Discussion on supersaturated design and its data analysis method in computer experiments

抄録

Supersaturated designs provide the means to reduce a large number of factors down to a few active factors that influence the response of experimental results. Various data analysis methods for supersaturated designs are proposed to address the difficulty of factor estimation. However, few proposals have been made regarding which supersaturated design and data analysis method should be used to most accurately identify the active factors in computer experiments. This paper describes a series of numerical evaluation conducted with the aim of determining which combination of supersaturated design and data analysis method works better in accomplishing this task. Several models for computer experiments are examined using various combinations of existing supersaturated designs and analysis methods. We use 12×22,12×66.24×46,24×69,48×93 supersaturated designs, with Forward Stepwise selection, Model-Averaging, LASSO, and the Dantzig-Selector as the analysis methods. Numerical evaluation indicates that there is no single combination that always produces good results. Rather, it is found that the best combination depends on the conditions including design size, magnitude of active factors and so forth.It would appear that it is better to select the combination when the number of experiments is small or when the number of columns is large. In addition, the sign of the effect can influence the results for some supersaturated designs. To manage this problem, we propose a supersaturated design that gives relatively stable results regardless of the sign of the effect.