超飽和設計因子篩選方法比較

Abstract

近年來有許多學者對大量因子的實驗設計感興趣，但是這類實驗可能僅有少數真正重要的因子，採用完全因子設計或傳統的部分因子設計來配置實驗可能不利於成本的控制，此時就可以考慮使用超飽和設計來篩選因子。

本文首先討論超飽和設計的矩陣建構方法，包含Lin和Wu分別提出的折半法和交互法，並進行比較。接下來介紹逐步向前法、最小絕對值壓縮選擇法(LASSO)以及Dantzig selector三種分析分法應用在超飽和設計的因子篩選上。最後在不同的模擬條件設定下，引入重要因子挑選比比較三種因子篩選方法在超飽和設計表現的優劣，並應用於實例之中。

In recent years, there are many scholars interested in experimental designs of a large number of factors, but such experiments may only have a few really important factors. It is detrimental to cost control if we using full factorial designs or traditional fractional factorial designs to construct these experiments, so we could consider using supersaturated designs in this situation to do factor screening.

In this article, we first discuss the design matrix construction methods of supersaturated designs, including the split-half method and the interaction method proposed by Lin and Wu, and then compare with them. Next, we introduce forward stepwise selection, LASSO and Dantzig selector as three factor selection methods of supersaturated designs. Finally, we compare the three factor selection methods of supersaturated designs by important factor selection ratio under different simulation conditions, and applied it to real examples.