Blocked Designs for Experiments With Correlated 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 general methods of obtaining efficient blocked 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 often 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 two strategies: unrestricted algorithmic search and blocking of an optimal design for the corresponding Generalized Linear Model (GLM). Designs from each strategy are critically compared and shown to be more efficient than use of a random allocation to blocks of the points from an optimal GLM design. The designs are compared for a range of values of the intra-block working correlation and for exchangeable, autoregressive, and nearest-neighbor structures. A general equivalence theorem is provided for continuous blocked designs. An analysis strategy is developed for binary data that allows estimation from experiments with sparse data, and its effectiveness demonstrated. The design strategies are motivated and demonstrated through the planning of an experiment from the aeronautics industry.

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