[R-sig-eco] Question on Quadratic and Cubic Parameters
Alexandre Fadigas de Souza
alexsouza at cb.ufrn.br
Mon Oct 7 15:52:58 CEST 2013
Hi Scott, Hi Pedro,
Scott, thank you for the comments on the polynomials.
Regarding the NMDS axes, I was influenced by the ecological literature, in which nmds axes are taken as independent axes.
I replaced the nmds axes by PCA axes obtained on hellinger-transformed species abundances, since Legender and Gallagher argued that this transformation allowed the formerly inadequate pca to be used on compositional abundances.
Alexandre
Dr. Alexandre F. Souza
Professor Adjunto II Departamento de Botanica, Ecologia e Zoologia Universidade Federal do Rio Grande do Norte (UFRN) http://www.docente.ufrn.br/alexsouza Curriculo: lattes.cnpq.br/7844758818522706
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Enviadas: Sat, 05 Oct 2013 07:00:01 -0300 (BRT)
Assunto: R-sig-ecology Digest, Vol 67, Issue 3
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Today's Topics:
1. Re: Question on Quadratic and Cubic Parameters (Scott Foster)
2. Re: Question on Quadratic and Cubic Parameters (Pedro Pequeno)
3. Re: Animal movement packages (Lutfor)
----------------------------------------------------------------------
Message: 1
Date: Fri, 4 Oct 2013 20:27:21 +1000
From: Scott Foster <scott.foster at csiro.au>
To: <r-sig-ecology at r-project.org>
Subject: Re: [R-sig-eco] Question on Quadratic and Cubic Parameters
Message-ID: <524E9809.1060806 at csiro.au>
Content-Type: text/plain; charset="UTF-8"; format=flowed
Hi,
Centring will help reduce the correlation amongst covariates -- it is a good (and old) trick. A surer way is to use orthogonal polynomials. They are
slightly harder to interpret, but often this is immaterial. Try poly(x,3) and ?poly. Another option would be to ditch the idea of using a global
polynomial and use semi-parametric methods, such as B-splines (in library splines), or GAMMs (in library mgcv).
I fear that this is all fairly academic though. Cubics may be good enough -- check the model through diagnostics. Even though this is not trivial
for mixed models.
What concerns me a bit is the comment that the dependent variable is obtained from an NMDS. How is the uncertainty in the original data propagated
through the NMDS and the mixed model? At all? Are there any comments / opinions about this? Intrigued.
Scott
On 04/10/13 01:38, Zoltan Botta-Dukat wrote:
> Dear Alexandre,
>
> If your variables have only positive values, there will be strong correlation between linear, quadratic and cubic terms that leads to high VIF. You
> can avoid it by centering the variables before calculating quadratic and cubic terms:
>
> quadratic<-(x-mean(x))^2
> cubic<-(x-mean(x))^3
>
> Regards,
>
> Zoltan
>
>
> 2013.10.03. 14:49 keltez?ssel, Alexandre Fadigas de Souza ?rta:
>> Dear colleagues,
>>
>> I am working on a Linear Mixed Model with nested structure, based on the book of Zuur et al. 2009. Mixed Effects Models and Extensions in
>> Ecology with R, and have a question to ask to those of you more experienced with this model family.
>>
>> I am using several topographic variables (elevation, slope, convexity, facing) and one light-related variable (canopy openness) to explain
>> species abundance variation in 85 plots placed on 17 transects dispersed through a coastal vegetation complex on sandy soils in northeastern
>> Brazil. The dependent variable is axes of a floristic ordination (e.g., NMDS), with one separate model adjusted for each axis.
>>
>> I will use two levels of spatial aggregation as random factors: the transects (5 plots per transect) and broad transect clusters (transect
>> clusters were logistically conditioned).
>>
>> In the ecological literature, I have seen the suggestion of including quadratic and even cubic versions of the fixed effects variables (in this
>> case topographic and light) as a means to account for possible nonlinear effects of these variables on the dependent variable. One recent example is
>>
>> Brunbjerg, A.K., Ejrn?s, R., Svenning, J.-C., 2012. Species sorting dominates plant metacommunity structure in coastal dunes. Acta Oecologica 39,
>> 33?42.
>>
>> However, the inclusion of such quadratic and/or cubic terms in the model produces high colinearity levels (VIF > 25, sometimes even 38!).
>>
>> Do you think this is a valid procedure, the inclusion of these polynomial terms?
>> Thank you in advance for any ideas,
>>
>> Alexandre
>>
>> Dr. Alexandre F. Souza
>> Professor Adjunto II Departamento de Botanica, Ecologia e Zoologia Universidade Federal do Rio Grande do Norte (UFRN)
>> http://www.docente.ufrn.br/alexsouza Curriculo: lattes.cnpq.br/7844758818522706
>>
>> _______________________________________________
>> R-sig-ecology mailing list
>> R-sig-ecology at r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>
--
Scott Foster
Computational Informatics
CSIRO
E scott.foster at csiro.au T +61 3 6232 5178
Postal address: CSIRO Computational Informatics, GPO Box 1538, Hobart TAS 7001
Street Address: CSIRO Computational Informatics, Castray Esplanade, Hobart Tas 7001, Australia
www.csiro.au
------------------------------
Message: 2
Date: Fri, 4 Oct 2013 11:20:53 -0300
From: Pedro Pequeno <pacolipe at gmail.com>
To: scott.foster at csiro.au
Cc: "r-sig-ecology at r-project.org" <r-sig-ecology at r-project.org>
Subject: Re: [R-sig-eco] Question on Quadratic and Cubic Parameters
Message-ID:
<CAC4PjDvq7O8FQPWO1cyN8rCt+FcUYdopJcUxxWwAGjhz_YCpSA at mail.gmail.com>
Content-Type: text/plain
Hi all,
besides the question of uncertainty propagation (which is not obvious to me
either), I think there is another, more basic issue: NMDS "axes" actually
represent a single, joint solution; they are not indepedent. Thus, modeling
each separately is not a good idea (e.g.
http://www.r-forge.r-project.org/forum/forum.php?thread_id=4213&forum_id=194&group_id=68).
