[R] loess: choose span to minimize AIC?

[Thomas Lumley]

On Thu, 17 Nov 2005, Michael Friendly wrote:

> Is there an R implementation of a scheme for automatic smoothing
> parameter selection with loess, e.g., by minimizing one of the AIC/GCV
> statistics discussed by Hurvich, Simonoff & Tsai (1998)?

If you particularly want loess smoothing then I don't know, but if 
penalised spline smoothing will do then in gam() in the mgcv package does 
minimize GCV.

 	-thomas

> Below is a function that calculates the relevant values of AICC,
> AICC1 and GCV--- I think, because I to guess from the names of the
> components returned in a loess object.
>
> I guess I could use optimize(), or do a simple line search on span=,
> but I'm not sure how to use loess.aic to write a function
> that would act as a wrapper for loess() and return the mimimizing
> loess fit for a specified criterion.
>
> loess.aic <- function (x) {
> 	# extract values from loess object
> 	if (!(inherits(x,"loess"))) stop("Error: argument must be a loess object")
> 	span <- x$pars$span
> 	n <- x$n
> 	traceL <- x$trace.hat
> 	sigma2 <- sum( x$residuals^2 ) / (n-1)
> 	delta1 <- x$one.delta
> 	delta2 <- x$two.delta
> 	enp <- x$enp
>
> 	aicc <- log(sigma2) + 1 + 2* (2*(traceL+1)) / (n-traceL-2)
> 	aicc1<- n*log(sigma2) + n* (
> (delta1/(delta2*(n+enp)))/(delta1^2/delta2)-2 )
> 	gcv  <- n*sigma2 / (n-traceL)^2
>
> 	result <- list(span=span, aicc=aicc, aicc1=aicc1, gcv=gcv)
> 	return(result)
> }
>
>
> > cars.lo <- loess(dist ~ speed, cars)
> >
> > (values <- loess.aic(cars.lo))
> $span
> [1] 0.75
>
> $aicc
> [1] 6.93678
>
> $aicc1
> [1] 167.7267
>
> $gcv
> [1] 5.275487
>
> >
>
>
> -- 
> Michael Friendly     Email: friendly AT yorku DOT ca
> Professor, Psychology Dept.
> York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
> 4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html
> Toronto, ONT  M3J 1P3 CANADA
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle