[R-sig-eco] Question on Quadratic and Cubic Parameters

[Scott Foster]

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  Curriculo: lattes.cnpq.br/7844758818522706
>>
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>
>

-- 
Scott Foster
Computational Informatics
CSIRO
E scott.foster at csiro.au T +61 3 6232 5178
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