Difference between gam() and loess().

Ravi Varadhan wrote:

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.

There was one other thing I found that I shared with Rolf off-list.
In loess.control() there is an iterations argument which is related
to the robustness of the estimates.  I would think that could also
account for tail departures especially.

I don't gave the gam package installed, so can't test these myself
at the moment.

----- 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