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. 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.

Table 29.5 Input Data Represented by a Contingency Table

Response

Population

1

2  Total

1     2           s     