ANLY 545 HW #4
Lushan
9/26/2018
Exercise 5.1 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) Use loglm() to test whether there is an association between Year and Age. Is there evidence that dropping of charges in relation to age changed over the years recorded here?
library(vcd)## Loading required package: gridlibrary(logmult)## Loading required package: gnm## Warning: package 'gnm' was built under R version 3.4.4##
## Attaching package: 'logmult'## The following object is masked from 'package:gnm':
##
## se## The following object is masked from 'package:vcd':
##
## assoclibrary(vcdExtra)
library(MASS)
data("criminal")
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 430loglm(Freq ~ Year + Age, data = criminal)## Call:
## loglm(formula = Freq ~ Year + Age, data = criminal)
##
## Statistics:
## X^2 df P(> X^2)
## Likelihood Ratio 38.24466 12 0.0001400372
## Pearson 38.41033 12 0.0001315495The value of likelihood ratio and Pearson suggests, the year recorded is independent of age changes.
(b) Use mosaic() with the option shade=TRUE to display the pattern of signs and magnitudes of the residuals. Compare this with the result of mosaic() using “Friendly shading,” from the option gp=shading_Friendly. Describe verbally what you see in each regarding the pattern of association in this table.
mosaic(criminal,shade = TRUE, labeling = labeling_residuals, supress = 0)
mosaic(criminal, shade = TRUE, gp = shading_Friendly, labeling = labeling_residuals)
These plots show that there exsits associations between Year 1955 and Age 19 and Year 1958 and Age 15.
Exercise 5.9 Bertin (1983, pp. 30–31) used a 4-way table of frequencies of traffic accident victims in France in 1958 to illustrate his scheme for classifying data sets by numerous variables, each of which could have various types and could be assigned to various visual attributes. His data are contained in Accident in vcdExtra, a frequency data frame representing his 5 × 2 × 4 × 2 table of the variables age, result (died or injured), mode of transportation, and gender.
(a) Use loglm() to fit the model of mutual independence, Freq ~ age+mode+gender+result to this data set.
data("Accident")
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 1362loglm(Freq ~ age + mode + gender + result, data = Accident)## Call:
## loglm(formula = Freq ~ age + mode + gender + result, data = Accident)
##
## Statistics:
## X^2 df P(> X^2)
## Likelihood Ratio 60320.05 70 0
## Pearson 76865.31 70 0(b) Use mosaic() to produce an interpretable mosaic plot of the associations among all variables under the model of mutual independence. Try different orders of the variables in the mosaic. (Hint: the abbreviate component of the labeling_args argument to mosaic() will be useful to avoid some overlap of the category labels.)
mosaic(Freq ~ gender + mode + age + result, data = Accident, shade = TRUE, labeling_args = list(clip = c(result = TRUE)))
mosaic(Freq ~ age + mode + gender + result, data = Accident, shade = TRUE, labeling_args = list(clip = c(result = TRUE)))
mosaic(Freq ~ mode + result + gender + age, data = Accident, shade = TRUE, labeling_args = list(clip = c(result = TRUE)))
(c) Treat result (“Died” vs. “Injured”) as the response variable, and fit the model Freq ~ age*mode gender + result that asserts independence of result from all others jointly.
loglm(Freq ~ age * mode * gender + result, data = Accident)## Call:
## loglm(formula = Freq ~ age * mode * gender + result, data = Accident)
##
## Statistics:
## X^2 df P(> X^2)
## Likelihood Ratio 2217.72 39 0
## Pearson 2347.60 39 0(d) Construct a mosaic display for the residual associations in this model. Which combinations of the predictor factors are more likely to result in death?
mosaic(loglm(Freq ~ age*mode*gender + result, Accident), shade = TRUE, labeling = labeling_residuals, rot_labels = c(20, 20, 20, 0))
It shows both age (50+) and gender (male) plays an important role here, in this combination it’s morelikely to result in death