MATH 4330: Activity 2
Marion Fernandes, Salvador Freire, Monica Liu, Lois Li
September 18, 2017
knitr::opts_chunk$set(comment=NA) # suppresses '## ' in output1) Introduction
In this report, our group was working on a data story “Greene”, involving 7 variables (judge, nation, rater, decision, language, location and success) and filling up in 1990, in which refugee claimants who were forced to leave by the Canadian Immigration and Refugee Board, asked the Federal Court of Appeal for leave to appeal the negative ruling of the Board. To be more specific, we wanted to find the correlation between the nation and judge with rater, decision and success. According to our analysis, we found a similar pattern between the rater, decision and success when conditioned on the nation, continent and judge.
2) Data Biography
We downloaded the “greene.txt” and started our analysis.We needed to know more about the detailed information we were looking at so that we could better understand the patterns we were finding. In this case, the first thing we needed to do was find out where the information was coming from. The data reflected about people with judge’s name and their status (decision, rater, and success….) from website “http://socserv.socsci.mcmaster.ca/jfox/Books/Applied-Regression-3E/datasets/Greene.txt”. Next, we would like to figure out who collected these data. Unfortunately, we have no idea about that part. From the data provided, it is clear that there is a strong relationship between the rater and decision based on individual nations and judges. We can see that the rater is fairly accurate in determining the decision outcome based on judges preciding over the case, or based on the nation except for a few cases. These discrepancies are observed to be caused by a small number of appeal cases in those nations. For example, only a few people on the file came from Iran and Sri.Lanka.
3) Data Directory
Variables:
judge: Name of judge hearing case: Desjardins, Heald, Hugessen, Iacobucci, MacGuigan, Mahoney, Marceau, Pratte, Stone, Urie.
nation: Nation of origin of claimant: Argentina, Bulgaria, China, Czechoslovakia, El.Salvador, Fiji, Ghana, Guatemala, India, Iran, Lebanon, Nicaragua, Nigeria, Pakistan, Poland, Somalia, Sri.Lanka.
rater: Judgment of independent rater: no, case has no merit; yes, case has some merit (leave to appeal should be granted).
decision: Judge’s decision: no, leave to appeal not granted; yes, leave to appeal granted. language: Language of case: English, French.
location: Location of original refugee claim: Montreal, other, Toronto.
success: Logit of success rate, for all cases from the applicant’s nation.
4) Interesting questions
- How are the values obtained for success?
- Where does the independent rater come from?
- Can we state that the judge’s decision depends on the nation that the refugees come from, according to the data?
5) Data displays using tables and barcharts
Package required
library(car)
library(spida2)
library(lattice)
library(latticeExtra)Loading required package: RColorBrewerlibrary(RColorBrewer)
library(Hmisc)Loading required package: survivalLoading required package: FormulaLoading required package: ggplot2
Attaching package: 'ggplot2'The following object is masked from 'package:latticeExtra':
layerThe following object is masked from 'package:spida2':
labs
Attaching package: 'Hmisc'The following objects are masked from 'package:spida2':
fillin, na.includeThe following objects are masked from 'package:base':
format.pval, round.POSIXt, trunc.POSIXt, unitsDownload data
download.file("http://socserv.socsci.mcmaster.ca/jfox/Books/Applied-Regression-3E/datasets/Greene.txt",
"Greene.txt")
greene <- read.table("Greene.txt", header = T)Summary
summary(greene) judge nation rater decision language
