Alias‐informed model selection (AIMS) for 7 and 8 factor no‐confounding 16‐run fractional factorial designs

Nonregular fractional factorial designs are a preferable alternative to regular resolution IV designs because they avoid confounding 2‐factor interactions. As a result, nonregular designs can estimate and identify a few active 2‐factor interactions. However, due to the sometimes complex alias structure of nonregular designs, standard factor screening strategies can fail to identify all active effects. We report on a screening technique that takes advantage of the alias structure of these nonregular designs. This alias‐informed‐model‐selection (AIMS) technique has been used previously for a specific 6‐factor nonregular design. We show how the AIMS technique can be applied to 7‐ and 8‐factor nonregular designs, completing the exposition of this method for all 16‐run 2‐level designs that are viable alternatives to standard Resolution IV fractional factorial designs. We compare AIMS to three other standard analysis methods for nonregular designs, stepwise regression, the lasso, and the Dantzig selector. AIMS consistently outperforms these methods in identifying the set of active factors.