#AM 010.R LOCALIZED POLYNOMIAL REGRESSION & SPLINES
#READING AND SORTING DATA FRAME ON LENGTH
setwd("c:/DATA/Models")
L=read.table("clams.txt",header=T)
L
LL=L[order(L$LENGTH) , ] 
#order() SORTS DATA FRAME BY ROWS USING VARIALBLE LENGTH
#NOTE USE OF , TO INDICATE SORT BY ROWS
LL
length(LL$AFD)


#USING loess() FIT OF DATA IN R BASE PACKAGE
LOW=loess(AFD~LENGTH,data=LL)
summary(LOW)

#PLOTTING ORIGINAL DATA & loess() PREDICTION
#BY CALLING VARIABLES WITHIN LL USING $
plot(LL$LENGTH,LL$AFD,pch=19,col='blue',xlab="LENGTH",ylab="AFD")
points(LL$LENGTH,predict(LOW),type='l',col='red')

#CUBIC SPLINE
library(mgcv)
LLG=gam(AFD~s(LENGTH,fx=F,k=-1,bs='cr'),data=LL)
summary(LLG)
summary(LLG)

#CALCULATING FIT & CONFIDENCE BOUNDS
LLGpred=predict(LLG,se=T,type='response')LLGpredF=LLGpred$fit
LLGpredU=LLGpred$fit+2*LLGpred$se
LLGpredL=LLGpred$fit-2*LLGpred$se

#PLOTTING DATA & gam() FIT WITH APPROXIMATE 95% CONFIDENCE BOUNDS 
plot(LL$LENGTH,LL$AFD,pch=19,col='blue',xlab="LENGTH",ylab="AFD")
points(LL$LENGTH,LLGpredF,type='l',col='green')
points(LL$LENGTH,LLGpredU,type='l',col='red')
points(LL$LENGTH,LLGpredL,type='l',col='brown')