Department of Statistics, University of California, Los Angeles.
Department of Psychiatry and Behavioral Sciences, University of Washington.
Psychol Methods. 2022 Feb;27(1):121-141. doi: 10.1037/met0000440.
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).
回归模型在心理学领域中无处不在。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，如果因变量与有意义的预测变量之间是非线性建模的，那么系数估计的推论效用就会受到限制。在常见的建模策略中，如非线性预测器设计和/或广义线性模型中，就会出现这种问题。在前一种情况下，系数可能对应于乘积、幂、对数和/或指数变换单位。在后一种情况下，预测器与因变量之间的关系是通过因变量的函数来建模的，而不是原始单位的因变量。在这两种情况下，仅通过解释系数本身无法直接总结数据，而且实际上可能会产生误导。我们通过整合两个关键特征来解决这些问题，提出了回归效应的框架。首先，我们在提供所需解释的单位中明确地对实质变量进行建模。其次，我们使用偏导数来总结实质预测器和因变量之间的关系，以解释因建模策略而产生的非线性。我们展示了如何在解释性单位中得出感兴趣的数量的估计值和标准误差，以及以有意义的方式呈现变量之间关系的技术。最后，我们在广泛的模型和估计程序中提供了模拟和真实数据的演示。（PsycInfo 数据库记录（c）2022 APA，保留所有权利）。
