Hi everybody, I would like to compare using the Akaike Information Criteria (AIC) a quadratic model and a piecewise fitted model.
Is it correct to use AIC to compare this models with such a different structure?
Thanks in advance
Angel


# A simple example
a<-1
b<-2
xx<-seq(-15,15,length=50) # Generate sequence of xs
yy<- 2 + 1.2*xx -0.2*xx^2 + runif(50, 0,8) #add some noise

## FIT models
lmXX<-lm(yy~xx) # Fit linear model
cuad<-lm(yy~xx+I(xx^2)) # Fit quadratic model

require(quantreg)
segXX<-segmented(lmXX,seg.Z=~xx,psi=list(xx=5)) # Fit piecewise model

## Visualize results
plot(xx,yy)
plot.segmented(segXX,add=T)
lines(xx,coef(cuad)[1]+coef(cuad)[2]*xx + coef(cuad)[3]*xx^2,col="blue")

c(AIC_cuadratic=AIC(cuad),AIC_segmented=AIC(segXX)) # Obviously AIC for the cuadratic model is lower than piecewise, so I would chose this model over a piecewise fit in this case. But is the use of AIC correct?
	[[alternative HTML version deleted]]

