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correlation structure induced by the split-plot struc- surface designs in cuboidal regions, the excellent per-
ture. Generalized linear mixed models (GLMMs), formance of the central composite designs when the
generalized estimating equations (GEEs), and hierar- quadratic model is correct is tempered when bias is
chical generalized linear models (HGLMs) are useful present. The Box-Behnken designs are found to have
tools for modeling non-normal, exponential family superior robustness to the presence of missing cubic
responses in a split-plot setting. These tools are espe- terms. For a screening design scenario, the amount of
cially useful when interest focuses on the mean and bias present leads to different conclusions as to which
variance of the response. As an alternative, this article design is best.
demonstrates the utility of Bayesian methods when The final article in the issue is by Christopher
the user may be interested in functions of the response Gotwalt, Bradley Jones, and David Steinberg
distribution, itself, such as specific quantiles or the and titled “Fast Computation of Designs Robust
proportion of items within specifications. The authors to Parameter Uncertainty for Nonlinear Settings.”
present and solve several such questions for a particu- Experimental design in nonlinear settings, includ-
lar split-plot experiment. ing nonlinear models and generalized linear models,
Many fractional factorial experiments provide no is complicated by the efficiency of a design depend-
data to compute a model-free estimate of the experi- ing on the unknown parameter values. Thus, good
mental error variance, complicating statistical infer- designs need to be efficient over a range of likely
ence. One possible solution is to include replicates at parameter values. Bayesian design criteria provide a
a select number of design points. This is the problem natural framework for achieving such robustness by
tackled by Chen-Tuo Liao and Feng-Shun Chai averaging local design criteria over a prior distribution
in their article, “Design and Analysis of Two-Level on the parameters. A major drawback to the use of
Factorial Experiments with Partial Replication.” Their such criteria has been the heavy computational burden
construction method takes advantage of “parallel flats” they impose. The authors present a clever quadrature
and generates designs with two identical parallel flats scheme that greatly improves the feasibility for using
that allow estimation of a set of specified effects and Bayesian design criteria and illustrate the method on a
the pure error variance. A set of sufficient conditions is number of designed experiments. ■
presented for the designs to be D-optimal for the spec-
ified effects, assuming the other effects
are negligible, over the class of compet-
ing parallel-flats designs. Furthermore,
an algorithm is developed to generate
the D-optimal designs with a choice of
flexible degrees of freedom for the pure
error variance. The proposed designs are
highly efficient in estimating the possibly
active effects and provide a replication-
based estimate of the error variance.
When comparing designs for an
experiment, optimality criteria and other
measures frequently depend on the cor-
rectness of an assumed model. Some
effective graphical methods for evaluat-
ing and comparing designs when faced
with uncertainty about the model are
developed by Anderson-Cook, Connie
Borror, and Bradley Jones in their
article, “Graphical Tools for Assessing
the Sensitivity of Response Surface
Designs to Model Misspecification.”
They develop and illustrate an approach
for comparing designs given the poten-
tial effect of bias due to an underspeci-
fied model. They illustrate this approach
using graphical summaries of the expect-
ed mean squared error that allow for
assessment of the robustness of designs
to model misspecification. For response
FEBRUARY 2009 AMSTAT NEWS 21
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