Mimicking SPSS weighted least squares

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Peter Dalgaard
Sent: March-11-08 11:27 AM
To: John Fox
Cc: r-help at r-project.org; 'Ben Domingue'
Subject: Re: [R] Mimicking SPSS weighted least squares

John Fox wrote:

Dear JRG, Rolf, Ben, and Peter,

"Frequency" weights, possibly even non-integer weights, are useful

for

surveys where observations are sampled with unequal probabilities of
selection. The approach in SPSS gives correct point estimates in this
situation but incorrect standard errors. The survey package, for

example,

provides a better solution.

Regards,
 John

Actually, I count this as a 3rd variant of weighting. I believe that
SPSS 's standard errors are actually OK for the case where one data
line
actually represents a number of identical replicates. To my mind, there
are three (main) kinds of weighting:

(1) Variance weighting (weights proportional to inverse variances)
(2) Case weights (weights identical to number of replicates)
(3) Inverse probability weights (weights inversely proportional to
sampling freq.)

All three give the same point estimates, beta=inv(X'WX)X'WY but the SEs
and DF are different (W is the diagonal matrix of weights). I think the
formulas are as follows (please correct if I goofed):

in (1) you get sigma^2=Y'(W-WX' inv(X'WX)X'W)Y/(n-rank(X)) ,
                        VCOV= sigma^2 inv(X'WX),

in (3) it is sigma^2=Y'(I-WX inv(X'WX)X') (I- X inv(X'WX)X'W)Y/(n-
rank(X)),
                   VCOV=sigma^2 inv(X'WX) X'WWX inv(X'WX)

in both these cases, the DF are n-rank(X)  (glossing over complications
that arise when the weights become zero) and the VCOV are stable to
proportional scaling of W.

in (2) you get sigma^2=Y'(W-WX' inv(X'WX)X'W)Y/(tr(W)-rank(X)),
                         VCOV= sigma^2 inv(X'WX),

This is deceptively similar to (1), but notice the denominator of
sigma^2. In this case, multiplying the weights by, say, 2 will roughly
halve the VCOV, which is fair enough since it means that you have twice
as much data.

--------------------------------
John Fox, Professor
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 r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of JRG
Sent: March-10-08 10:27 PM
To: Rolf Turner; r-help at r-project.org; Ben Domingue
Cc: r-help at r-project.org
Subject: Re: [R] Mimicking SPSS weighted least squares

On 11 Mar 2008 at 14:09, Rolf Turner wrote:

It would appear that the SPSS procedure would then give exactly the

same

point estimates of the parameters, and change the inference

structure

by

changing the ``denominator degrees of freedom'' from n-p to sum(w)

-

p.

Well, if that IS what SPSS does, then it sounds like what Stata

calls

frequency weights, the
general idea being that each "observation" in fact represents some

non-

negative number (w) of
actual observations that have identical values.  Not much more than

a

glorified version of a
frequency distribution table.

I don't see anything fundamentally wrong with frequency weights,

given

an appropriate situation.

---JRG

John R. Gleason

This seems to me to make little sense ...  But then, it ***is***
SPSS. :-)

	cheers,

		Rolf

On 11/03/2008, at 11:35 AM, Peter Dalgaard wrote:

Rolf Turner wrote:

On 11/03/2008, at 4:04 AM, Ben Domingue wrote:

Howdy,
In SPSS, there are 2 ways to weight a least squares regression:
1. You can do it from the regression menu.
2. You can set a global weight switch from the data menu.
These two options have no, in my experience, been equivalent.
Now, when I run lm in R with the weights= switch set

accordingly,

I

get the same set of results you would see with option #1 in

SPSS.

Does anybody know how to duplicate option #2 from SPSS in R?

I think it's up to you to find out what ``option #2 from SPSS''
actually
*does*.  If you know that, then you can (with a modicum of

effort)

duplicate that option in R.  The help file for lm() tells you

that

R uses the weights by minimizing sum(w*e^2) where w = weights and
e = ``errors'' or residuals.

I believe case weighting in SPSS effectively replicates the
relevant row (not sure if anything sensible comes out if weights
are non-integer).  So

lm(...., data=mydata[rep(1:nrow(mydata),w),])

or thereabouts should do it. Might not be too efficient though.

--
  O__  ---- Peter Dalgaard             ?ster Farimagsgade 5,

Entr.B

 c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45)
35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45)
35327907

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--
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45)
35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45)
35327907