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

$\text{[math]}$	=	number of populations or samples (= number of rows in the underlying contingency table)
$\text{[math]}$	=	number of response categories (= number of columns in the underlying contingency table)
$\text{[math]}$	=	number of response functions computed for each population
$\text{[math]}$	=	number of parameters

Notation

$\text{[math]}$	Denotes a column vector of 1s.
$\text{[math]}$	Denotes a square matrix of 1s.
$\text{[math]}$	Denotes the sum over all the possible values of $\text{[math]}$ .
$\text{[math]}$	Denotes the row sum $\text{[math]}$ .
$\text{[math]}$	Denotes the diagonal matrix formed from the first $\text{[math]}$ elements of the vector $\text{[math]}$ .
$\text{[math]}$	Denotes the inverse of $\text{[math]}$ .
$\text{[math]}$	Denotes a block diagonal matrix with the $\text{[math]}$ 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	$\text{[math]}$	$\text{[math]}$	Total
1	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
2	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
s	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$