Block designs for experiments with non-normal response

Abstract

Many experiments measure a response that cannot be adequately described by a linear model with
normally distributed errors and are often run in blocks of homogeneous experimental units. We
develop the first methods of obtaining efficient block designs for experiments with an exponential
family response described by a marginal model fitted via Generalized Estimating Equations. This
methodology is appropriate when the blocking factor is a nuisance variable as, for example, occurs
in industrial experiments. A D-optimality criterion is developed for finding designs robust to the
values of the marginal model parameters and applied using three strategies: unrestricted algorithmic
search, use of minimum-support designs, and blocking of an optimal design for the corresponding
Generalized Linear Model. Designs obtained from each strategy are critically compared and shown
to be much more efficient than designs that ignore the blocking structure. The designs are compared
for a range of values of the intra-block working correlation and for exchangeable, autoregressive and
nearest neighbor structures. An analysis strategy is developed for a binomial response that allows es-
timation from experiments with sparse data, and its efectiveness demonstrated. The design strategies
are motivated and demonstrated through the planning of an experiment from the aeronautics industry

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Identifiers

ORCID for D.C. Woods: orcid.org/0000-0001-7648-429X

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