Applied Statistics Using SPSS, STATISTICA, MATLAB and R

346 8 Data Structure Analysis
A: Only the first four eigenvalues satisfy the Kaiser criterion. The first two
eigenvalues are responsible for about 58% of the total variance; therefore, when
discarding the remaining eigenvalues, we are discarding a substantial amount of
the information from the dataset (see Exercise 8.12).
We can conveniently interpret the data by using a graphic display of the
standardised data projected onto the plane of the first two principal components,
say F1 and F2, superimposed over the correlation plot. In STATISTICA, this
overlaid graphic display can be obtained by first creating a datasheet with the
projections (“factor scores”) and the correlations (“factor loadings”). For this
purpose, we first extract the scrollsheet of the “factor scores” (click with the right
button of the mouse over the corresponding “factor scores” sheet in the workbook
and select Extract as stand alone window). Then, secondly, we join
the factor loadings in the same F1 and F2 columns and create a grouping variable
that labels the data classes and the original variables. Finally, a scatter plot with all
the information, as shown in Figure 8.10, is obtained.
By visual inspection of Figure 8.10, we see that F1 has high correlations with
chemical features, i.e., reflects the chemical composition of the rocks. We see,
namely, that F1 discriminates between the silica-rich rocks such as granites and
diorites from the lime-rich rocks such as marbles and limestones. On the other
hand, F2 reflects physical properties of the rocks, such as density (MVAP),
porosity (PAOA) and water absorption (AAPN). F2 discriminates dense and
compact rocks (e.g. marbles) from less dense and more porous counterparts (e.g.
some limestones).
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
F2
Granite
Diorite
Marble
Slate
Limestone
F1-type variable
F2-type variable
Fe2O3
Al2O3Na2O
SiO2 K2O
MVAP
F1
PAOAAAPN
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Figure 8.10. Partial view of the standardised rock dataset projected onto the F1-F2
principal component plane, overlaid with the correlation plot.
CaO