[Vegan-commits] r1440 - pkg/vegan/inst/doc

[noreply at r-forge.r-project.org]

Author: jarioksa
Date: 2011-01-07 17:13:56 +0100 (Fri, 07 Jan 2011)
New Revision: 1440

Modified:
   pkg/vegan/inst/doc/decision-vegan.Rnw
Log:
CANOCO scaling may need some work with pen, paper and calculator

Modified: pkg/vegan/inst/doc/decision-vegan.Rnw
===================================================================
--- pkg/vegan/inst/doc/decision-vegan.Rnw	2011-01-07 16:05:02 UTC (rev 1439)
+++ pkg/vegan/inst/doc/decision-vegan.Rnw	2011-01-07 16:13:56 UTC (rev 1440)
@@ -247,7 +247,8 @@
     species standard deviations ($s_j$). In \texttt{rda},
     $\mathrm{const} = \sqrt[4]{(n-1) \sum \lambda_k}$.  Corresponding
     negative scaling in \texttt{vegan}
-    and corresponding positive scaling in \texttt{Canoco 3}  is derived
+   % and corresponding positive scaling in \texttt{Canoco 3}  
+    is derived
     dividing each  species by its standard deviation $s_j$ (possibly
     with some additional constant multiplier).  }
 \begin{tabular}{lcc}
@@ -269,17 +270,17 @@
 \texttt{rda, scaling < 0} &
 $u_{ik}^*$ &
 $\sqrt{\sum \lambda_k /(n-1)} s_j^{-1} v_{jk}^*$
-\\
-\texttt{Canoco 3, scaling=-1} &
-$u_{ik} \sqrt{n-1} \sqrt{\lambda_k / \sum \lambda_k}$ &
-$v_{jk} \sqrt{n}$ \\
-\texttt{Canoco 3, scaling=-2} &
-$u_{ik} \sqrt{n-1}$ &
-$v_{jk} \sqrt{n} \sqrt{\lambda_k / \sum \lambda_k}$
-\\
-\texttt{Canoco 3, scaling=-3} &
-$u_{ik} \sqrt{n-1} \sqrt[4]{\lambda_k / \sum \lambda_k}$ &
-$v_{jk} \sqrt{n} \sqrt[4]{\lambda_k / \sum \lambda_k}$
+% \\
+% \texttt{Canoco 3, scaling=-1} &
+% $u_{ik} \sqrt{n-1} \sqrt{\lambda_k / \sum \lambda_k}$ &
+% $v_{jk} \sqrt{n}$ \\
+% \texttt{Canoco 3, scaling=-2} &
+% $u_{ik} \sqrt{n-1}$ &
+% $v_{jk} \sqrt{n} \sqrt{\lambda_k / \sum \lambda_k}$
+% \\
+% \texttt{Canoco 3, scaling=-3} &
+% $u_{ik} \sqrt{n-1} \sqrt[4]{\lambda_k / \sum \lambda_k}$ &
+% $v_{jk} \sqrt{n} \sqrt[4]{\lambda_k / \sum \lambda_k}$
 \end{tabular}
 \end{table}
 
@@ -291,14 +292,15 @@
 constant.  In functions \texttt{princomp}, \texttt{prcomp} and
 \texttt{rda}, $c=1$ and the plotted scores are a biplot so that the
 singular values (or eigenvalues) are expressed for sites, and species
-are left unscaled.  For \texttt{Canoco 3} $c = n^{-1} \sqrt{n-1}
-\sqrt{\sum \lambda_k}$ with negative \texttt{Canoco} scaling
-values. All these $c$ are constants for a matrix, so these are all
-biplots with different internal scaling of species and site scores
-with respect to each other.  For \texttt{Canoco} with positive scaling
-values and \texttt{vegan} with negative scaling values, no constant
-$c$ can be found, but the correction is dependent on species standard
-deviations $s_j$, and these scores do not define a biplot.
+are left unscaled.  
+% For \texttt{Canoco 3} $c = n^{-1} \sqrt{n-1}
+% \sqrt{\sum \lambda_k}$ with negative \texttt{Canoco} scaling
+% values. All these $c$ are constants for a matrix, so these are all
+% biplots with different internal scaling of species and site scores
+% with respect to each other.  For \texttt{Canoco} with positive scaling
+% values and \texttt{vegan} with negative scaling values, no constant
+% $c$ can be found, but the correction is dependent on species standard
+% deviations $s_j$, and these scores do not define a biplot.
 
 There is no natural way of scaling species and site scores to each
 other.  The eigenvalues in redundancy and principal components