MacGuigan :70 Lebanon :71 no :254 no :270 English:253
Hugessen :62 China :68 yes:130 yes:114 French :131
Desjardins:46 Sri.Lanka :63
Pratte :42 Bulgaria :36
Heald :36 Somalia :29
Stone :33 El.Salvador:26
(Other) :95 (Other) :91
location success
Montreal:138 Min. :-2.0907
other : 55 1st Qu.:-1.0986
Toronto :191 Median :-0.9946
Mean :-1.0204
3rd Qu.:-0.7538
Max. : 0.4055
xqplot(greene) #raw values 
Adding a column ‘probability’ to the dataset using success values
probability <- 1/(1+exp(-greene$success))
Greene_new <- cbind(greene, probability)
summary(probability) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1100 0.2500 0.2700 0.2762 0.3200 0.6000 Tables
Greene_new %>%
tab__(~ rater + decision + language, pct = c(1,2)) %>%
round(1) %>%
ftable language English French
rater decision
no no 63.7 36.3
yes 73.6 26.4
yes no 59.4 40.6
yes 73.8 26.2Greene_new %>%
tab__(~ rater + decision + location, pct = c(1,2)) %>%
round(1) %>%
ftable location Montreal other Toronto
rater decision
no no 37.3 14.9 47.8
yes 28.3 17.0 54.7
yes no 43.5 11.6 44.9
yes 29.5 13.1 57.4tab(Greene_new, ~ rater + decision + nation, pct = 0), , nation = Argentina
decision
rater no yes Total
no 0.5208333 0.0000000 0.5208333
yes 0.2604167 0.5208333 0.7812500
Total 0.7812500 0.5208333 1.3020833
, , nation = Bulgaria
decision
rater no yes Total
no 7.5520833 0.5208333 8.0729167
yes 0.7812500 0.5208333 1.3020833
Total 8.3333333 1.0416667 9.3750000
, , nation = China
decision
rater no yes Total
no 11.1979167 2.6041667 13.8020833
yes 1.8229167 2.0833333 3.9062500
Total 13.0208333 4.6875000 17.7083333
, , nation = Czechoslovakia
decision
rater no yes Total
no 1.8229167 1.8229167 3.6458333
yes 0.2604167 2.3437500 2.6041667
Total 2.0833333 4.1666667 6.2500000
, , nation = El.Salvador
decision
rater no yes Total
no 2.3437500 0.7812500 3.1250000
yes 2.0833333 1.5625000 3.6458333
Total 4.4270833 2.3437500 6.7708333
, , nation = Fiji
decision
rater no yes Total
no 0.2604167 0.0000000 0.2604167
yes 0.0000000 0.0000000 0.0000000
Total 0.2604167 0.0000000 0.2604167
, , nation = Ghana
decision
rater no yes Total
no 1.3020833 0.2604167 1.5625000
yes 0.7812500 0.0000000 0.7812500
Total 2.0833333 0.2604167 2.3437500
, , nation = Guatemala
decision
rater no yes Total
no 0.7812500 0.2604167 1.0416667
yes 0.2604167 0.0000000 0.2604167
Total 1.0416667 0.2604167 1.3020833
, , nation = India
decision
rater no yes Total
no 0.0000000 0.2604167 0.2604167
yes 0.0000000 0.5208333 0.5208333
Total 0.0000000 0.7812500 0.7812500
, , nation = Iran
decision
rater no yes Total
no 2.3437500 0.5208333 2.8645833
yes 1.0416667 0.2604167 1.3020833
Total 3.3854167 0.7812500 4.1666667
, , nation = Lebanon
decision
rater no yes Total
no 10.6770833 2.6041667 13.2812500
yes 3.1250000 2.0833333 5.2083333
Total 13.8020833 4.6875000 18.4895833
, , nation = Nicaragua
decision
rater no yes Total
no 0.2604167 0.2604167 0.5208333
yes 0.7812500 0.2604167 1.0416667
Total 1.0416667 0.5208333 1.5625000
, , nation = Nigeria
decision
rater no yes Total
no 1.0416667 0.0000000 1.0416667
yes 0.5208333 0.2604167 0.7812500
Total 1.5625000 0.2604167 1.8229167
, , nation = Pakistan
decision
rater no yes Total
no 0.0000000 0.2604167 0.2604167
yes 0.5208333 0.2604167 0.7812500
Total 0.5208333 0.5208333 1.0416667
, , nation = Poland
decision
rater no yes Total
no 1.8229167 0.0000000 1.8229167
yes 1.0416667 0.0000000 1.0416667
Total 2.8645833 0.0000000 2.8645833
, , nation = Somalia
decision
rater no yes Total
no 3.3854167 1.3020833 4.6875000
yes 2.0833333 0.7812500 2.8645833
Total 5.4687500 2.0833333 7.5520833
, , nation = Sri.Lanka
decision
rater no yes Total
no 7.0312500 2.3437500 9.3750000
yes 2.6041667 4.4270833 7.0312500
Total 9.6354167 6.7708333 16.4062500
, , nation = Total
decision
rater no yes Total
no 52.3437500 13.8020833 66.1458333
yes 17.9687500 15.8854167 33.8541667
