dimension 1 in the plot separates income groups, indicating a co-relation between Job satisfaction with respective to income groups. The first dimension is mostly ordered by job satisfaction with little dissatisfaction group at the top and very dissatisfied groups at the bottom. we can see 25-40 k income groups are less dissatisfied and 15-25k are very much dissatisfied with their job.
Exercise 6.11 Refer to Exercise 5.9 for a description of the Accident data set in vcdExtra. The data set is in the form of a frequency data frame, so first convert to table form.
data("Accident", package="vcdExtra")
Accident## age result mode gender Freq
## 1 50+ Died Pedestrian Male 704
## 2 50+ Died Pedestrian Female 378
## 3 50+ Died Bicycle Male 396
## 4 50+ Died Bicycle Female 56
## 5 50+ Died Motorcycle Male 742
## 6 50+ Died Motorcycle Female 78
## 7 50+ Died 4-Wheeled Male 513
## 8 50+ Died 4-Wheeled Female 253
## 9 50+ Injured Pedestrian Male 5206
## 10 50+ Injured Pedestrian Female 5449
## 11 50+ Injured Bicycle Male 3863
## 12 50+ Injured Bicycle Female 1030
## 13 50+ Injured Motorcycle Male 8597
## 14 50+ Injured Motorcycle Female 1387
## 15 50+ Injured 4-Wheeled Male 7423
## 16 50+ Injured 4-Wheeled Female 5552
## 17 30-49 Died Pedestrian Male 223
## 18 30-49 Died Pedestrian Female 49
## 19 30-49 Died Bicycle Male 146
## 20 30-49 Died Bicycle Female 24
## 21 30-49 Died Motorcycle Male 889
## 22 30-49 Died Motorcycle Female 98
## 23 30-49 Died 4-Wheeled Male 720
## 24 30-49 Died 4-Wheeled Female 199
## 25 30-49 Injured Pedestrian Male 3178
## 26 30-49 Injured Pedestrian Female 1814
## 27 30-49 Injured Bicycle Male 3024
## 28 30-49 Injured Bicycle Female 1118
## 29 30-49 Injured Motorcycle Male 18909
## 30 30-49 Injured Motorcycle Female 3664
## 31 30-49 Injured 4-Wheeled Male 15086
## 32 30-49 Injured 4-Wheeled Female 7712
## 33 20-29 Died Pedestrian Male 78
## 34 20-29 Died Pedestrian Female 24
## 35 20-29 Died Bicycle Male 55
## 36 20-29 Died Bicycle Female 10
## 37 20-29 Died Motorcycle Male 660
## 38 20-29 Died Motorcycle Female 82
## 39 20-29 Died 4-Wheeled Male 353
## 40 20-29 Died 4-Wheeled Female 107
## 41 20-29 Injured Pedestrian Male 1521
## 42 20-29 Injured Pedestrian Female 864
## 43 20-29 Injured Bicycle Male 1565
## 44 20-29 Injured Bicycle Female 609
## 45 20-29 Injured Motorcycle Male 18558
## 46 20-29 Injured Motorcycle Female 4010
## 47 20-29 Injured 4-Wheeled Male 9084
## 48 20-29 Injured 4-Wheeled Female 4361
## 49 10-19 Died Pedestrian Male 70
## 50 10-19 Died Pedestrian Female 28
## 51 10-19 Died Bicycle Male 76
## 52 10-19 Died Bicycle Female 31
## 53 10-19 Died Motorcycle Male 362
## 54 10-19 Died Motorcycle Female 54
## 55 10-19 Died 4-Wheeled Male 150
## 56 10-19 Died 4-Wheeled Female 61
## 57 10-19 Injured Pedestrian Male 1827
## 58 10-19 Injured Pedestrian Female 1495
## 59 10-19 Injured Bicycle Male 3407
## 60 10-19 Injured Bicycle Female 7218
## 61 10-19 Injured Motorcycle Male 12311
## 62 10-19 Injured Motorcycle Female 3587
## 63 10-19 Injured 4-Wheeled Male 3543
## 64 10-19 Injured 4-Wheeled Female 2593
## 65 0-9 Died Pedestrian Male 150
## 66 0-9 Died Pedestrian Female 89
## 67 0-9 Died Bicycle Male 26
## 68 0-9 Died Bicycle Female 5
## 69 0-9 Died Motorcycle Male 6
## 70 0-9 Died Motorcycle Female 6
## 71 0-9 Died 4-Wheeled Male 70
## 72 0-9 Died 4-Wheeled Female 65
## 73 0-9 Injured Pedestrian Male 3341
## 74 0-9 Injured Pedestrian Female 1967
## 75 0-9 Injured Bicycle Male 378
## 76 0-9 Injured Bicycle Female 126
## 77 0-9 Injured Motorcycle Male 181
## 78 0-9 Injured Motorcycle Female 131
## 79 0-9 Injured 4-Wheeled Male 1593
## 80 0-9 Injured 4-Wheeled Female 1362accident_tab <- xtabs(Freq ~ gender+mode+age+result, data=Accident)
accident_tab## , , age = 0-9, result = Died
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 65 5 6 89
## Male 70 26 6 150
##
## , , age = 10-19, result = Died
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 61 31 54 28
## Male 150 76 362 70
##
## , , age = 20-29, result = Died
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 107 10 82 24
## Male 353 55 660 78
##
## , , age = 30-49, result = Died
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 199 24 98 49
## Male 720 146 889 223
##
## , , age = 50+, result = Died
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 253 56 78 378
## Male 513 396 742 704
##
## , , age = 0-9, result = Injured
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 1362 126 131 1967
## Male 1593 378 181 3341
##
## , , age = 10-19, result = Injured
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 2593 7218 3587 1495
## Male 3543 3407 12311 1827
##
## , , age = 20-29, result = Injured
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 4361 609 4010 864
## Male 9084 1565 18558 1521
##
## , , age = 30-49, result = Injured
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 7712 1118 3664 1814
## Male 15086 3024 18909 3178
##
## , , age = 50+, result = Injured
##
## mode
## gender 4-Wheeled Bicycle Motorcycle Pedestrian
## Female 5552 1030 1387 5449
## Male 7423 3863 8597 5206(a) Use mjca() to carry out an MCA on the four-way table accident.tab. How do you explain the summary results?
accident.mca <- mjca(accident_tab)
summary(accident.mca)##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.025429 46.5 46.5 ****************
## 2 0.011848 21.7 68.1 *******
## 3 0.001889 3.5 71.6 *
## 4 0.000491 0.9 72.5
## -------- -----
## Total: 0.054700
##
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | gender:Female | 77 788 77 | -203 686 126 | 78 101 40 |
## 2 | gender:Male | 173 788 35 | 91 686 56 | -35 101 18 |
## 3 | mode:4-Wheeled | 81 230 73 | -8 2 0 | -80 228 43 |
## 4 | mode:Bicycle | 31 762 98 | -156 127 30 | 349 635 320 |
## 5 | mode:Motorcycle | 99 686 70 | 209 684 170 | 11 2 1 |
## 6 | mode:Pedestrian | 38 677 100 | -401 600 241 | -144 77 66 |
## 7 | age:0-9 | 13 672 107 | -551 561 152 | -246 111 65 |
## 8 | age:10-19 | 49 678 91 | -40 13 3 | 292 665 354 |
## 9 | age:20-29 | 56 784 85 | 215 747 102 | -48 37 11 |
## 10 | age:30-49 | 76 546 75 | 103 396 32 | -63 149 26 |
## 11 | age:50+ | 56 687 85 | -196 616 84 | -67 72 21 |
## 12 | result:Died | 11 515 100 | -90 92 3 | -192 422 34 |
## 13 | result:Injured | 239 515 5 | 4 92 0 | 9 422 2 |It can be seen that 68.1% of the ??2 for this model is accounted for in the first two dimensions. The scree plot display above shows that the association between gender and mode is two-dimensional,the fisrt dimension in the analysis has inertia (0.025429)
(b) Construct an informative 2D plot of the solution, and interpret in terms of how the variable result varies in relation to the other factors. Please explain everything in detail (all the relationships that you see)
plot(accident.mca)