  Conditional models with one pair of conditional and conditioned factors in
Mukerjee et al. (2017) are extended to two pairs in this paper. The extension
includes the parametrization, effect hierarchy, sufficient conditions for
universal optimality, aberration, complementary set theory and the strategy for
finding minimum aberration designs. A catalog of 16-run minimum aberration
designs under conditional models is provided. For five to twelve factors, all
16-run minimum aberration designs under conditional models are also minimum
aberration under traditional models.