Still, you could use some other method that really accomplishes this such
as PCoA.
Pedro
2013/10/4 Scott Foster <scott.foster at csiro.au>
> Hi,
>
> Centring will help reduce the correlation amongst covariates -- it is a
> good (and old) trick. A surer way is to use orthogonal polynomials. They
> are slightly harder to interpret, but often this is immaterial. Try
> poly(x,3) and ?poly. Another option would be to ditch the idea of using a
> global polynomial and use semi-parametric methods, such as B-splines (in
> library splines), or GAMMs (in library mgcv).
>
> I fear that this is all fairly academic though. Cubics may be good enough
> -- check the model through diagnostics. Even though this is not trivial
> for mixed models.
>
> What concerns me a bit is the comment that the dependent variable is
> obtained from an NMDS. How is the uncertainty in the original data
> propagated through the NMDS and the mixed model? At all? Are there any
> comments / opinions about this? Intrigued.
>
> Scott
>
>
> On 04/10/13 01:38, Zoltan Botta-Dukat wrote:
>
>> Dear Alexandre,
>>
>> If your variables have only positive values, there will be strong
>> correlation between linear, quadratic and cubic terms that leads to high
>> VIF. You can avoid it by centering the variables before calculating
>> quadratic and cubic terms:
>>
>> quadratic<-(x-mean(x))^2
>> cubic<-(x-mean(x))^3
>>
>> Regards,
>>
>> Zoltan
>>
>>
>> 2013.10.03. 14:49 keltez�ssel, Alexandre Fadigas de Souza �rta:
>>
>>> Dear colleagues,
>>>
>>> I am working on a Linear Mixed Model with nested structure, based on
>>> the book of Zuur et al. 2009. Mixed Effects Models and Extensions in
>>> Ecology with R, and have a question to ask to those of you more experienced
>>> with this model family.
>>>
>>> I am using several topographic variables (elevation, slope,
>>> convexity, facing) and one light-related variable (canopy openness) to
>>> explain species abundance variation in 85 plots placed on 17 transects
>>> dispersed through a coastal vegetation complex on sandy soils in
>>> northeastern Brazil. The dependent variable is axes of a floristic
>>> ordination (e.g., NMDS), with one separate model adjusted for each axis.
>>>
>>> I will use two levels of spatial aggregation as random factors: the
>>> transects (5 plots per transect) and broad transect clusters (transect
>>> clusters were logistically conditioned).
>>>
>>> In the ecological literature, I have seen the suggestion of
>>> including quadratic and even cubic versions of the fixed effects variables
>>> (in this case topographic and light) as a means to account for possible
>>> nonlinear effects of these variables on the dependent variable. One recent
>>> example is
>>>
>>> Brunbjerg, A.K., Ejrn�s, R., Svenning, J.-C., 2012. Species sorting
>>> dominates plant metacommunity structure in coastal dunes. Acta Oecologica
>>> 39, 33�42.
>>>
>>> However, the inclusion of such quadratic and/or cubic terms in the
>>> model produces high colinearity levels (VIF > 25, sometimes even 38!).
>>>
>>> Do you think this is a valid procedure, the inclusion of these
>>> polynomial terms?
>>> Thank you in advance for any ideas,
>>>
>>> Alexandre
>>>
>>> Dr. Alexandre F. Souza
>>> Professor Adjunto II Departamento de Botanica, Ecologia e Zoologia
>>> Universidade Federal do Rio Grande do Norte (UFRN)
>>> http://www.docente.ufrn.br/**alexsouza<http://www.docente.ufrn.br/alexsouza> Curriculo:
>>> lattes.cnpq.br/**7844758818522706<http://lattes.cnpq.br/7844758818522706>
>>>
>>> ______________________________**_________________
>>> R-sig-ecology mailing list
>>> R-sig-ecology at r-project.org
>>> https://stat.ethz.ch/mailman/**listinfo/r-sig-ecology<https://stat.ethz.ch/mailman/listinfo/r-sig-ecology>
>>>
>>
>>
>>
> --
> Scott Foster
> Computational Informatics
> CSIRO
> E scott.foster at csiro.au T +61 3 6232 5178
> Postal address: CSIRO Computational Informatics, GPO Box 1538, Hobart TAS
> 7001
> Street Address: CSIRO Computational Informatics, Castray Esplanade, Hobart
> Tas 7001, Australia
> www.csiro.au
>
>
> ______________________________**_________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/**listinfo/r-sig-ecology<https://stat.ethz.ch/mailman/listinfo/r-sig-ecology>
>
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------------------------------
Message: 3
Date: Fri, 4 Oct 2013 09:14:06 -0700 (PDT)
From: Lutfor <rahmannorthampton at gmail.com>
To: r-sig-ecology at r-project.org
Subject: Re: [R-sig-eco] Animal movement packages
Message-ID: <1380903246900-7578439.post at n2.nabble.com>
Content-Type: text/plain; charset=us-ascii
Following packages might help:
Adehabitat, AdehabitatHR
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