标题： 理解与使用基于正交变换的相对重要性度量 显示英文标题

标题： Understanding and Using the Relative Importance Measures Based on Orthonormality Transformation

摘要： 基于正交性变换的相对重要性度量类（OTMs）已被发现能够有效近似广义优势指数（GD）。 特别是，Johnson的相对权重（RW）在文献中被认为是最成功的OTM。 然而，OTMs的理论基础仍然不明确。 为了进一步理解OTMs，我们提供了一个广义框架，将OTM分解为两个功能步骤：正交化和重新分配。 为了评估每个步骤对OTMs性能的影响，我们在各种预测变量相关结构和响应变量分布下进行了广泛的蒙特卡洛模拟。 我们的研究结果表明，Johnson的最小变换始终优于其他常见的正交化方法。 我们还总结了在四种预测变量相关结构场景下，重新分配方法在第一主成分和方差膨胀因子（VIF）方面的表现。 该分析为在不同场景下选择适当的重新分配方法提供了指导，通过真实世界数据集示例进行说明。 我们的研究提供了对OTMs的更深入理解，并为寻求在各种建模情境中准确测量变量重要性的实践者提供了有价值的见解。 显示英文摘要

摘要： A class of relative importance measures based on orthonormality transformation (OTMs), has been found to effectively approximate the General Dominance index (GD). In particular, Johnson's Relative Weight (RW) has been deemed the most successful OTM in the literature. Nevertheless, the theoretical foundation of the OTMs remains unclear. To further understand the OTMs, we provide a generalized framework that breaks down the OTM into two functional steps: orthogonalization and reallocation. To assess the impact of each step on the performance of OTMs, we conduct extensive Monte Carlo simulations under various predictors' correlation structures and response variable distributions. Our findings reveal that Johnson's minimal transformation consistently outperforms other common orthogonalization methods. We also summarize the performance of reallocation methods under four scenarios of predictors' correlation structures in terms of the first principal component and the variance inflation factor (VIF). This analysis provides guidelines for selecting appropriate reallocation methods in different scenarios, illustrated with real-world dataset examples. Our research offers a deeper understanding of OTMs and provides valuable insights for practitioners seeking to accurately measure variable importance in various modeling contexts.