Two-way tables: biplots associated with correspondence analysis - Understanding Biplots - page 312

a p × q matrix of frequencies. The output of Chisq.dist is a two-component list
with elements:

A symmetric p p matrix containing the squared chi-squared

distances between the rows of its matrix argument X : p

× Sq.Chis2.dis

× q .

A symmetric p × p matrix containing the squared Euclidean
distances between the rows of its matrix argument X : p × q .

Sq.Euclid.dis

7.5.5 Function cabipl.doubling

This is a function for implementing the doubling procedure as described in Section 7.4.

Arguments

A p × q matrix with elements the number of favourable ratings for
each of q attributes of p products by N judges.

X

The number of judges asked to rate each of q attributes of p different
products as satisfactory or not.

N

... Any set of arguments to pass to cabipl .

Value

The matrix of positive and negative assessments of the form of Table 7.4 is returned
together with two biplots: a CA biplot of the doubled matrix of the number of positive
and negative assessments of the q attributes of p products; and a biplot with the positive
and negative extremities of each attribute connected with lines that divide its two ends
in the ratio c k : Np − c k as explained in Section 7.4.

7.6 Examples

7.6.1 The RSA crime data set

The RSA crime data set is used extensively in this section to illustrate the different
biplots that can be constructed to approximate various aspects of model (7.1). It consists
of the annual number of 14 serious crimes reported to the South African police in each
of the nine provinces of South Africa for the period 2001 - 08. It is tabulated according
to the nature of the crime, with province boundaries standardized at 2007 boundaries.
The data have been extracted from the official website of the South African police
(http://www.saps.gov.za/) and can be represented in the form of 9 14 contingency

tables. The R object RSACrime.data is a list with seven matrices as elements. Each of
these matrices represents the 10

×

× 14 contingency table for one of the periods 2001/02,

2002/03, ... , 2007/08. The extra row is the aggregate over all provinces. Here is a brief