ChainLadder_with_lm_and_design_matrix.R

## Ideas from: http://pirategrunt.wordpress.com/2013/01/02/you-cant-spell-loss-reserving-without-r/

library(ChainLadder)
## example triangle
data(RAA)

## transform triangles into data frames with prior and current columns
triangle2dat <- function(myTriangle){
  Cumulative <- as.data.frame(as.triangle(myTriangle), na.rm=TRUE)
  names(Cumulative)[3] <- "Cumulative"
  PriorCumulative <- transform(Cumulative, dev=dev + 1)
  names(PriorCumulative)[3] <- "PriorCumulative"
  dat <- merge(Cumulative, PriorCumulative)
  dat <- dat[order(dat$dev),]
  dat <- transform(dat, dev=factor(dev))
  return(dat)
}

dat <- triangle2dat(RAA)
head(dat,10)
tail(dat,10)

## Create design matrix
dm <- with(dat, model.matrix(PriorCumulative ~ dev + 0) * PriorCumulative)
delta <- 1 
## Weighted linear regression through the origin to get chain ladder link ratios
Fit = with(dat, lm(Cumulative ~ dm + 0, weights=1/PriorCumulative^delta))

summary(Fit)
coef(Fit)

op <- par(mfrow=c(2,2))
plot(Fit)
par(op)

library(lattice)
xyplot(Cumulative/1000 ~ PriorCumulative/1000 | dev, groups=origin, 
       data=dat, auto.key=list(space="right", 
                               title="origin\nyear",
                               cex.title=1),
       main=paste0("Red line: Weighted linear regression though origin\n",
                   "Black line: Linear regression with intercept"),
       as.table=TRUE, 
       panel=function(x,y,...){
         panel.xyplot(x,y)
         if(length(x)>1){
           panel.abline(lm(y~x+0, weights=1/x), col="red")
           panel.abline(lm(y~x))         
         }
       }
       )