On optimal two-level supersaturated designs

Abstract

A popular measure to assess two-level supersaturated designs is the $E(s^2)$ criteria. Recently, Jones and Majumdar (2014) introduced the $\mbox{{\it UE}}(s^2)$ criteria and obtained optimal designs under the criteria. Effect-sparsity principle states that only a very small proportion of the factors have effects that are large. These factors with large effects are called {\it active} factors. Therefore, the basis of using a supersaturated design is the inherent assumption that there are very few active factors which one has to identify. Though there are only a few active factors, it is not known a priori what these active factors are. The identification of the active factors, say $k$ in number, is based on model building regression diagnostics (e.g. forward selection method) wherein one has to desirably use a supersaturated design which on an average estimates the model parameters optimally during the sequential introduction of factors in the model building process. Accordingly, to overcome possible lacuna on existing criteria of measuring the goodness of a supersaturated design, we meaningfully define the $ave(s^2_k)$ and $ave(s^2)_\rho$ criteria, where $\rho$ is the maximum number of active factors. We obtain superior $\mbox{{\it UE}}(s^2)$-optimal designs in ${\cal D}_U(m,n)$ and compare them against $E(s^2)$-optimal designs under the more meaningful criteria of $ave(s^2_k)$ and $ave(s^2)_\rho$. It is seen that $E(s^2)$-optimal designs perform fairly well or better even against superior $\mbox{{\it UE}}(s^2)$-optimal designs with respect to $ave(s^2_k)$ and $ave_d(s^2)_\rho$ criteria.