## Working notes on the abcd spline, presidental polling data
## December 14, 2007

polls<-read.csv("http://www.stat.wisc.edu/~eng/spline1/KEpollhouse.csv",header=T)
polls<-polls[order(polls$Date),]
polls$fDate<-as.Date(polls$fDate)


# Build a basis on weeks
  weeks       <- seq(min(polls$fDate)+7,max(polls$fDate),by=7)
  weeks.b1    <- sapply(weeks,function(x)as.numeric(polls$fDate>=x))
  colnames(weeks.b1)<-as.character(weeks)
  weeks.qr    <- qr(weeks.b1)
  weeks.basis <- weeks.b1[,weeks.qr$pivot[1:weeks.qr$rank]]
  weeks       <- weeks[weeks.qr$pivot[1:weeks.qr$rank]]

# Build random effects on houses
  house<-as.character(polls$house)
  index<-c(2,5,9,10,13,14,15,16,21,22,23,26)
  house[house %in% sort(names(table(polls$house))[index])]<-"Independent"
  house[house %in% c("WNBC","NBC")]<-"NBC"
  house<-factor(house)

# Primary model is of the form
# formula = Favor ~ Date, 

# abcd spline functions to follow.