Polynomial regression is an old and commonly discussed modeling technique, though recommendations for its usage are widely variable. Here, we make the case that polynomial regression with second- and third-order terms should be part of every applied practitioners standard model-building toolbox, and should be taught to new students of the subject as the default technique to model nonlinearity. We argue that polynomial regression is superior to nonparametric alternatives for nonstatisticians due to its ease of interpretation, flexibility, and its nonreliance on sophisticated mathematics, like knots and kernel smoothing. This makes it the ideal default for nonstatisticians interested in building realistic models that can capture global as well as local effects of predictors on a response variable. Low-order polynomial regression can effectively model compact floor and ceiling effects, local linearity, and prevent inferring the presence of spurious interaction effects between distinct predictors when none are present. We also argue that the case against polynomial regression is largely specious, relying on either misconceptions around the method, strawman arguments, or historical artifacts. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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曲线的情况：使用预测变量的二阶和三阶多项式函数进行参数回归应该是常规的。


多项式回归是一种古老且经常讨论的建模技术，尽管对其使用的建议差异很大。在这里，我们认为具有二阶和三阶项的多项式回归应该成为每个应用实践者标准模型构建工具箱的一部分，并且应该作为非线性建模的默认技术教授给该学科的新生。我们认为，对于非统计学家来说，多项式回归优于非参数替代方案，因为它易于解释、灵活且不依赖复杂的数学（如结和核平滑）。这使得它成为有兴趣构建现实模型的非统计学家的理想默认值，这些模型可以捕获预测变量对响应变量的全局和局部影响。低阶多项式回归可以有效地模拟紧凑的下限和上限效应、局部线性，并防止在不存在时推断不同预测变量之间存在虚假交互效应。我们还认为，反对多项式回归的理由在很大程度上是似是而非的，要么依赖于对该方法的误解、稻草人论证，要么依赖于历史文物。 （PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。