Block designs for experiments with non-normal response

Abstract

Many experiments measure a response that cannot be adequately described by a linear model withnormally distributed errors and are often run in blocks of homogeneous experimental units. Wedevelop the first methods of obtaining efficient block designs for experiments with an exponentialfamily response described by a marginal model fitted via Generalized Estimating Equations. Thismethodology is appropriate when the blocking factor is a nuisance variable as, for example, occursin industrial experiments. A D-optimality criterion is developed for finding designs robust to thevalues of the marginal model parameters and applied using three strategies: unrestricted algorithmicsearch, use of minimum-support designs, and blocking of an optimal design for the correspondingGeneralized Linear Model. Designs obtained from each strategy are critically compared and shownto be much more efficient than designs that ignore the blocking structure. The designs are comparedfor a range of values of the intra-block working correlation and for exchangeable, autoregressive andnearest 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 strategiesare motivated and demonstrated through the planning of an experiment from the aeronautics industr