Multiple correspondence analysis - Understanding Biplots - page 402

the readability of the biplot. We provide the optimal z-scores for the variables in
Figure 8.22. This figure shows that some ordinal categories are tied ( R9 and R10 ; Res1,
Res2 and Res3 ; Q2 , Q3 , Q4 , Q5 ,and Q6 ) while others are almost similar ( R5 and R6 ;
Res5 and Res6 ; A4 and A5 ). A final categorical PCA biplot of the remuneration data is
given in Figure 8.23, in which we show the biplot with all axes translated to peripheral
positions so as not to interfere with the sample points.

Rank Rnk5 Rnk4

Rnk3 Q1

Q2*Q3*Q4*Q5*Q6

Rnk2

Q7

Q8 Rnk1

AQual

Q9

F9

F7

F3

F F F1

Res0

F8

Age

Res1*Res2*Res3

A7 A6

A A4

Res4

Res5

Res6

F5

A3

A2

Remun

Res7

R9*R10

R8 R7 R6 R5

Female

A1

F6

R4

Male

R3

Gender

R2

R1

Resrch Faclty

Figure 8.23 Categorical PCA biplot similar to Figure 8.20. In drawing this figure, we
have used many of the devices discussed in earlier chapters to improve the display.
We have shifted the axes into peripheral positions and translated the axes into familiar
positions that are roughly horizontal and vertical. Rather than calibrate each nominal
variable according to its quantifications, we have used colour to demarcate the different
levels of Gender and Faclty . For the remaining variables - all ordinal - we increase
the width of the axis to demarcate the different levels of the ordinal categories. With
large samples, it is impracticable to label individual samples or even to plot them all.
If we are interested in possible gender differences we can enclose the sample points
with 0.95-bags for each level of Gender . The cyan-coloured bag denotes the males and
the orange coloured bag the females. Similarly, if we are interested in, for example, the
differences between the various faculties we can use the levels of Faclty for constructing
the bags. Optionally density plots, convex hulls or concentration ellipses (see Section 2.9)
are also available to the user.