Example 24.4: Optimal Design Using an Augmented Best Design

Details of the OPTEX Procedure

Example 24.4: Optimal Design Using an Augmented Best Design

See OPTEX4 in the SAS/QC Sample Library

This example is a continuation of Example 24.2.

You can specify a set of points that you want included in the final design found by the OPTEX procedure, using the AUGMENT= option in the GENERATE statement to specify a data set that contains a design to be augmented.

In this case, you can try to speed up the search for a 50-run design by first finding an optimal 25-run design and then augmenting that design with another 25 runs, as shown in the following statements:

   proc optex data=a seed=36926;
       model af|egr|sa@2 af*af egr*egr sa*sa;
       generate n=25 method=detmax;
       output out=b;
   proc optex data=a seed=37034;
       model af|egr|sa@2 af*af egr*egr sa*sa;
       generate n=50 method=detmax augment=b;
   run;

The result (see Output 24.4.1 and Output 24.4.2) is a design with almost 100% D-efficiency and A-efficiency relative to the best design found by the first attempt. However, this approach is not much faster than the original approach, since the run time for the DETMAX algorithm is essentially linear in the size of the design (see "Memory and Run-Time Considerations" .)

Output 24.4.1: Efficiencies for the 25-point Design to be Augmented

The OPTEX Procedure

Design Number	D-Efficiency	A-Efficiency	G-Efficiency	Average Prediction Standard Error
1	46.2975	26.0374	91.1822	0.5849
2	46.2171	25.9733	86.4608	0.5859
3	46.1720	25.9378	88.3293	0.5860
4	46.1374	25.9128	86.1895	0.5866
5	46.0808	22.6647	86.1502	0.6169
6	46.0620	24.7326	89.7179	0.6012
7	45.9992	25.4549	90.3330	0.5946
8	45.9630	24.7610	88.2701	0.5991
9	45.9627	25.5310	88.5737	0.5894
10	45.7994	24.5645	87.7544	0.6005

Output 24.4.2: Efficiencies for the Augmented 50-point Design

The OPTEX Procedure

Design Number	D-Efficiency	A-Efficiency	G-Efficiency	Average Prediction Standard Error
1	46.4957	25.0858	94.8160	0.4195
2	46.4773	25.0696	95.0646	0.4195
3	46.4684	24.5519	96.1259	0.4234
4	46.4676	24.5002	95.6830	0.4238
5	46.4587	25.0709	94.6650	0.4196
6	46.4555	24.8087	95.7768	0.4209
7	46.4471	24.5460	95.0073	0.4240
8	46.4373	25.0740	94.4640	0.4194
9	46.3899	25.0007	95.2162	0.4201
10	46.3662	24.4013	94.9539	0.4242

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