  We consider cDNA microarray experiments when the cell populations have a
factorial structure, and investigate the problem of their optimal designing
under a baseline parametrization where the objects of interest differ from
those under the more common orthogonal parametrization. First, analytical
results are given for the $2\times 2$ factorial. Since practical applications
often involve a more complex factorial structure, we next explore general
factorials and obtain a collection of optimal designs in the saturated, that
is, most economic, case. This, in turn, is seen to yield an approach for
finding optimal or efficient designs in the practically more important nearly
saturated cases. Thereafter, the findings are extended to the more intricate
situation where the underlying model incorporates dye-coloring effects, and the
role of dye-swapping is critically examined.
