Rotation designs: Orthogonal first-order designs with higher order projectivity

In many factorial experiments, just a few of the experimental factors account for most of the variation in the response, a situation known as factor sparsity. Accurate modelling of the factor-response relationship may require use of higher-order terms in the active factors. In such settings, it may be desirable to use a design that is able, simultaneously, to screen out the important factors and to fit higher-order models in those factors. We derive a useful class of designs by rotating standard two-level fractional factorials. A special class of rotations is developed that has some appealing symmetry properties and can accommodate more factors than the rotation designs in Bursztyn and Steinberg (J. Stat. Plann. Inference 2001;97:399). A comparison of designs based on their projection and alias matrices shows that the new designs are better than many other alternatives.