Interpretation of RDA triplot where x axis is RDA vector and y axis is PCA vector

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Interpretation of RDA triplot where x axis is RDA vector and y axis is PCA vector

Marko Djurakic
Dear r-sig-ecology community,

I appreciate if someone can tell me is it meaningful to interpret
redundancy analysis (RDA) and triplot of RDA where x axis represent RDA
vector and y axis is PCA vector?

For instance, I performed RDA in vegan where response matrix was
Hellinger-transformed absolute abundance of several types of chromosomal
inversions and explanatory matrix consisted of 19 bioclim variables.
With a full set of bioclim variables model was overfitted and I reduced
number of explanatory variables using VIF and afterwards (if necessary)
performed forward selection. In the final model, there was only one
explanatory variable in the model, thus there is one RDA axis, and
several PCA axes (unconstrained residual variance). Therefore RDA
triplot shows RDA vector as x axis and PCA vector on the y axis. Is is
meaningful to interpret such RDA and its graph?

Kind regards,

Marko

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Re: Interpretation of RDA triplot where x axis is RDA vector and y axis is PCA vector

François Gillet
Dear Marko,

First, you should not exclude explanatory variables with high VIF before
the forward selection, but use VIF afterwards to check the result of this
selection.
Second, if you select only one (numeric or binary) explanatory variable,
then you get only one constrained axis and the adjusted R-square gives you
the variation in the response matrix explained by this single variable. You
can plot the first unconstrained axis, which shows the main residual
variation in your data. So yes, this RDA and its triplot are meaningful.

Best wishes,

François

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Pr *François Gillet*
Université de Franche-Comté - CNRS
UMR 6249 Chrono-environnement
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Google Scholar: http://scholar.google.com.au/citations?user=a5xiIfQAAAAJ

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2017-06-05 17:54 GMT+02:00 Marko Djurakic <[hidden email]>:

> Dear r-sig-ecology community,
>
> I appreciate if someone can tell me is it meaningful to interpret
> redundancy analysis (RDA) and triplot of RDA where x axis represent RDA
> vector and y axis is PCA vector?
>
> For instance, I performed RDA in vegan where response matrix was
> Hellinger-transformed absolute abundance of several types of chromosomal
> inversions and explanatory matrix consisted of 19 bioclim variables. With a
> full set of bioclim variables model was overfitted and I reduced number of
> explanatory variables using VIF and afterwards (if necessary) performed
> forward selection. In the final model, there was only one explanatory
> variable in the model, thus there is one RDA axis, and several PCA axes
> (unconstrained residual variance). Therefore RDA triplot shows RDA vector
> as x axis and PCA vector on the y axis. Is is meaningful to interpret such
> RDA and its graph?
>
> Kind regards,
>
> Marko
>
> _______________________________________________
> R-sig-ecology mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>

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