[R] loess: choose span to minimize AIC?

[John Fox]

Dear Mike,

You could try

bestLoess <- function(model, criterion=c("aicc", "aicc1", "gcv"),
spans=c(.05, .95)){
    criterion <- match.arg(criterion)
    f <- function(span) {
        mod <- update(model, span=span)
        loess.aic(mod)[[criterion]]
        }
    result <- optimize(f, spans)
    list(span=result$minimum, criterion=result$objective)
    } 

A little experimentation suggests that aicc1 doesn't seem to behave
reasonably.

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> Michael Friendly
> Sent: Thursday, November 17, 2005 9:58 AM
> To: R-help at stat.math.ethz.ch
> Subject: [R] loess: choose span to minimize AIC?
> 
> 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)?
> 
> 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
> 
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