Alternative Transformations to Handle Extreme Values of the Dependent Variable
处理因变量极端值的替代变换AI 解读 ↓
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处理因变量极端值的替代变换
- 研究问题
- 当因变量包含正值、负值和零值时，如何通过变换减弱极端观测对回归系数估计的影响，并比较不同变换的适用性？
- 方法与思路
- 作者比较扩展 Box–Cox 与反双曲正弦变换，并用双倍长度回归技术，在加拿大家庭净财富数据上检验两种变换。
- 材料陈述的贡献
- 摘要称反双曲正弦变换的对数似然可处理零值，而所讨论的 Box–Cox 变换不能；该数据集的检验支持前者。
- 阅读关注点
- 核对两种变换的参数化、似然构造和检验条件，特别关注零值与负值的处理，以及变换后回归系数的解释。
- 阅读边界
- 仅据版本未注明的索引摘要，不能判断检验的有限样本表现，也不能把单个财富数据集的结果推广为普遍优越性。
原文摘要
Transformations that could be used to reduce the influence of extreme observations of dependent variables, which can assume either sign, on regression coefficient estimates are studied in this article. Two that seem reasonable on a priori grounds—the extended Box—Cox (BC) and the inverse hyperbolic sine (IHS)—are evaluated in detail. One feature is that the log-likelihood function for IHS is defined for zero values of the dependent variable, which is not true of BC. The double-length regression technique (Davidson and MacKinnon 1984) is used to perform hypothesis tests of one transformation against the other using Canadian data on household net worth. These tests support the use of IHS instead of BC for this data set. Empirical investigators in economics often work with a logged dependent variable (taking the natural logarithm of a data series is, of course, a special case of BC) to reduce the weight their particular estimation procedure might otherwise attach to extreme values of the dependent variable. Logging dependent and independent variables has the added attraction that slope coefficients may be interpreted as elasticities. In the event that the dependent variable assumes nonpositive values, some researchers (e.g., Diamond and Hausman 1984; King and Dicks-Mireaux 1982) have dropped the nonpositive values and others have added a constant so that each observation is positive. An alternative transformation, which is defined for any real number, is the IHS transformation, sinh-1(x) = log(x + (x 2 + l)1/2). This was proposed in Johnson (1949) and is just as easy to employ as the BC transformation.