Computer Experiments With Both Qualitative and Quantitative Variables

Computer experiments have received a great deal of attention in many fields of science and technology. Most literature assumes that all the input variables are quantitative. However, researchers often encounter computer experiments involving both qualitative and quantitative variables (BQQV). In this article, a new interface on design and analysis for computer experiments with BQQV is proposed. The new designs are one kind of sliced Latin hypercube designs with points clustered in the design region and possess good uniformity for each slice. For computer experiments with BQQV, such designs help to measure the similarities among responses of different level-combinations in the qualitative variables. An adaptive analysis strategy intended for the proposed designs is developed. The proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response. The interface between the proposed design and the analysis strategy is demonstrated to be effective via simulation and a real-life example from the food engineering literature. Supplementary materials for this article are available online.

计算机实验已在众多科技领域受到广泛关注。绝大多数现有文献均假设所有输入变量均为定量变量。然而，研究人员常需处理涉及兼具定性与定量变量（BQQV）的计算机实验。本文提出一套面向含BQQV的计算机实验的设计与分析新框架。所提出的新型设计属于一类切片拉丁超立方设计（sliced Latin hypercube designs），其采样点在设计区域内呈聚类分布，且各切片均具备良好的均匀性。针对含BQQV的计算机实验，这类设计有助于量化定性变量不同水平组合对应的响应间的相似度。本文同时开发了适配该新型设计的自适应分析策略，该策略可自动从有效辅助响应中提取信息，以提升目标响应的预测精度。通过仿真实验与食品工程领域的真实案例验证，本文所提设计与分析策略的结合框架展现出优良的有效性。本文补充材料可在线获取。