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 Details of the FACTEX Procedure

## Example 15.8: Mixed-Level Design Using Pseudo-Factors

 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 q, you can construct the design using pseudo-factors, where the levels of k q-level pseudo-factors are associated with the levels of a single derived factor with qk levels. Refer to Section 5 of Chakravarti (1956) and see "Types of Factors" for details.

For example, the following statements create a design for one four-level factor (A) and three two-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 two-level pseudo-factors (A1 and A2) are used to represent the four levels of A. Hence the three degrees of freedom associated with A will be 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, as well as 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 four-level factor A. The data set DESIGNA is listed in Output 15.8.1.

Output 15.8.1: 4×23 Design of Resolution IV in 16 Runs

 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

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