library(tidyverse)
library(magrittr)
library(vcd)
library(vcdExtra)
library(HistData)

Exercise 4.2

The data set Abortion in vcdExtra gives a 2 × 2 × 2 table of opinions regarding abortion in relation to sex and status of the respondent. This table has the following structure:

Abortion <- vcdExtra::Abortion
str(Abortion)
##  table [1:2, 1:2, 1:2] 171 152 138 167 79 148 112 133
##  - attr(*, "dimnames")=List of 3
##   ..$ Sex             : chr [1:2] "Female" "Male"
##   ..$ Status          : chr [1:2] "Lo" "Hi"
##   ..$ Support_Abortion: chr [1:2] "Yes" "No"
  1. Taking support for abortion as the outcome variable, produce fourfold displays showing the association with sex, stratified by status.
abort1 = aperm(Abortion, c(3,1,2))
abort1
## , , Status = Lo
## 
##                 Sex
## Support_Abortion Female Male
##              Yes    171  152
##              No      79  148
## 
## , , Status = Hi
## 
##                 Sex
## Support_Abortion Female Male
##              Yes    138  167
##              No     112  133
fourfoldplot(abort1,color = c("blue", "green"), conf.level = 0.95, std = c("ind.max"), space = 0.3, main = NULL, mfrow = NULL, mfcol = NULL)

  1. Do the same for the association of support for abortion with status, stratified by sex.
abort2 = aperm(Abortion, c(3,2,1))
abort2
## , , Sex = Female
## 
##                 Status
## Support_Abortion  Lo  Hi
##              Yes 171 138
##              No   79 112
## 
## , , Sex = Male
## 
##                 Status
## Support_Abortion  Lo  Hi
##              Yes 152 167
##              No  148 133
fourfoldplot(abort2 ,color = c("blue", "green"), conf.level = 0.95, std = c("ind.max"), space = 0.3, main = NULL, mfrow = NULL, mfcol = NULL)

  1. For each of the problems above, use oddsratio () to calculate the numerical values of the odds ratio, as stratified in the question.
# stratified by status
oddsratio(abort1)
## log odds ratios for Support_Abortion and Sex by Status 
## 
##          Lo          Hi 
##  0.74554746 -0.01888987
# stratified by sex
oddsratio(abort2)
## log odds ratios for Support_Abortion and Status by Sex 
## 
##     Female       Male 
##  0.5634609 -0.2009764
  1. Write a brief summary of how support for abortion depends on sex and status.

From the fourfold plot stratified by status we can see when status is Hi, the odds seems to be similar for Females and Males to support or not support abortion; but when status is low, the odds for females not support abortion is clearly less than males.

From the fourfold plot stratified by sex we can see when sex is male the odds seems to be similar for the two status to support or not support abortion; but when sex is female, the odds for status lo not support abortion is clearly less then status Hi.

Exercise 4.7

Agresti and Winner (1997) gave the data in below on the ratings of 160 movies by the reviewers Gene Siskel and Roger Ebert for the period from April 1995 through September 1996. The rating categories were Con (“thumbs down”), Mixed, and Pro (“thumbs up”).

  1. Assess the strength of agreement between the raters using Cohen’s κ, both unweighted and weighted.
datav <- matrix(c(24, 8, 13, 8, 13, 11, 10, 9, 64),
                nrow = 3, ncol = 3, byrow = TRUE)
datav <- as.table(datav)
rownames(datav) <- c('Con', 'Mixed', 'Pro')
colnames(datav) <- c('Con', 'Mixed', 'Pro')
datav
##       Con Mixed Pro
## Con    24     8  13
## Mixed   8    13  11
## Pro    10     9  64
Kappa(datav)
##             value     ASE     z         Pr(>|z|)
## Unweighted 0.3888 0.05979 6.503 0.00000000007870
## Weighted   0.4269 0.06350 6.723 0.00000000001781

From the cohen’s kappa we saw both p values for unweighted and weighted are smaller than alpha, but the k value is not very close to 1. Thus, we can conclude there is marginal agreement between the two reviewers.

(b). Use agreementplot () for a graphical display of agreement here.

agreementplot(datav, main="Unweighted", weights=1)

agreementplot(datav, main="Weighted")