Second-order extensions to nearly orthogonal-and-balanced (NOAB) mixed-factor experimental designs

When simulation studies involve many quantitative (i.e., discrete and continuous) and qualitative (i.e., categorical) input factors with different numbers of levels for each, meta-models of simulation responses can benefit from the use of mixed-factor space-filling designs. The first-order nearly orthogonal-and-balanced (NOAB) design is a popular approach in these situations. This research develops second-order extensions for an existing construction method of NOAB designs, estimating the pairwise correlations between possible first-order and second-order terms. These extensions permit additional linear constraints in the mixed-integer linear programming (MILP) formulations previously developed for first-order NOAB designs. A case study is presented for NOAB designs of different sizes and construction approaches. The second-order MILP extensions show improvements in design performance measures for parameter estimation and prediction variance for an assumed second-order model as well as for model misspecification with respect to second-order terms for an assumed first-order model.