Computational Method 
The notation used in PROC CATMOD differs slightly from that used in the literature. The following table provides a summary of the basic dimensions and the notation for a contingency table. See the section Computational Formulas for a complete description.

= 
number of populations or samples (= number of rows in the underlying contingency table) 

= 
number of response categories (= number of columns in the underlying contingency table) 

= 
number of response functions computed for each population 

= 
number of parameters 

Denotes a column vector of 1s. 
Denotes a square matrix of 1s. 

Denotes the sum over all the possible values of . 

Denotes the row sum . 

Denotes the diagonal matrix formed from the first elements of the vector . 

Denotes the inverse of . 

Denotes a block diagonal matrix with the matrices on the main diagonal. 
Input data can be represented by a contingency table, as shown in Table 29.5.
Response 


Population 
1 
2 

Total 

1 





2 











s 




