The hierarchy principle in designed industrial experiments

The general question of appropriate criteria for the development of models from a designed experiment is considered. Since models that are found in this setting are generally not mechanistic but rather empirical in nature, the arbitrary requirement of hierarchy may often lead to a model choice that is inferior in terms of satisfying the goals of the experiment. The non-hierarchial model may be no less interpretable than a hierarchial one and may allow for appreciably better predictive capability. Leaving highly insignificant terms in the model for the sake of hierarchy can increase standard errors and result in poor prediction. Parsimony in empirical modeling is often an important virtue. The broader research question revolves around the choice of criteria for model building, variable selection and model discrimination.