[R] Robust nonlinear regression - better example

[Spencer Graves]

      1.  The question of "linear" vs. "nonlinear" means "linear in the 
parameters to be estimated.  All the examples you have given so far are 
linear in the parameters to be estimated.  The fact that they are 
nonlinear in "x" is immaterial. 

      2.  With this hint and the posting guide 
"http://www.R-project.org/posting-guide.html", you may find more 
information.  A search there exposed much discussion of "robust 
regression" and even "robust nonlinear regression", if you actually 
still need that.  In addition, I found useful information on robust 
regression in Venables and Ripley (2002) Modern Applied Statistics with 
S, 4th ed. (Springer). 

      hope this helps. 
      spencer graves

cstrato wrote:

> Dear all
>
> Here is a hopefully better example with regards to
> nonlinear robust fitting:
>
> # fitting a polynomial:
> x <- seq(-10,10,0.2)
> y <- 10*x + 4*x*x - 2*x*x*x
> plot(x,y)
> z <- jitter(y,amount=300)
> plot(x,z)
> df <- as.data.frame(cbind(x,z))
> nf <- nls(z ~ a*x + b*x*x + c*x*x*x, data=df,
> +           start=list(a=4,b=2,c=1), trace = TRUE)
> 127697531 :  4 2 1
> 2974480 :  10.972123  3.793426 -1.942278
>
> # introducing outliers before fitting the  polynomial:
> z1 <- z
> z1[c(16,22,23,34,36,42,67,69,72,76)] <-
> + c(2000,1900,2000,1900,1600,1600,500,-2000,-1700,-1800)
> plot(x,z1)
> df1 <- as.data.frame(cbind(x,z1))
> nf1 <- nls(z1 ~ a*x + b*x*x + c*x*x*x, data=df1,
> +           start=list(a=4,b=2,c=1), trace = TRUE)
> 159359174 :  4 2 1
> 24098548 :  -59.053288   4.169518  -1.072027
>
> # plotting the results:
> y1 <- 10.97*x + 3.79*x*x - 1.94*x*x*x
> y2 <- -59.05*x + 4.17*x*x - 1.07*x*x*x
> oldpar <- par(pty="s",mfrow=c(2,2),mar=c(5,5,4,1))
> plot(x,y)
> plot(x,z1)
> plot(x,y1)
> plot(x,y2)
> par(oldpar)
>
> In my opinion this fit could hardly be considered
> to be robust.
>
> Are there functions in R which can do robust fitting?
> (Sorrowly, at the moment I could not test the package
> nlrq mentioned by Roger Koenker)
>
> Best regards
> Christian
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