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@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 keltezéssel, Alexandre Fadigas de Souza írta:
>>
>>> 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., Ejrnæs, 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>
>>>
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>>>
>>
>>
>>
> --
> Scott Foster
> Computational Informatics
> CSIRO
> E scott.foster@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
>
>
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