Burt Tables

Multiple correspondence analysis expects as input (i.e., the program will compute prior to the analysis) a so-called Burt table. The Burt table is the result of the inner product of a design or indicator matrix. If you denote the data (design or indicator matrix) 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.

 

SURVIVAL

AGE

LOCATION

NO

YES

<50

50-69

69+

TOKYO

BOSTON

GLAMORGN

SURVIVAL:NO
SURVIVAL:YES

AGE:UNDER_50
AGE:A_50TO69

AGE:OVER_69 

LOCATION:TOKYO
LOCATION:BOSTON

LOCATION:GLAMORGN

210
0

68
93

49

60
82

68

0
554

212
258

84

230
171

153

68
212

280
0

0

151
58

71

93
258

0
351

0

 120
122

109

49
  84

0
0

133

 19
73

41

 60
230 

151
120

  19

290
    0

    0

 82
171 

  58
122

   73 

    0
253

    0

 68
 153 

  71
109

  41

   0
   0

221

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 off-diagonal elements in each partition in this example are all 0. If the cases in the design or indicator matrix are assigned to categories via fuzzy coding, then the off-diagonal elements of the diagonal partitions are not necessarily equal to 0. For more information, refer to the description of correspondence analysis, and to the description of Burt tables in the context of that module.