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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

Notation

denotes a column vector of 1s.

denotes a square matrix of 1s.

is the sum over all the possible values of .

denotes the row sum .

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

is 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
 

Response

 

Population

1

2

Total

1

2

s


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