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

[Zoltan Botta-Dukat]

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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-- 
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu


Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu