Data divisions and fit in R

Question

I have the following precipitation data for 1951:

dat.1951=c(122,122,122,122,122,122,122,122,122,122,122,121,121,121,121,120,119,119,117,117,117,115,115,115,114,112,112,111,110,109,106,105,104,103,102,99,97,95,91,89,88,86,84,83,83,82,82,79,77,77,76,74,74,72,72,71,70,69,66,65,64,61,61,58,56,56,54,53,51,49,48,47,46,46,46,45,42,40,39,38,37,36,36,35,34,33,33,32,30,30,29,28,28,27,25,25,23,22,21,20,20,20,20,20,19,19,18,18,18,16,16,15,15,15,15,15,14,14,14,14,14,14,14,14,14,14,14,13,13,12,12,11,11,11,11,11,11,11,11,11,11,11,11,11,11,10,10,10,9,8,8,8,8,8,8,8,8,8,8,8,8,7,7,6,6,6,6,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1) 

I want to match this data. I break this data into 2 areas (head and tail). One, where the points are less than 100 (head), and the rest (for> 100) is the tail. I could match the exponential part of the head (see code below). For the tail, I want to fit the curve and want to build both parts on the same plot along with the data. Can anyone help?

 dat.1951<-dat.1951[dat.1951 > 0] dat.1951.tail<-dat.1951[dat.1951 >= 100] dat.1951.head<-dat.1951[dat.1951 < 100] x.head<-seq(1,length(dat.1951.head)) log.data<-log(dat.1951.head) idf.head<-data.frame(x.head,dat.1951.head) idf.head$dat.1951.head<-log(idf.head$dat.1951.head) model=lm(idf.head$dat.1951.head ~ idf.head$x.head,data=idf.head) summary(model) plot(dat.1951.head) lines(idf.head$x.head,exp(fitted(model)),col="blue") 

Answer 1

I'm not sure why you want (1) to split the data into two regions, (2) eliminate the records where there was no precipitation, and (3) fit the model you are describing. You can consult statistics on these issues.

To answer your question, I came up with an example for the second model and demonstrated the techniques of both models on the same site.

 x <- seq(dat.1951) sel <- dat.1951 >= 100 model1 <- lm(dat.1951[sel] ~ poly(x[sel], 2)) model2 <- lm(log(dat.1951[!sel]) ~ x[!sel]) plot(dat.1951, cex=1.5) lines(x[sel], fitted(model1), col="blue", lwd=3) lines(x[!sel], exp(fitted(model2)), col="navy", lwd=3) 

Just for fun, I added a third model that matches all the data with the generalized additive model using the gam() function from the mgcv package.

 library(mgcv) model3 <- gam(dat.1951 ~ s(x)) lines(x, fitted(model3), col="orange", lwd=3, lty=2)