The R Book

An example with strongly humped data

The ethanol dataframe contains 88 sets of measurements for variables from an experiment in which ethanol was burned in a single cylinder automobile test engine. The response variable, NO_x, is the concentration of nitric oxide (NO) and nitrogen dioxide (NO₂) in engine exhaust, normalized by the work done by the engine, and the two continuous explanatory variables are C (the compression ratio of the engine), and E (the equivalence ratio at which the engine was run, which is a measure of the richness of the air–ethanol mix).

install.packages("SemiPar")
library(SemiPar)
data(ethanol)
attach(ethanol)
names(ethanol)

[1] "Nox" "C" "E"

Because NOx is such a strongly humped function of the equivalence ratio, E, we start with a model, NOx ~ s(E) + C, that fits this as a smoothed term and estimates a parametric term for the compression ratio:

model<-gam(NOx~s(E)+C)
par(mfrow=c(1,2))
plot.gam(model,residuals=T,pch=16,all.terms=T)

The coplot function is helpful in showing where the effect of C on NOx was most marked:

coplot(NOx~C|E,panel=panel.smooth)

There is a pronounced positive effect of C on NO_x only in panel 2 (ethanol 0.7 < E < 0.9 from the shingles ...