Total 70.3125000 29.6875000 100.0000000tab(Greene_new, ~ rater + decision + judge, pct = 0), , judge = Desjardins
decision
rater no yes Total
no 3.9062500 3.1250000 7.0312500
yes 1.8229167 3.1250000 4.9479167
Total 5.7291667 6.2500000 11.9791667
, , judge = Heald
decision
rater no yes Total
no 5.2083333 1.0416667 6.2500000
yes 1.3020833 1.8229167 3.1250000
Total 6.5104167 2.8645833 9.3750000
, , judge = Hugessen
decision
rater no yes Total
no 8.8541667 1.3020833 10.1562500
yes 4.1666667 1.8229167 5.9895833
Total 13.0208333 3.1250000 16.1458333
, , judge = Iacobucci
decision
rater no yes Total
no 5.4687500 0.0000000 5.4687500
yes 1.3020833 0.7812500 2.0833333
Total 6.7708333 0.7812500 7.5520833
, , judge = MacGuigan
decision
rater no yes Total
no 10.4166667 2.0833333 12.5000000
yes 3.3854167 2.3437500 5.7291667
Total 13.8020833 4.4270833 18.2291667
, , judge = Mahoney
decision
rater no yes Total
no 3.1250000 1.0416667 4.1666667
yes 1.3020833 2.3437500 3.6458333
Total 4.4270833 3.3854167 7.8125000
, , judge = Marceau
decision
rater no yes Total
no 2.3437500 2.8645833 5.2083333
yes 0.2604167 1.0416667 1.3020833
Total 2.6041667 3.9062500 6.5104167
, , judge = Pratte
decision
rater no yes Total
no 6.5104167 0.7812500 7.2916667
yes 2.8645833 0.7812500 3.6458333
Total 9.3750000 1.5625000 10.9375000
, , judge = Stone
decision
rater no yes Total
no 4.9479167 0.7812500 5.7291667
yes 1.5625000 1.3020833 2.8645833
Total 6.5104167 2.0833333 8.5937500
, , judge = Urie
decision
rater no yes Total
no 1.5625000 0.7812500 2.3437500
yes 0.0000000 0.5208333 0.5208333
Total 1.5625000 1.3020833 2.8645833
, , judge = Total
decision
rater no yes Total
no 52.3437500 13.8020833 66.1458333
yes 17.9687500 15.8854167 33.8541667
Total 70.3125000 29.6875000 100.0000000Table to look at % of yes/no from decisions and raters for each nation
tab__(Greene_new, ~ decision + nation, pct = 2) %>%
round(1) nation
decision Argentina Bulgaria China Czechoslovakia El.Salvador Fiji Ghana
no 60.0 88.9 73.5 33.3 65.4 100.0 88.9
yes 40.0 11.1 26.5 66.7 34.6 0.0 11.1
nation
decision Guatemala India Iran Lebanon Nicaragua Nigeria Pakistan Poland
no 80.0 0.0 81.2 74.6 66.7 85.7 50.0 100.0
yes 20.0 100.0 18.8 25.4 33.3 14.3 50.0 0.0
nation
decision Somalia Sri.Lanka
no 72.4 58.7
yes 27.6 41.3tab__(Greene_new, ~ rater + nation, pct = 2) %>%
round(1) nation
rater Argentina Bulgaria China Czechoslovakia El.Salvador Fiji Ghana
no 40.0 86.1 77.9 58.3 46.2 100.0 66.7
yes 60.0 13.9 22.1 41.7 53.8 0.0 33.3
nation
rater Guatemala India Iran Lebanon Nicaragua Nigeria Pakistan Poland
no 80.0 33.3 68.8 71.8 33.3 57.1 25.0 63.6
yes 20.0 66.7 31.2 28.2 66.7 42.9 75.0 36.4
nation
rater Somalia Sri.Lanka
no 62.1 57.1
yes 37.9 42.9unique(probability) * 100 # Somalia and China have same probability of success [1] 25.00004 32.00004 25.99997 60.00012 23.00002 27.00005 14.00000
[8] 16.99996 34.00009 12.99999 11.00001 30.99999 36.99993 37.99996Creating a new table to compare decision and probability for each nation
NewTable <- data.frame(nation = c("Argentina","Bulgaria","China","Czechoslovakia","El.Salvador","Fiji","Ghana","Guatemala","India","Iran","Lebanon","Nicaragua","Nigeria","Pakistan","Poland","Somalia","Sri.Lanka"),
decision = c("40.0","11.1","26.5","66.7","34.6","0.0","11.1","20.0","100.0","18.8","25.4","33.3","14.3","50.0","0.0","27.6","41.3"))
NewTable$probability = Greene_new$probability[match(NewTable$nation, Greene_new$nation)]*100Table to look at % of yes/no from decisions and raters for each judge
tab__(Greene_new, ~ decision + judge, pct = 2) %>%
round(1) judge
decision Desjardins Heald Hugessen Iacobucci MacGuigan Mahoney Marceau
no 47.8 69.4 80.6 89.7 75.7 56.7 40.0
yes 52.2 30.6 19.4 10.3 24.3 43.3 60.0
judge
decision Pratte Stone Urie
no 85.7 75.8 54.5
