R help - Dec 2007 - "gam()" in "gam" package

R-users
E-mail: r-help@r-project.org

   I have a quenstion on "gam()" in "gam" package.
The help of gam() says:
      'gam' uses the _backfitting
     algorithm_ to combine different smoothing or fitting methods.

On the other hand,  lm.wfit(), which is a routine of gam.fit() contains:

        z <- .Fortran("dqrls", qr = x * wts, n = n, p = p, y = y *
        wts, ny = ny, tol = as.double(tol), coefficients = mat.or.vec(p,
        ny), residuals = y, effects = mat.or.vec(n, ny), rank = integer(1),
        pivot = 1:p, qraux = double(p), work = double(2 * p),
        PACKAGE = "base")

It may indicate that QR decomposition is used to derive an additive model
instead of backfitting.
   I am wondering if my guess is correct, or this "the _backfitting
algorithm"
has another meaning.

   ********     E-mail: takezawa@affrc.go.jp     ********
***** http://cse.naro.affrc.go.jp/takezawa/intro.html *****

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R-users
E-mail: r-help@r-project.org
>Please don't ask the same question multiple times!
   I am really sorry about it. I thought that my first mail did not
work.
>And no, backfitting and QR are unrelated concepts. You need to read up
>on the theory,
   To derive an additive model, we have two methods: (1) backfitting,
(2) solving multiple linear equation using QR decomposition.
>If i read the code correctly, lm.wfit is called iteratively in gam.fit,
>via the line
>       fit <- eval(bf.call)
>The iteration is necessary to the backfitting algorithm.
   This iteration seems to be for "iteratively reweighted least
squares" not
for backfitting. And lm.wfit may solve multiple linear equation using
QR decomposition; but I am not sure.
-- 
*****    r.otasuke@gmail.com    *****
http://cse.naro.affrc.go.jp/takezawa/intro.html

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R-users
E-mail: r-help@r-project.org
> This iteration seems to be for "iteratively reweighted least
squares" not
>for backfitting. And lm.wfit may solve multiple linear equation using
>QR decomposition; but I am not sure.
   Let me tell you something about my guess above.
The iteration below is from 1 to maxit.

  for (iter in 1:maxit) {
        ------
        fit <- eval(bf.call)
        ------
  }

The help of "gam.control()" says:
   maxit: maximum number of local scoring iterations
   bf.maxit: maximum number of backfitting iterations

Therefore the iteration above is local scoring iteration not
backfitting iteration.

   The first line of "lm.wfit()" is:
function (x, y, w, offset = NULL, method = "qr", tol = 1e-07,
 singular.ok = TRUE, ...)
There is no "bf.maxit" or its equivalent in these arguments. And it
contains 'method = "qr"'; it may mean that this routine solves
a multiple linear equation using QR decomposition.
-- 
*****    r.otasuke@gmail.com    *****
http://cse.naro.affrc.go.jp/takezawa/intro.html

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