[R] Question on WLS (gls vs lm)

[Joris Meys]

Indeed, WLS is a special case of GLS, where the error covariance
matrix is a diagonal matrix. OLS is a special case of GLS, where the
error is considered homoscedastic and all weights are equal to 1. And
I now realized that the varIdent() indeed makes a diagonal covariance
matrix, so the results should be the same in fact. Sorry for missing
that one.

A closer inspection shows that the results don't differ too much. The
fitting method differs between both functions; lm.wfit uses the QR
decomposition, whereas gls() uses restricted maximum likelihood. In
Asymptopia, they should give the same result.

Cheers
Joris


On Thu, Jun 24, 2010 at 12:54 PM, Stats Wolf <stats.wolf at gmail.com> wrote:
> Thanks for reply.
>
> Yes, they do differ, but does not gls() with the weights argument
> (correlation being unchanged) make the special version of GLS, as this
> sentence from the page you provided says: "The method leading to this
> result is called Generalized Least Squares estimation (GLS), of which
> WLS is just a special case"?
>
> Best,
> Stats Wolf
>
>
>
> On Thu, Jun 24, 2010 at 12:49 PM, Joris Meys <jorismeys at gmail.com> wrote:
>> Isn't that exactly what you would expect when using a _generalized_
>> least squares compared to a normal least squares? GLS is not the same
>> as WLS.
>>
>> http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_least_squares_generalized.htm
>>
>> Cheers
>> Joris
>>
>> On Thu, Jun 24, 2010 at 9:16 AM, Stats Wolf <stats.wolf at gmail.com> wrote:
>>> Hi all,
>>>
>>> I understand that gls() uses generalized least squares, but I thought
>>> that maybe optimum weights from gls might be used as weights in lm (as
>>> shown below), but apparently this is not the case. See:
>>>
>>> library(nlme)
>>> f1 <- gls(Petal.Width ~ Species / Petal.Length, data = iris,  weights
>>> = varIdent(form = ~ 1 | Species))
>>> aa <- attributes(summary(f1)$modelStruct$varStruct)$weights
>>> f2 <- lm(Petal.Width ~ Species / Petal.Length, data = iris, weights = aa)
>>>
>>> summary(f1)$tTable; summary(f2)
>>>
>>> So, the two models with the very same weights do differ (in terms of
>>> standard errors). Could you please explain why? Are these different
>>> types of weights?
>>>
>>> Many thanks in advance,
>>> Stats Wolf
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
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>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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>>>
>>
>>
>>
>> --
>> Joris Meys
>> Statistical consultant
>>
>> Ghent University
>> Faculty of Bioscience Engineering
>> Department of Applied mathematics, biometrics and process control
>>
>> tel : +32 9 264 59 87
>> Joris.Meys at Ugent.be
>> -------------------------------
>> Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php
>>
>



-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
Joris.Meys at Ugent.be
-------------------------------
Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php