Correspondence
Analysis Introductory Overview  Burt Table
Multiple correspondence
analysis expects as input (i.e., the program will compute prior to
the analysis) a socalled Burt table.
The Burt table is the result of the inner product of a design or indicator
matrix, and the multiple correspondence analysis results are identical
to the results you would obtain for the column points from a simple correspondence
analysis of the indicator or design matrix (see also Introductory
Overview  MCA).
For example, suppose you had entered data concerning the Survival
for different Age groups
in different Locations like this:

SURVIVAL 
AGE 
LOCATION 
Case No. 
NO 
YES 
LESST50 
A50TO69 
OVER69 
TOKYO 
BOSTON 
GLAMORGN 
1 
0 
1 
0 
1 
0 
0 
0 
1 
2 
1 
0 
1 
0 
0 
1 
0 
0 
3 
0 
1 
0 
1 
0 
0 
1 
0 
4 
0 
1 
0 
0 
1 
0 
0 
1 
... 
. 
. 
. 
. 
. 
. 
. 
. 
... 
. 
. 
. 
. 
. 
. 
. 
. 
... 
. 
. 
. 
. 
. 
. 
. 
. 
762 
1 
0 
0 
1 
0 
1 
0 
0 
763 
0 
1 
1 
0 
0 
0 
1 
0 
764 
0 
1 
0 
1 
0 
0 
0 
1 
In this data arrangement, for each case a 1
was entered to indicate to which category, of a particular set
of categories, a case belongs (e.g.,
Survival, with the categories No
and Yes). For example,
case 1 survived (a 0
was entered for variable No,
and a 1 was entered for variable
Yes), case 1
is between age 50 and 69 (a 1
was entered for variable A50to69),
and was observed in Glamorgn).
Overall there are 764 observations
in the dataset.
If you denote the data (design or indicator matrix) shown above as matrix
X,
then matrix product X'X
is a Burt table); shown below
is an example of a Burt table
that one might obtain in this manner.
The Burt table has a clearly
defined structure. Overall, the data matrix is symmetrical. In the case
of 3 categorical variables (as shown above), the data matrix consists
3 x 3 = 9 partitions, created by each variable being tabulated against
itself, and against the categories of all other variables. Note that the
sum of the diagonal elements in each diagonal partition (i.e., where the
respective variables are tabulated against themselves) is constant (equal
to 764 in this case).
The offdiagonal elements in each diagonal partition in this example
are all 0. If the cases in the
design or indicator matrix are assigned to categories via fuzzy coding
(i.e., if probabilities are used to indicate likelihood of membership
in a category, rather than 0/1 coding to indicate actual membership),
then the offdiagonal elements of the diagonal partitions are not necessarily
equal to 0. Note that complex coding schemes can easily be implemented
and the respective Burt table
computed via STATISTICA Visual BASIC.
You can then specify as input a Burt
table directly (choose the option Frequencies
w/out grouping vars in the Input
group box of the Table
Specifications dialog). Refer to the Introductory
Overview  MCA section for additional details.
See also, Exploratory
Data Analysis and Data Mining Techniques.