Difference between gam() and loess().

Good try, Kevin.  But that doesn't seem to do it. 

set.seed(123)

x <- sort(runif(100))

y <- sin(4*pi*x) + rnorm(100, sd=0.2)

ans.lo2 <- loess(y ~ x, degree=2, span=0.75)

ans.gam2 <- gam(y ~ lo(x, degree=2, span=0.75))

summary(ans.lo2$fitted - ans.gam2$fitted) # larger differences, about 10%

ans.lo1 <- loess(y ~ x, degree=1, span=0.75)

ans.gam1 <- gam(y ~ lo(x, degree=1, span=0.75))

summary(ans.lo1$fitted - ans.gam1$fitted) # smaller differences, about 2-5 percent

I also tried a number of other things including changing the "family", and parameters in "loess.control", but to no avail.  I looked at the Fortran codes from both loess and gam.  They are daunting, to say the least. They are dense, and there are absolutely no comments whatsoever.  But one thing is clear - they are using different Fortran codes.

So, the best bet might be to get Trevor Hastie or Bill Cleveland to help you out.  

But, before that:  why is this an issue, Rolf?  Is it important that these two results be identical?

Best,
Ravi.

----- Original Message -----
From: "Kevin E. Thorpe" <kevin.thorpe at utoronto.ca>
Date: Thursday, March 19, 2009 8:23 pm
Subject: Re: [R] Difference between gam() and loess().
To: Rolf Turner <r.turner at auckland.ac.nz>
Cc: R-help Forum <r-help at r-project.org>

Rolf Turner wrote:

 > 
 > It seems that in general
 > 
 >     gam(y~lo(x)) # gam() from the gam package.
 > 
 > and
 >     loess(y~x)
 > 
 > give slightly different results (in respect of the predicted/fitted 

 > values).
 > Most noticeable at the endpoints of the range of x.
 > 
 > Can anyone enlighten me about the reason for this difference?
 > 
 > Is it possible to twiddle the control parameters, for either or 

both 

 > functions,
 > so as to obtain identical results?

 
 There are two obvious differences in the defaults.  In lo() from the 
gam 
 package, span=0.5 and degree=1 while for loess(), span=0.75 and degree=2.
 
 Try gam(y~lo(x,span=0.75,degree=2)) and see if that helps.
 
 Kevin