The CATMOD Procedure

## Computational Method

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

### Summary of Basic Dimensions

 s = number of populations or samples ( = number of rows in the underlying contingency table) r = number of response categories (= number of columns in the underlying contingency table) q = number of response functions computed for each population d = number of parameters

### Notation

 j denotes a column vector of 1s. J denotes a square matrix of 1s. is the sum over all the possible values of k. ni denotes the row sum . DIAGn(p) is the diagonal matrix formed from the first n elements of the vector p. DIAGn-1(p) is the inverse of DIAGn(p). DIAG(A1, A2, ... , Ak) denotes a block diagonal matrix with the A matrices on the main diagonal.

Input data can be represented by a contingency table, as shown in Table 22.4.

Table 22.4: Input Data Represented by a Contingency Table
 Response Population 1 2 ... r Total 1 n11 n12 ... n1r n1 2 n21 n22 ... n2r n2      s ns1 ns2 ... nsr ns