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Subsections



What is a Biplot?

Biplots are statistical graphics that represent in the same plane both the variables and the cases. Usually variables are represented by arrows, while points represent cases. See the example in 1.

A Biplot can be constructed from a data matrix, where conventionally each column represent a variable, and each row includes the variables value for a given case.

The general layout of the computations is:

\begin{displaymath}
\begin{picture}(160,22)
\thicklines\put(10,20) {\makebox(0,0...
...put(135,10){\makebox(0,0) {${\bf F}$, ${\bf G}$}}
\end{picture}\end{displaymath}


Kinds of analysis, kinds of biplots

According to the previous scheme of the computations, there are several possibilities for the construccion of a Biplot. Some of them are more usual, and we include four of them as "Canned analyisis". They are accessible via the Define data processing... in the Biplot... menu button.

PCA without normalisation
centring of columns $\rightarrow$ SVD, etc...
PCA with normalisation
centring of columns $\rightarrow$ normalisation of columns $\rightarrow$ SVD, etc...
simple CA
transform to Pearson contingency ratios $\rightarrow$ apply row and columns masses $\rightarrow$ (weighted) double-centring $\rightarrow$ (weighted) SVD, etc...
logratio analysis (Aitchison)
transform to logarithms $\rightarrow$ double-centring $\rightarrow$ SVD, etc...
ratio maps (Greenacre, or spectral mapping, Lewi)
transform to logarithms $\rightarrow$ apply row and column masses $\rightarrow$ (weighted) double-centring $\rightarrow$ (weighted) SVD, etc...

There are three types of coordinates (Standard, Principal, and Canonical), and four standard Biplot/map options that are accessible through the Biplot type item in the Biplot... menu button.

Asymmetric map (form Biplot) of the rows.

Asymmetric map (covariance Biplot) of the columns.

Symmetric map (not a Biplot).

Symmetric (canonical?) Biplot.


next up previous
Next: Inputing data to XLS-Biplot Up: XLS-Biplot User's Manual (Version Previous: Basics of XLS-Biplot
Frederic Udina
2005-03-15