Analyzing Supersaturated
Experimental Designs
A supersaturated experimental design is one
in which the number of observations is less than the number of factors.
The construction and analysis of supersaturated experimental designs have been
active areas of research for the past 15 years. Methods of construction
include various combinatorial approaches such as those developed by Wu (1993),
Lin (1995), and numerical approaches such as those based on the E(s2)
criterion (Li and Wu, 1997), Bayesian D-optimality (Jones, Lynn, and
Nachtsheim, 2005), and model robust design (Jones, Li, and Nachtsheim,
2008). Popular methods of analysis include stepwise regression and best
subsets regression. In a widely-cited 1999 paper, Abraham and Chipman
evaluated the efficacy of the stepwise and best subsets approaches. The
less-than-stellar performances of these methods led these authors to exercise
caution when considering the use of a supersaturated designs. Since that
time a number of new methods have been introduced both for design construction,
and for variable selection. Examples of the latter include the lasso, the
Dantzig selector, and a new method based on inverse regression and dimension
reduction (Cook and Li 2009) for exponential family predictors. In this
paper we take one more look at the supersaturated design and analysis problem,
considering both the choice of design and the concomitant choice of analysis
method. We evaluate the various approaches both from the perspective of
variable selection and prediction.