[R-sig-eco] GLS, GEE or LMM ??

Jens Oldeland oldeland at gmx.de
Fri Apr 16 14:34:38 CEST 2010


Dear Thierry,

thank you very much for your help! However, I think I have not explained 
my approach very good.
I am using this formula

M1.1.lme <- lme(aWert ~ Salinity +  pH + chl.a + NO3 + oyster_qm + 
meanspring,  random = ~ 1 | bank,  na.action=na.omit, method="ML",  
data=mussels,  correlation = corAR1(form = ~ datumszahl))

hence six variables for the fixed effect, bank (station) as the location 
effect and "datumszahl" for the time effect. Datumszahl is a numeric 
that replaces a certain date. For example 35932  would be 17. May 98. 
Hence I am not using year 2000 but day..35000? oops :-)

Do you still think that six variables are not enough to calculate a LMM 
or GEE?
But than...what is the purpose of such models when they do not work with 
a small set of variables?

thinking,
Jens



ONKELINX, Thierry schrieb:
> Dear Jens,
>
> A random effect with only three levels is not a good idea. You are
> estimating a variance on only three numbers. Have a look at the plot
> below. It gives the confidence interval of the ratio between the
> estimated variance and the true variance. Note that with three levels,
> the estimated variance can be from 40 times smaller up to 3.7 times
> larger than the true variance. If you have 30 (thirty) levels, this
> range is reduced: from 1.8 times smaller up to 1.5 times larger.
>
> n <- seq(2, 100)
> low <- qchisq(p = 0.025, df = n - 1) / (n - 1)
> high <- qchisq(p = 0.975, df = n - 1) / (n - 1)
> plot(n, high, type = "l", ylim = c(0, 5))
> lines(n, low)
> abline(h = 1, lty = 2)
>
> Therefore I recommend that you add the site variable to the fixed
> effects and drop the random effects.
>
> A) Centering continuous data will mostly only affect the estimates of
> the intercept. The intercept is the expected value of your respons when
> all variables are zero (or at their reference level). So if you have a
> timeseries ranging from 2000 to 2010, then the intercept is the value in
> the year 0. When you center year to 2000 (year = 2000 --> cyear = 0),
> then the intercept will be the expected value in the year 2000. The
> first is non sense given your time series, the latter has a practical
> interpretation. Note that both model will be mathematically identical
> but just use a different parametrisation.
>
> B) Given that you have only three levels, neither a LMM nor GEE will be
> a good model. So comparing them is not a good idea.
>
> C) Lower AIC is always better. So -10 is better than -5. AIC = 2 k - 2
> log(L) with k = number of parameters, L = likelihood. Models with a high
> likelihood will have a lower AIC (if the number of parameters are
> equal).
>
> HTH,
>
> Thierry
>
>
> ------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek
> team Biometrie & Kwaliteitszorg
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> Research Institute for Nature and Forest
> team Biometrics & Quality Assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to
> say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of
> data.
> ~ John Tukey
>   
>
>   
>> -----Oorspronkelijk bericht-----
>> Van: r-sig-ecology-bounces at r-project.org 
>> [mailto:r-sig-ecology-bounces at r-project.org] Namens Jens Oldeland
>> Verzonden: vrijdag 16 april 2010 12:50
>> Aan: r-sig-ecology at r-project.org
>> Onderwerp: [R-sig-eco] GLS, GEE or LMM ??
>>
>> Dear All, 
>>
>> I have run into a number of questions, and thus I hope you 
>> could help me out. I am modelling the effect of oyster 
>> density and nutrients on the bodyweight of mussels 
>> (population average).
>> Data was sampled at three different stations over 8 years, 
>> with values measured in springtime once per year.
>>
>> I was following Zuur et al 2009 Mixed Effects Models 
>> (wonderful book!), but got lost at some points since 
>> different models lead to totally different results.
>>
>> a) the first question is about "centring data". Zuur suggest 
>> to center parameters (p.334) if they are highly correlated 
>> with the intercept. 
>> When I apply a lme (family=gaussian, random ~ 1 | bank,  
>> correlation = corAR1(form = ~ daycount)) I have to center 
>> nearly all the values. When I apply a GEE then there is no 
>> correlation at all (r=0.14).
>> Actually, centring the data leads to the same output at the 
>> end (for the
>> lme)
>>
>> b) Choosing GEE, the effect of one parameter (salinity) is 
>> highly significant, while using the LMM approach it is not, 
>> which would be better for our interpretation...
>> But why? Is it because GEE should not be used on normally 
>> distributed data? I know that GEE uses sandwich estimator and 
>> LMM uses ML. Which one would be more "trustworthy" or conservative?
>>
>> c) one last qeustion: negative AICs, which one is better. 
>> AIC: -10 or -5 ? I have read contrasting statements. Is there 
>> any proof?? Does it hold for BIC as well?
>>
>> thank you in advance!
>> Jens
>>
>> -- 
>> +++++++++++++++++++++++++++++++++++++++++
>> Dipl.Biol. Jens Oldeland
>> Biodiversity of Plants
>> Biocentre Klein Flottbek and Botanical Garden University of 
>> Hamburg Ohnhorststr. 18
>> 22609 Hamburg,
>> Germany
>>
>> Tel:    0049-(0)40-42816-407
>> Fax:    0049-(0)40-42816-543
>> Mail: 	Oldeland at botanik.uni-hamburg.de
>>         Oldeland at gmx.de 	(for attachments > 2mb!!)
>> Skype:	jens.oldeland
>> http://www.biologie.uni-hamburg.de/bzf/fbda005/fbda005.htm
>> +++++++++++++++++++++++++++++++++++++++++
>>
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>>
>>     
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-- 
+++++++++++++++++++++++++++++++++++++++++
Dipl.Biol. Jens Oldeland
Biodiversity of Plants
Biocentre Klein Flottbek and Botanical Garden
University of Hamburg 
Ohnhorststr. 18
22609 Hamburg,
Germany

Tel:    0049-(0)40-42816-407
Fax:    0049-(0)40-42816-543
Mail: 	Oldeland at botanik.uni-hamburg.de
        Oldeland at gmx.de 	(for attachments > 2mb!!)
Skype:	jens.oldeland
http://www.biologie.uni-hamburg.de/bzf/fbda005/fbda005.htm
http://jensoldeland.wordpress.com
+++++++++++++++++++++++++++++++++++++++++



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