A fresh look at effect aliasing and interactions: some new wine in old bottles
  Interactions and effect aliasing are among the fundamental concepts in
experimental design. In this paper, some new insights and approaches are
provided on these subjects. In the literature, the "de-aliasing" of aliased
effects is deemed to be impossible. We argue that this "impossibility" can
indeed be resolved by employing a new approach which consists of
reparametrization of effects and exploitation of effect non-orthogonality. This
approach is successfully applied to three classes of designs: regular and
nonregular two-level fractional factorial designs, and three-level fractional
factorial designs. For reparametrization, the notion of conditional main
effects (cme's) is employed for two-level regular designs, while the
linear-quadratic system is used for three-level designs. For nonregular
two-level designs, reparametrization is not needed because the partial aliasing
of their effects already induces non-orthogonality. The approach can be
extended to general observational data by using a new bi-level variable
selection technique based on the cme's. A historical recollection is given on
how these ideas were discovered.
