[R] loess: choose span to minimize AIC?

[Liaw, Andy]

The locfit package (which, I believe, contains an independent implementation
of loess, plus more) contains the gcvplot() and aicplot() functions that I
think can do this.

Best,
Andy

> From: Michael Friendly
> 
> Thanks very much, John
> 
> The formula for AICC1 was transscribed from an ambiguously
> rendered version (in the SAS documentation).  This is a
> corrected version.
> 
> loess.aic <- function (x) {
> 	if (!(inherits(x,"loess"))) stop("Error: argument must 
> be a loess object")
> 	# extract values from 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 )
> 	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)
> }
> 
> 
> John Fox wrote:
> 
> > 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
> >>
> >>______________________________________________
> >>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
> 
> -- 
> 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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