Example 15.8: Mixed-Level Design Using Pseudo-Factors

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 q^k 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

Chapter Contents
Previous
Next
Top