Forward screening and post-screening inference in factorial designs

Oregon Convention Center 

Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment levels may grow exponentially with the number of treatment factors, which motivates the forward screening strategy based on the sparsity, hierarchy, and heredity principles for factorial effects. Although this strategy is intuitive and has been widely used in practice, its rigorous statistical theory has not been formally established. To fill this gap, we establish design-based theory for forward factor screening in factorial designs based on the potential outcome framework. We not only prove a consistency property for the factor screening procedure but also discuss statistical inference after factor screening. In particular, with perfect screening, we quantify the advantages of forward screening based on asymptotic efficiency gain in estimating factorial effects. With imperfect screening in higher-order interactions, we propose two novel strategies and investigate their impact on subsequent inference. Our formulation differs from the existing literatu

Causal inference

Design-based inference

Forward selection

Post-selection inference 

IMS