Biplot basics - Understanding Biplots - page 11

2 Biplot basics

In accordance with our aim of understanding biplots, the focus in this chapter is to look
at biplot basics from the viewpoint of an ordinary scatterplot.
The chapter begins by introducing two- and three-dimensional biplots as ordinary
scatterplots of two or three variables. In Section 2.2 biplots are considered as extensions
of the ordinary scatterplot by providing for more than three variables. Generalizing, a
biplot provides for a graphical display, in at most three dimensions, of data that typi-
cally exist in a higher-dimensional space. The concept of approximating a data matrix is
thus crucial in biplot methodology. Subsequent sections explore how to represent mul-
tidimensional sample points in a biplot, how to equip the biplot with calibrated axes
representing the variables and how to refine the biplot display. Emphasis is placed on
how to use biplot axes analogously to axes in a scatterplot, that is, for adding new samples
to the plot (interpolation) and reading off for any sample point its values for the differ-
ent variables (prediction). It is then shown how to use a regression method for adding
new variables to the plot. Various enhancements to configurations of sample points in
a biplot, including how to describe large data sets, are discussed next. Finally, some
examples are given, together with the R code for constructing all the graphical displays
shown in the chapter. We strongly suggest that readers work through these examples
for a thorough understanding of the basics of biplot construction. In later chapters, we
provide only the function calls to more elaborate R functions for fine-tuning the various
types of biplot.

2.1 A simple example revisited

The data of Table 1.1 are available in the accompanying R package UBbipl in the form
of the dataframe aircraft.data . We first convert columns 3 to 6 to a data matrix,
aircraft.mat , with row names the first column of Table 1.1 and column names the