#======================================================
# Illustration of Poisson regression for ungrouped data
# Example: Car insurance data
#======================================================

# Read data on number of claims for private cars and select the sedans 
data="http://www.uio.no/studier/emner/matnat/math/STK3100/data/car.txt"
car=read.table(data,header=T,sep=",")
car0=car[car$veh_body=="SEDAN",c(2,7,8,10,4)]
head(car0)

# Definition of variables:
#   exposure:  proportion of period insured
#   veh_age:   age of vehicle: 1 (newest), 2, 3, 4
#   gender:    gender of driver: M, F
#   agecat:    driver's age category: 1 (youngest), 2, 3, 4, 5, 6
#   numclaims: number of claims

# Summaries of number of claims:
table(car0$numclaims)
mean(car0$numclaims)  
var(car0$numclaim)

# Fit Poisson GLM with logarithmic link:
fit1=glm(numclaims~offset(log(exposure))+factor(veh_age)+gender +factor(agecat), family=poisson,data=car0)
summary(fit1)
drop1(fit1,test="LRT")

# Omit gender:
fit2=glm(numclaims~offset(log(exposure))+factor(veh_age) +factor(agecat),family=poisson,data=car0)
summary(fit2)
drop1(fit2,test="LRT")

# Print rate ratios for age groups 2-6 (relative to the youngest)
exp(fit2$coef[5:9])

# Print rate ratios for age of vehicle groups 2-4 (relative to the newest)
exp(fit2$coef[2:4])

# Prediction for a driver in the oldest age category
# who has a new car and has been insured the whole period
new.covar=data.frame(exposure=1,veh_age=1,agecat=6)
predict(fit2,newdata=new.covar,type="response")

# Prediction for a driver in the youngest age category
# who has an old car and has been insured the whole period
new.covar=data.frame(exposure=1,veh_age=4,agecat=1)
predict(fit2,newdata=new.covar,type="response")