Congruence hypotheses play a major role in many areas of psychology. They refer to, for example, the consequences of person-environment fit, similarity, or self-other agreement. For example, are people psychologically better adjusted when their self-view is in line with their reputation? A valid statistical approach that can be applied to investigate congruence hypotheses of this kind is quadratic Response Surface Analysis (RSA) in which a second-order polynomial model is fit to the data and appropriately interpreted. However, quadratic RSA does not allow researchers to investigate more precise expectations about a congruence effect. Do the data support an asymmetric congruence effect, in the sense that congruence leads to the highest (or lowest) outcome, but incongruence in one direction (e.g., self-view exceeds reputation) affects the outcome differently than incongruence in the other direction (e.g., self-view falls behind reputation)? Is there a level-dependent congruence effect, such that the amount of congruence is more strongly related to the outcome variable for some levels of the predictors (e.g., high self-view and reputation) than for others (e.g., low self-view and reputation)? Such complex congruence hypotheses have frequently been suggested in the literature, but they could not be investigated because an appropriate statistical approach has yet to be developed. Here, we present analytical strategies, based on third-order polynomial models, that enable users to investigate asymmetric and level-dependent congruence effects, respectively. To facilitate the correct application of the suggested approaches, we provide respective step-by-step guidelines, corresponding R syntax, and illustrative analyses using simulated and real data. (PsycInfo Database Record (c) 2020 APA, all rights reserved)

中文翻译：

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三次响应面分析：使用三阶多项式模型研究不对称和水平相关的同余效应。

一致性假设在心理学的许多领域都发挥着重要作用。例如，它们指的是人与环境的契合度、相似性或自我认同的结果。例如，当人们的自我看法与他们的声誉一致时，他们的心理是否会更好地调整？可用于研究此类全等假设的有效统计方法是二次响应面分析 (RSA)，其中二阶多项式模型适合数据并进行适当解释。然而，二次 RSA 不允许研究人员更精确地调查关于同余效应的预期。数据是否支持非对称一致效应，即一致导致最高（或最低）结果，但一个方向的不一致（例如，自我看法超过声誉）与另一方向的不一致（例如，自我看法落后）对结果的影响不同名声）？是否存在水平依赖同余效应，这样对于某些级别的预测变量（例如，高自我评价和声誉），同余量与结果变量的相关性比其他水平（例如，低自我评价和声誉）更强烈？文献中经常提出这种复杂的全等假设，但由于尚未开发出适当的统计方法，因此无法对其进行研究。在这里，我们提出了基于三阶多项式模型的分析策略，使用户能够分别研究不对称和依赖于水平的同余效应。为了促进建议方法的正确应用，我们提供了相应的分步指南、相应的 R 语法以及使用模拟和真实数据的说明性分析。（PsycInfo 数据库记录 (c) 2020 APA，保留所有权利）