[R] Question on WLS (gls vs lm)

[Viechtbauer Wolfgang (STAT)]

The weights in 'aa' are the inverse standard deviations. But you want to use the inverse variances as the weights:

aa <- (attributes(summary(f1)$modelStruct$varStruct)$weights)^2

And then the results are essentially identical.

Best,

--
Wolfgang Viechtbauer                        http://www.wvbauer.com/
Department of Methodology and Statistics    Tel: +31 (0)43 388-2277
School for Public Health and Primary Care   Office Location:
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----Original Message----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Stats Wolf Sent:
Thursday, June 24, 2010 15:00 To: Joris Meys
Cc: r-help at r-project.org
Subject: Re: [R] Question on WLS (gls vs lm)

> Indeed, they should give the same results, and hence I was worried to
> see that the results were not that same. Suffice it to look at
> standard errors and p-values: they do differ, and the differences are
> not really that small.
>
>
> Thanks,
> Stats Wolf
>
>
>
> On Thu, Jun 24, 2010 at 2:39 PM, Joris Meys <jorismeys at gmail.com>
> wrote:
>> 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_square
>>>> s_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
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide
>>>>> http://www.R-project.org/posting-guide.html
>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> 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
>>
>
> ______________________________________________
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