The partial derivative framework for substantive regression effects.
The partial derivative framework for substantive regression effects.
复制标题
实质性回归效应的偏导数框架。
DOI：
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发表时间：
2022
影响因子：
7
通讯作者：
Connor J. McCabe
中科院分区：
文献类型：
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作者：
Dale S Kim;Connor J. McCabe
回归模型在心理科学中无处不在。报告和解释回归模型的标准做法是呈现和解释系数估计值以及相关的标准误差、置信区间和p值。然而，系数估计有限的推理效用，如果结果是非线性建模的实质性解释的预测。这在常见的建模策略中是有问题的，例如非线性预测器设计和/或广义线性模型。在前者中，系数可以对应于乘积、幂、对数和/或指数变换的单位。在后者中，预测因子和结果之间的关系是通过结果的函数来建模的，而不是以其原始单位的结果。在这两种情况下，仅对系数的解释并不能提供数据的直接摘要，事实上可能会产生误导。我们通过整合两个关键特征来开发回归效应框架来解决这些问题。首先，我们明确建模的单位，提供所需的解释实质性变量。其次，我们使用偏导数来总结实质性预测变量和结果变量之间的关系，以解释建模策略产生的非线性。我们展示了如何获得的估计和标准误差的解释单位的数量感兴趣，以及技术，以有意义的方式呈现变量之间的关系。最后，我们提供了各种各样的模型和估计程序的模拟和真实的数据的演示。（PsycInfo数据库记录（c）2022阿帕，保留所有权利）。
egression models are ubiquitous in the psychological sciences. The standard practice in reporting and interpreting regression models are to present and interpret coefficient estimates and the associated standard errors, confidence intervals and p-values. However, coefficient estimates have limited inferential utility if the outcome is modeled nonlinearly with respect to the substantively interpreted predictors. This is problematic in common modeling strategies, such as nonlinear predictor designs and/or generalized linear models. In the former, coefficients may correspond to product, power, log, and/or exponentially transformed units. In the latter, the relationship between the predictors and outcome are modeled via a function of the outcome, rather than the outcome in its original units. In both cases, the interpretation of the coefficients alone do not provide straightforward summaries of the data, and in fact may be misleading. We address these issues by developing a framework of regression effects by integrating two critical features. First, we explicitly model substantive variables in the units that provide the desired interpretation. Second, we use partial derivatives to summarize the relations between the substantive predictors and outcome variables to account for nonlinearities arising from modeling strategies. We show how to derive estimates and standard errors for quantities of interest in the interpretive units, as well as techniques to present the relationships between variables in meaningful ways. Finally, we provide demonstrations in both simulated and real data over a wide variety of models and estimation procedures. (PsycInfo Database Record (c) 2022 APA, all rights reserved).