Optimal experimental designs for non-linear problems depend on the values of the underlying unknown parameters in the model. For various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters. This paper shows that, for a certain class of generalized linear models, the problem can be reduced to a canonical form. This simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments.Consider the case of c-optimality. With design space X, we maximize
Experiments using designs with complex aliasing patterns are often performed-for example, twolevel nongeometric Plackett-Burman designs, multilevel and mixed-level fractional factorial designs, two-level fractional factorial designs with hard-to-control factors, and supersaturated designs. Hamada and Wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions. Their strategy provides a restricted search in a rather large model space, however. This article provides an efficient methodology based on a Bayesian variable-selection algorithm for searching the model space more thoroughly. We show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models. The proposed methodology is demonstrated with four examples, three of which come from actual industrial experiments.
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