[R-sig-eco] GLS, GEE or LMM ??
ONKELINX, Thierry
Thierry.ONKELINX at inbo.be
Fri Apr 16 15:05:40 CEST 2010
Jens,
Please do read my e-mail again (and replace "three levels" with "four levels"). I was trying to explain that you have not enough levels of bank to use a mixed model.
And read chapter 6 of Zuur et al again. Do you have a trend in the observed values or in the residuals. The first requires time as a covariate in the fixed effects (or as a random slope). The latter requires a correlation structure along time.
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: Jens Oldeland [mailto:oldeland at gmx.de]
> Verzonden: vrijdag 16 april 2010 14:59
> Aan: Ben Bolker
> CC: ONKELINX, Thierry; r-sig-ecology at r-project.org
> Onderwerp: Re: [R-sig-eco] GLS, GEE or LMM ??
>
> Dear Ben,
>
> > How many levels of "bank" are there?
>
> there are four banks, thus four levels and ...
>
> > How many observations do you have overall?
>
> fourty values overall which are roughly equally distributed
> i.e. 10, 7,10,13.
>
> > I take it that there are not trends in date?
> There is a clear trend in date. That´s why I used the
> AR1-correlation structure.
>
>
> > What is the nature of aWert? Counts, continuous measurements?
> the aWert is a continous unitless measure of the
> "fleshweight" of a mussel. Originally we had many many single
> values for aWert but since we had always the same values pH
> etc. for each bank at each date, we averaged the aWert to a
> population average per bank.
>
>
>
> > The usual point of random-effects models is to analyze data where
> > there are a *large* number of groups, possibly with
> relatively small
> > numbers of samples per group.
>
> Hmmm, I see that this is might not be the case in our data.
> But what is "large" and what is relatively small... is 4
> groups with 10 samples a large number of groups, or not?
> Sorry, I am lacking experience in this question :(
>
> best
> jens
>
>
>
> Ben Bolker schrieb:
> > Jens Oldeland wrote:
> >
> >> 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 :-)
> >>
> >
> > How many levels of "bank" are there? That's the critical
> question.
> > I take it that there are not trends in date? If so, you
> should have
> > 'datumszahl' in the fixed effects as well as in the
> correlation structure.
> > What is the nature of aWert? Counts, continuous
> measurements? Are
> > the counts small numbers?
> >
> > How many observations do you have overall?
> >
> >
> >> 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?
> >>
> >
> > The usual point of random-effects models is to analyze data where
> > there are a *large* number of groups, possibly with
> relatively small
> > numbers of samples per group.
> >
> >> 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
> >>>> +++++++++++++++++++++++++++++++++++++++++
> >>>>
> >>>> _______________________________________________
> >>>> R-sig-ecology mailing list
> >>>> R-sig-ecology at r-project.org
> >>>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> >>>>
> >>>>
> >>>>
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> >>> Please do not print this message unnecessarily.
> >>>
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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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