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Abstract：
The marginality principle guides analysts to avoid omitting lower-order terms from models in which higher-order terms are included as covariates. Lower-order terms are viewed as \"marginal\" to higher-order terms. We consider how this principle applies to three cases: regression models that may include the ratio of two measured variables; polynomial transformations of a measured variable; and factorial arrangements of defined interventions. For each case, we show that which terms or transformations are considered to be lower-order, and therefore marginal, depends on the scale of measurement, which is frequently arbitrary. Understanding the implications of this point leads to an intuitive understanding of the curse of dimensionality. We conclude that the marginality principle may be useful to analysts in some specific cases but caution against invoking it as a context-free recipe.
摘要：
边际原则指导分析师避免从包含高阶项作为协变量的模型中省略低阶项。低阶术语被视为“边际”到高阶术语。我们考虑该原理如何适用于三种情况：可能包括两个测量变量之比的回归模型；测量变量的多项式变换；以及已定义干预措施的阶乘安排。对于每种情况，我们展示了哪些项或变换被认为是低阶的，因此是边缘的，取决于测量的尺度，这往往是任意的。理解这一点的含义会导致对维度诅咒的直观理解。我们得出的结论是，在某些特定情况下，边际原则可能对分析师有用，但请注意不要将其用作无上下文的食谱。
