[R] Fractional Factorial Design
S Ellison
S.Ellison at lgc.co.uk
Mon Apr 28 17:48:49 CEST 2008
Paul;
You asked
>using .......
> optFederov(~.,dat,6)
>... does the job with good efficiency.
>
>I would be interested to know what your objection to this is S
I have no issue with AlgDesign in principle, but the question was
specifically about _fractional_ factorials, so I answered that.
As to which is best - well, first pick your definition of 'best'. Both
can improve drastically on full factorials. For me, he advantage of a
fractional factorial is that it retains balance and, more importantly
from a design perspective, I get to choose which effects are confounded
and can arrange matters so that some effects are guaranteed
unconfounded. The deterministic nature of the selection also makes it a
bit easier to build power considerations into the process if you're so
minded. The price of that is that the number of observations is
typically larger than the smallest algorithmic design that might do a
broadly similar job, though never as large as a full factorial.
As I see it, the main advantage of algorithmic design is that you get
to pick the size of the experiment. A second plus is that you can handle
arbitrarily constrained designs much more easily, which is a feature
I've sometimes found important. The disadvantage is that you may incur
bias in some of the effect estimates, and because the selection process
to fit an arbitrary experiment size typically involves some random
selection from a candidate list, you don't necessarily get to choose
which effects are biased. I guess you will also have a more interesting
job deciding how many observations you need for a given power, if that's
relevant.
Steve E.
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