Scripting Guide - SAS

154 Data Structures Chapter 7
Matrices
Create Design Matrices
The Design() function creates a matrix of design columns for a vector or list. There is one column for each
unique value in the vector or list. The design columns have the elements 0 and 1. For example, x below has
values 1, 2, and 3, then the design matrix has a column for 1s, a column for 2s, and a column for 3s. Each
row of the matrix has a 1 in the column representing that row’s value. So, the first row (1) has a 1 in the 1s
column (the first column) and 0s elsewhere; the second row (2) has a 1 in the 2’s column and 0s elsewhere;
and so on.
x=[1, 2, 3, 2, 1];
Design(x);
[1 0 0,
0 1 0,
0 0 1,
0 1 0,
1 0 0]
A variation is the DesignNom() or Design F() function, which removes the last column and subtracts it
from the others. Therefore, the elements of DesignNom() or Design F() matrices are 0, 1, and –1. And
the DesignNom() or Design F() matrix has one less column than the vector or list has unique values.
This operator makes full-rank versions of design matrices for effects.
x=[1, 2, 3, 2, 1];
DesignNom(x);
[1 0,
0 1,
-1 -1,
0 1,
1 0]
DesignNom() is further demonstrated in the “ANOVA Example” on page 165.
To facilitate ordinal factor coding, use the DesignOrd() function. This function produces a full-rank
coding with one less column than the number of unique values in the vector or list. The row for the lowest
value in the vector or list is all zeros. Each succeeding value adds an additional 1 to the row of the design
matrix.
x=[1, 2, 3, 4, 5, 6];
DesignOrd(x);
[0 0 0 0 0,
1 0 0 0 0,
1 1 0 0 0,
1 1 1 0 0,
1 1 1 1 0,
1 1 1 1 1]
Design(), DesignNom(), and DesignOrd() support a second argument that specifies the levels to be
looked up and their order. This feature allows design matrices to be created one row at a time.
• Design(values, levels) creates a design matrix of indicator columns.
• DesignNom(values, levels) creates a full-rank design matrix of indicator columns.
Note the following:
• The values argument can be a single element or a matrix or list of elements.