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Details of the OPTEX Procedure 
See OPTEX7 in the SAS/QC Sample Library 
Suppose you want a design in 20 runs for seven twolevel factors. There are 29 terms in a full secondorder model, so you will not be able to estimate all main effects and twofactor interactions. If the number of runs were a power of 2, a design of resolution 4 could be used to estimate all main effects free of the twofactor interactions, as well as to provide partial information on the interactions. However, when the number of runs is not a power of two, as in this case, DuMouchel and Jones (1994) suggest searching for a Bayesian optimal design by specifying nonzero prior precision values for the interactions. You can specify these values in the OPTEX procedure with the PRIOR= option in the MODEL statement. This says that you want to consider all main effects and interactions as potential effects, but you are willing to sacrifice information on the interactions to obtain maximal information on the main effects. When an orthogonal design of resolution 4 exists, it is optimal according to this Bayesian criterion.
You can use the following statements to generate the Bayesian Doptimal design:
proc factex; factors x1x7; output out=can; run; proc optex data=can seed=57922 coding=orth; model x1x7, x1x2x3x4x5x6x7@@2 / prior=0,16; generate n=20 method=m_fedorov; output out=des; run;With orthogonal coding, the value of the prior for an effect says roughly how many prior "observations' worth" of information you have for that effect. In this case, the PRIOR= precision values and the use of commas to group effects in the MODEL statement says that there is no prior information for the main effects and 16 runs' worth of information for each twofactor interaction. See "Design Coding" for details on orthogonal coding.
The efficiencies are shown in Output 24.6.1.
Output 24.6.1: Efficiencies for Bayesian Optimal Designsdata des; set des; y = ranuni(654231); proc glm data=des; model y = x1x7 x1x2x3x4x5x6x7@@2 / e aliasing; run;
The relevant part of the output is shown in Output 24.6.2. Most of the main effects are indeed unconfounded with twofactor interactions, although many twofactor interactions are confounded with each other.
Output 24.6.2: Aliasing Structure for Bayesian Optimal Design

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