Many effects of interest to sociologists are nonlinear. Additionally, many effects of interest are interaction effects—that is, the effect of one independent variable is contingent on the level of another independent variable. The proper way to estimate, interpret, and present these two types of effects individually are well known. However, many analyses that combine these two—that is, tests of interaction when the effects of interest are nonlinear—are not properly interpreted or tested. The consequences of approaching nonlinear interaction effects the way one would approach a linear interaction effect are severe and can often result in incorrect conclusions. I cover both nonlinear effects in the context of linear regression, and—most thoroughly—nonlinear effects in models for categorical outcomes (focusing on binary logit/probit). My goal in this article is to synthesize an evolving methodological literature and to provide straightforward advice and techniques to estimate,interpret, and present nonlinear interaction effects.

中文翻译：

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估计，解释和呈现非线性交互效应的最佳实践

社会学家感兴趣的许多影响都是非线性的。此外，许多感兴趣的效应是相互作用效应，也就是说，一个自变量的效应取决于另一个自变量的水平。分别估计，解释和呈现这两种类型的影响的正确方法是众所周知的。但是，许多将这两者结合的分析（即，当感兴趣的影响为非线性时的交互作用测试）没有得到适当的解释或测试。接近非线性相互作用效应的后果非常严重，通常可能导致错误的结论。我将介绍线性回归方面的非线性影响，以及最彻底的是分类结果模型中的非线性影响（着重于二进制logit / probit）。