* Evaluating Design Efficiencies;

* Here are some ideas for evaluating efficiencies of designs;
* Let's start with a single rep of a 2^3 design;

data design1;
 input x1-x3;
cards;
-1 -1 -1
 1 -1 -1
-1  1 -1
 1  1 -1
-1 -1  1
 1 -1  1
-1  1  1
 1  1  1
;
run;

proc optex data=design1;
 model x1 x2 x3;
 generate initdesign=design1 method=sequential;
 examine design;
run;

* You can use proc iml to obtain some if the matrices involved;
* and the D and A efficiencies of the designs;

proc iml;
x={1 -1 -1 -1,
   1  1 -1 -1,
   1 -1  1 -1,
   1  1  1 -1,
   1 -1 -1  1,
   1  1 -1  1,
   1 -1  1  1,
   1  1  1  1};
xpx=x`*x;
xpxinv=inv(xpx);
aeff=4/(8*trace(xpxinv));
m=xpx/8;
deff=det(m)**.25;
print m deff aeff;
quit;

* Now we do the same thing after adding 3 center points;

data design2;
 input x1-x3;
cards;
-1 -1 -1
 1 -1 -1
-1  1 -1
 1  1 -1
-1 -1  1
 1 -1  1
-1  1  1
 1  1  1
 0  0  0
 0  0  0
 0  0  0
;
run;

proc optex data=design2;
 model x1 x2 x3;
 generate initdesign=design2 method=sequential;
 examine design;
run;

* You can use proc iml to obtain some if the matrices involved;
* and the D and A efficiencies of the designs;

proc iml;
x={1 -1 -1 -1,
   1  1 -1 -1,
   1 -1  1 -1,
   1  1  1 -1,
   1 -1 -1  1,
   1  1 -1  1,
   1 -1  1  1,
   1  1  1  1,
   1  0  0  0,
   1  0  0  0,
   1  0  0  0};
xpx=x`*x;
xpxinv=inv(xpx);
aeff=4/(11*trace(xpxinv));
m=xpx/11;
deff=det(m)**.25;
print m deff aeff;
quit;