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

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

	Denotes a column vector of 1s.
	Denotes a square matrix of 1s.
	Denotes the sum over all the possible values of k.
	Denotes the row sum .
	Denotes the diagonal matrix formed from the first n 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 32.7.

Table 32.7: Input Data Represented by a Contingency Table

	Response
Population	1	2	r	Total
1
2

s