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The CATMOD Procedure |
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 |
j | denotes a column vector of 1s. |
J | denotes a square matrix of 1s. |
is the sum over all the possible values of k. | |
n_{i} | denotes the row sum . |
DIAG_{n}(p) | is the diagonal matrix formed from the first n elements of the vector p. |
DIAG_{n}^{-1}(p) | is the inverse of DIAG_{n}(p). |
DIAG(A_{1}, A_{2}, ... , A_{k}) | 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 | n_{11} | n_{12} | ... | n_{1r} | n_{1} |
2 | n_{21} | n_{22} | ... | n_{2r} | n_{2} |
s | n_{s1} | n_{s2} | ... | n_{sr} | n_{s} |
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