yes 14.3 24.2 45.5tab__(Greene_new, ~ rater + judge, pct = 2) %>%
round(1) judge
rater Desjardins Heald Hugessen Iacobucci MacGuigan Mahoney Marceau Pratte
no 58.7 66.7 62.9 72.4 68.6 53.3 80.0 66.7
yes 41.3 33.3 37.1 27.6 31.4 46.7 20.0 33.3
judge
rater Stone Urie
no 66.7 81.8
yes 33.3 18.2Bar Charts
colors = c("red","green")Barchart showing rater outcome vs. decision for each nation
tab__(Greene_new, ~ nation + decision + rater, pct = c(1,2)) %>%
barchart(ylab = list(label = "rater probability", cex = 1.5),
ylim = c(1,100),
xlab = list(label = "nation", cex = 1.5),
horizontal = FALSE,
stack = FALSE,
auto.key = list(space = list(space = "top"), title = "Rater vs. Decision for each nation", column = 2),
par.settings = list(superpose.polygon = list(col = colors)))
Adding column for continents to include in barchart
for(i in 1:nrow(greene)){
if(greene$nation[i] == "Bulgaria"){greene$continent[i] <- "Europe"}
else if (greene$nation[i] == "Argentina"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "China"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "Czechoslovakia"){greene$continent[i] <- "Europe"}
else if (greene$nation[i] == "El.Salvador"){greene$continent[i] <- "South America"}
else if (greene$nation[i] == "Fiji"){greene$continent[i] <- "Oceania"}
else if (greene$nation[i] == "Ghana"){greene$continent[i] <- "Africa"}
else if (greene$nation[i] == "Guatemala"){greene$continent[i] <- "South America"}
else if (greene$nation[i] == "India"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "Iran"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "Lebanon"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "Nicaragua"){greene$continent[i] <- "South America"}
else if (greene$nation[i] == "Nigeria"){greene$continent[i] <- "Africa"}
else if (greene$nation[i] == "Pakistan"){greene$continent[i] <- "Asia"}
else if (greene$nation[i] == "Poland"){greene$continent[i] <- "Europe"}
else if (greene$nation[i] == "Somalia"){greene$continent[i] <- "Africa"}
else if (greene$nation[i] == "Sri.Lanka"){greene$continent[i] <- "Asia"}
else {greene$continent[i] <- "N/A"}
}
Greene_new$continent <- factor(greene$continent)Barchart showing rater outcome vs. decision for each continent
tab__(Greene_new, ~ continent + decision + rater, pct = c(1,2)) %>%
barchart(ylab = list(label = "rater probability", cex = 1.5),
ylim = c(1,100),
xlab = list(label = "continent", cex = 1.5),
horizontal = FALSE,
stack = FALSE,
auto.key = list(space = list(space = "top"), title = "Rater vs. Decision for each continent", column = 2),
par.settings = list(superpose.polygon = list(col = colors)))
Barchart showing decision outcome vs. rater for each judge
tab__(Greene_new, ~ judge + rater + decision, pct = c(1,2)) %>%
barchart(ylab = list(label = "decision probability", cex = 1.5),
ylim = c(1,100),
xlab = list(label = "judge", cex = 1.5),
horizontal = FALSE,
stack = FALSE,
auto.key = list(space = list(space = "top"), title = "Decision vs. Rater for each judge", column = 2),
par.settings = list(superpose.polygon = list(col = colors)))
Axis variables: y-axis: rater probability, x-axis: nation & continent
Panel variables: decision
Grouping variables: Africa, Asia, Europe, North America, Oceania, South America
6) Conclusions
After analysing the data, we would like to do more. Unfortunately, the data set has some limitations, although we have tried to manipulate the data by adding new columns (eg continent) to study some relation between the explanatory variables. At this time, it is hard to get significant conclusions, but it is possible to suspect which direction we can follow. For example we can see strong patterns when the rater is no, the decision is normally no too. The nation/continent seems to not be correlated with the decision. Intuitively, the language and location don’t have any relation with the decision.