Generalized Degrees of Freedom
Generalized Degrees of Freedom
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广义自由度
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Shu
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文献类型：
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作者：
Shu
乘法误差模型的两种流行回归方法是最小无偏百分比误差和零百分比偏差方法下的最小百分比误差。最小无偏百分比误差方法（迭代重新加权最小二乘回归）不使用任何约束，而零百分比偏差方法下的最小百分比误差需要约束作为曲线拟合过程的一部分。然而，零百分比偏差下的最小百分比误差用户不会调整自由度来考虑回归过程中包含的约束。因此，零百分比偏差方程下的最小百分比误差的拟合统计数据（例如标准百分比误差和广义 R2）可能不正确且具有误导性。这导致零百分比偏差和最小无偏百分比误差方程下的最小百分比误差之间的拟合统计数据不兼容。本文详细介绍了为什么应调整自由度，并建议使用广义自由度度量来计算约束驱动的成本估计关系的拟合统计量。它还解释了为什么零百分比偏差标准误差下的最小百分比误差低估了成本估计关系误差分布的分布。提供了说明性示例。请注意，本文仅考虑等式约束；不平等约束的广义自由度是另一个主题。
Two popular regression methods for the multiplicative-error model are the Minimum-Unbiased-Percent Error and Minimum-Percentage Error under the Zero-Percentage Bias methods. The Minimum-Unbiased-Percent Error method, an Iteratively Reweighted Least Squares regression, does not use any constraints, while the Minimum-Percentage Error under the Zero-Percentage Bias method requires a constraint as part of the curve-fitting process. However, Minimum-Percentage Error under the Zero-Percentage Bias users do not adjust the degrees of freedom to account for constraints included in the regression process. As a result, fit statistics for the Minimum-Percentage Error under the Zero-Percentage bias equations, e.g., the standard percent error and generalized R2, can be incorrect and misleading. This results in incompatible fit statistics between Minimum-Percentage Error under the Zero-Percentage Bias and Minimum-Unbiased-Percent Error equations. This article details why degrees of freedom should be adjusted and recommends a Generalized Degrees of Freedom measure to calculate fit statistics for constraint-driven cost estimating relationships. It also explains why Minimum-Percentage Error under the Zero-Percentage Bias’s standard error underestimates the spread of the cost estimating relationship error distribution. Illustrative examples are provided. Note that this article only considers equality constraints; Generalized Degrees of Freedom for inequality constraints is another topic.