发表机构
Applied Analytics, Boston College; United States Air Force Test Pilot School（波士顿学院应用分析中心; 美国空军试飞员学校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出回顾性正交设计（ROD），可从观测数据重建响应面，在多模拟场景及加权明瑟应用中表现优异，能生成与项顺序无关的平方和分配，为ROD规划提供样本量指导。
AI 中文摘要
观测数据的回归估计可能受多重共线性下的模型设定影响，而顺序平方和（SS）则依赖于项的输入顺序。我们提出回顾性正交设计（Retrospective Orthogonal Design, ROD），该方法在概率均衡格上重建条件均值曲面。ROD保留观测到的单元格均值，补全无支撑单元格，应用加权张量积对比，并通过Freudenthal多面体上的分段仿射插值评估重建曲面。分辨率与补全方案通过秩容许候选集的验证共同选择，随后在未接触的测试集上重新拟合与评估。对于容许格，$\boldsymbol{X}^{\top}\boldsymbol{W}\boldsymbol{X}=c\boldsymbol{I}$，这在保留的对比空间内产生与设定无关的对比效应，以及唯一的、与顺序无关的SS。无响应投影校准将固定重建映射到指定的科学基础，并校正有限分辨率的恢复损失。在涵盖9种数据生成过程的6480种模拟条件下，ROD在5种过程中与多项式回归相当或更优，且在阈值、符号交互和局域曲面上表现最强；对于二次交互过程，样本外平均$R^2$仅相差0.0001，且校准后的系数偏差在预设目标范围内保持较小。基于Rao的信息调整为ROD规划提供了依赖相关性的样本量指导。在加权明瑟（Mincer）应用中，ROD产生了最高的样本外$R^2$点估计，与多项式回归的区间重叠显著，且提供了与项输入顺序无关的详尽SS分配。
英文摘要
Regression estimates from observational data can depend on specification under multicollinearity, while sequential sums of squares (SS) depend on term order. We introduce Retrospective Orthogonal Design (ROD), which reconstructs conditional mean surfaces on a probability-balanced lattice. ROD preserves observed cell means, completes unsupported cells, applies weighted tensor-product contrasts, and evaluates the reconstructed surface through piecewise-affine interpolation over Freudenthal polyhedra. Resolution and completion are selected jointly by validation among rank-admissible candidates, followed by refitting and evaluation on an untouched test set. For an admissible lattice, $\mathbf{X}^{\top}\mathbf{W}\mathbf{X}=c\mathbf{I}$, yielding specification-invariant contrast effects and unique, order-independent SS within the retained contrast space. Response-free projection calibration maps the fixed reconstruction onto a declared scientific basis and corrects finite-resolution recovery loss. Across 6,480 simulation conditions spanning nine data-generating processes, ROD matched or exceeded polynomial regression in five processes and performed strongest on threshold, sign-interaction, and localized surfaces. For the quadratic-interaction process, mean out-of-sample $R^2$ differed by only $0.0001$, while calibrated coefficient bias remained small across prespecified targets. A Rao-based information adjustment provides dependence-aware sample-size guidance for ROD planning. In a weighted Mincer application, ROD produced the highest out-of-sample $R^2$ point estimate, with substantial interval overlap with polynomial regression, and provided exhaustive SS allocations invariant to term-entry order.
