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The CATMOD Procedure

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.

Summary of Basic Dimensions


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 28.5.

Table 28.5 Input Data Represented by a Contingency Table










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