source('../../Data/get_cancer_data.R')
DF = get_cancer_data()

## Here we follow the code in the book for this exercise:
## 
age = rep(1:18, 5)
pop = c(DF$pop47, DF$pop51, DF$pop56, DF$pop61, DF$pop66)
death = c(DF$d47, DF$d51, DF$d56, DF$d61, DF$d66)
period = rep(1:5, each=18) ## period categories
cohort = age - period
cohort = cohort - min(cohort) + 1 ## categories start at one
cancer = cbind(death, pop, age, period, cohort)
cancer = data.frame(cancer)
print(head(cancer))

## A model with age and year periods: 
##
m1 = glm(death ~ as.factor(age) + as.factor(period), offset=log(pop), family=poisson, data=cancer)
print(summary(m1))

residuals1 = residuals(m1)
plot(residuals1)

## Plot the coefficients of the factor age:
##
coefs = coefficients(m1)
age_coefs = coefs[2:18]
period_coefs = coefs[19:22]

plot(age_coefs, pch=19, main='model 1: coefficients of the age factor')
grid()

plot(period_coefs, pch=19, main='model 1: coefficients of the period factor')
grid()

## A model with age, period, and cohort
##
m2 = glm(death ~ as.factor(age) + as.factor(period) + as.factor(cohort), offset=log(pop), family=poisson, data=cancer)
print(summary(m2))

## Lets see if the same pattern of the coefficients (as with model m1) holds in this model: 
##
coefs = coefficients(m2)
age_coefs = coefs[2:18]
period_coefs = coefs[19:22]
cohort_coefs = coefs[23:42]

plot(age_coefs, pch=19, main='model 2: coefficients of the age factor')
grid()

plot(period_coefs, pch=19, main='model 2: coefficients of the period factor')
grid()

plot(cohort_coefs, pch=19, main='model 2: coefficients of the cohort factor')
grid()