[See FACTEX6A in the SAS/QC Sample Library]If the numbers of levels for the factors of the mixed-level design are all powers of the same prime power , you can construct the design by using pseudo-factors, where the levels of -level pseudo-factors are associated with the levels of a single derived factor with levels. Refer to Section 5 of Chakravarti (1956) and see the section Types of Factors for details.
For example, the following statements create a design for one 4-level factor (A) and three 2-level factors (B, C, and D) in 16 runs (a half replicate):
proc factex; factors A1 A2 B C D; model estimate =(B C D A1|A2 ) nonnegligible=(B|C|D@2 A1|A2|B A1|A2|C A1|A2|D); size design=16; output out=DesignA [A1 A2]=A cvals = ('A' 'B' 'C' 'D'); proc print; var A B C D; run;
The levels of two 2-level pseudo-factors (A1 and A2) are used to represent the four levels of A. Hence the three degrees of freedom associated with A are given by the main effects of A1 and A2 and their interaction A1*A2, and you can thus refer to (A1|A2) as the main effect of A.
The MODEL statement specifies that the main effects of all factors are to be estimable, and that all of the two-factor interactions between B, C, and D, in addition to the interactions between each of these and (A1|A2), are to be nonnegligible. As a result, the mixed-level design has resolution 4. The design is saved in the data set DesignA, combining the levels of the two pseudo-factors, A1 and A2, to obtain the levels of the 4-level factor A. The data set DesignA is listed in Output 7.8.1.
Obs | A | B | C | D |
---|---|---|---|---|
1 | A | -1 | -1 | 1 |
2 | A | -1 | 1 | -1 |
3 | A | 1 | -1 | -1 |
4 | A | 1 | 1 | 1 |
5 | C | -1 | -1 | -1 |
6 | C | -1 | 1 | 1 |
7 | C | 1 | -1 | 1 |
8 | C | 1 | 1 | -1 |
9 | B | -1 | -1 | -1 |
10 | B | -1 | 1 | 1 |
11 | B | 1 | -1 | 1 |
12 | B | 1 | 1 | -1 |
13 | D | -1 | -1 | 1 |
14 | D | -1 | 1 | -1 |
15 | D | 1 | -1 | -1 |
16 | D | 1 | 1 | 1 |