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

[Alexandre Fadigas de Souza]

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