ANLY 545 51 Late Spring 2018 HW5 Hanwen Zhang
Hanwen.Zhang
5/8/2018
Exercise 6.2 The data set criminal in the package logmult gives the 4 × 5 table below of the number of men aged 15–19 charged with a criminal case for whom charges were dropped in Denmark from 1955–1958.
(a)What percentages of the Pearson χ2 for association are explained by the various dimensions?
library(vcd)## Loading required package: gridlibrary(ca)
library(vcdExtra)## Warning: package 'vcdExtra' was built under R version 3.4.2## Loading required package: gnmlibrary(logmult)## Warning: package 'logmult' was built under R version 3.4.2##
## Attaching package: 'logmult'## The following object is masked from 'package:gnm':
##
## se## The following object is masked from 'package:vcd':
##
## assocdata("criminal",package="logmult")
criminal## Age
## Year 15 16 17 18 19
## 1955 141 285 320 441 427
## 1956 144 292 342 441 396
## 1957 196 380 424 462 427
## 1958 212 424 399 442 430criminal.ca <- ca(criminal)
summary(criminal.ca)##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.004939 90.3 90.3 ***********************
## 2 0.000491 9.0 99.3 **
## 3 3.8e-050 0.7 100.0
## -------- -----
## Total: 0.005468 100.0
##
##
## Rows:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | 1955 | 230 996 347 | 88 939 361 | -22 58 223 |
## 2 | 1956 | 230 978 157 | 58 908 157 | 16 71 124 |
## 3 | 1957 | 269 984 111 | -39 669 82 | 27 315 391 |
## 4 | 1958 | 271 999 385 | -85 938 399 | -22 61 262 |
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | 15 | 99 998 185 | -101 992 203 | -7 5 11 |
## 2 | 16 | 197 996 312 | -91 959 331 | -18 37 128 |
## 3 | 17 | 211 991 75 | -23 281 23 | 37 710 594 |
## 4 | 18 | 254 989 235 | 70 980 255 | 7 9 24 |
## 5 | 19 | 239 990 194 | 62 877 188 | -22 112 243 |This shows that there is a 90.3% assoiation between people 18 to 15 who had charges dropped and a 9% between people who are 19 and had the charges dropped. 90.3 is Dimension 1 and 9% is Dimension 2.
(b)Plot the 2D correspondence analysis solution. Describe the pattern of association between year and age.
plot(criminal.ca)
According to above, people 18 and under had their charges drooped more frequently than people 19
Exercise 6.11 The data set Vietnam in vcdExtra gives a 2 × 5 × 4 contingency table in frequency form reflecting a survey of student opinion on the Vietnam War at the University of North Carolina in May 1967. The table variables are sex, year in school, and response, which has categories: (A) Defeat North Vietnam by widespread bombing and land invasion; (B) Maintain the present policy; (C) De-escalate military activity, stop bombing and begin negotiations; (D) Withdraw military forces immediately.
- Using the stacking approach, carry out a correspondence analysis corresponding to the loglinear model [R][YS], which asserts that the response is independent of the combinations of year an sex.
data("Vietnam",package="vcdExtra")
str(Vietnam)## 'data.frame': 40 obs. of 4 variables:
## $ sex : Factor w/ 2 levels "Female","Male": 1 1 1 1 1 1 1 1 1 1 ...
## $ year : int 1 1 1 1 2 2 2 2 3 3 ...
## $ response: Factor w/ 4 levels "A","B","C","D": 1 2 3 4 1 2 3 4 1 2 ...
## $ Freq : int 13 19 40 5 5 9 33 3 22 29 ...viet1 = within(Vietnam, {year_sex <- paste(year, toupper(substr(sex,1,1)))})
viet.tab = xtabs(Freq~ year_sex + response, data= viet1)
viet.tab## response
## year_sex A B C D
## 1 F 13 19 40 5
## 1 M 175 116 131 17
## 2 F 5 9 33 3
## 2 M 160 126 135 21
## 3 F 22 29 110 6
## 3 M 132 120 154 29
## 4 F 12 21 58 10
## 4 M 145 95 185 44
## 5 F 19 27 128 13
## 5 M 118 176 345 141viet1.ca = ca(viet.tab)
summary(viet1.ca)##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.085680 73.6 73.6 ******************
## 2 0.027881 23.9 97.5 ******
## 3 0.002854 2.5 100.0 *
## -------- -----
## Total: 0.116415 100.0
##
##
## Rows:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | 1F | 24 818 13 | -167 452 8 | -150 367 20 |
## 2 | 1M | 139 997 181 | 386 986 242 | -41 11 8 |
## 3 | 2F | 16 995 35 | -407 647 31 | -299 349 51 |
## 4 | 2M | 140 984 131 | 326 982 175 | -15 2 1 |
## 5 | 3F | 53 999 112 | -334 453 69 | -367 547 256 |
## 6 | 3M | 138 904 40 | 175 904 49 | -4 0 0 |
## 7 | 4F | 32 982 37 | -344 887 44 | -113 95 15 |
## 8 | 4M | 149 383 23 | 81 372 11 | 14 11 1 |
## 9 | 5F | 59 994 153 | -453 686 143 | -304 309 197 |
## 10 | 5M | 248 1000 276 | -281 608 228 | 225 391 451 |
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | A | 255 985 381 | 414 985 509 | -1 0 0 |
## 2 | B | 235 720 60 | 135 608 50 | 58 112 28 |
## 3 | C | 419 999 283 | -247 773 298 | -133 226 267 |
## 4 | D | 92 995 276 | -366 383 143 | 463 612 705 |- Construct an informative 2D plot of the solution, and interpret in terms of how the response varies with year for males and females.
plot(viet1.ca)
As shown above,
For female of year 1 and 4, C is more likely to be the resonse;
For male of year 3 and 4, B is more likely to be the response;
For male of year 1 and 2, A is more likely to be the response;
For male of year 5, D is more likely to be the response;
- Use mjca () to carry out an MCA on the three-way table. Make a useful plot of the solution and interpret in terms of the relationship of the response to year and sex.
viet1.mjca = mjca(viet.tab)
plot(viet1.mjca)
As shown above,
There is association for male of year 3 and 4 and response B
There is association for male of year 5 and response D
There is association for male of year 1 and 2 and response A
There is association for female of year 1 and 4 and response C