# Edps 589
# Fall 2018
# C.J.Andersion
#
#  Answer for Homework 5, problem 1 (3.18 from Agresti)
#
library(MASS)

setwd("C:\\Users\\cja\\Dropbox\\edps 589\\homework")

fights <- read.table("a2007_318_data.txt",header=TRUE)

# Method 1

summary(method1 <- glm(arrests ~  -1 + attend  , data=fights, family=poisson(link="identity")) )

# take into account measured in 1,000s
method1$coefficients[1]/1000

# Method 2

summary(method2 <- glm(arrests ~ offset(log(attend)), data=fights, family=poisson) )

alpha <- method2$coefficients[1]

# take into account measured in 1,000s
expalpha <- exp(alpha)/1000

# Graph
plot(fights$attend,fights$arrests, 
    type='p',
	xlim=c(75,500),
	xlab="Number Attending Game (in thousands)",
	ylab="Number Arrested",
    main="Soccer: Number of Arrests by Number Attending")
j <- order(fights$attend)
lines(fights$attend[j],method2$fitted[j],type="l",col="red")
text(fights$attend,fights$arrests,fights$team)

# Look at adjusted std residuals
fights$res <- rstandard(method2,type="pearson")
fights


# Negative binomial

summary( nb <- glm.nb(arrests ~ offset(log(attend)),data=fights) )

fights$res.nb <- rstandard(nb,type="pearson")
fights