Re: [R] Question on WLS (gls vs lm)

From: Joris Meys <jorismeys_at_gmail.com>
Date: Thu, 24 Jun 2010 15:43:21 +0200

Thanks! I was getting confused as wel, Wolf really had a point.

I have to admit that this is all a bit counterintuitive. I would expect those weights to be the inverse of the variances, as GLS uses the inverse of the variance-covariance matrix. I finally found in the help files ?nlme::varWeights the needed information, after you pointed out the problem and after strolling through quite a part of the help files...

Does this mean that the GLS algorithm uses 1/sd as weights (can't imagine that...), or is this one of the things in R that just are like that?

Cheers
Joris

On Thu, Jun 24, 2010 at 3:20 PM, Viechtbauer Wolfgang (STAT) <Wolfgang.Viechtbauer_at_stat.unimaas.nl> wrote:
> 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:
> Maastricht University, P.O. Box 616         Room B2.01 (second floor)
> 6200 MD Maastricht, The Netherlands         Debyeplein 1 (Randwyck)
>
>
> ----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
>>>
>>
>> ______________________________________________
>> 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

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