Wiedermann Wolfgang, Merkle Edgar C, von Eye Alexander
Department of Educational, School, and Counseling Psychology, University of Missouri, Columbia, Missouri, USA.
Department of Psychological Sciences, University of Missouri, Columbia, Missouri, USA.
Br J Math Stat Psychol. 2018 Feb;71(1):117-145. doi: 10.1111/bmsp.12111. Epub 2017 Sep 5.
Methods to determine the direction of a regression line, that is, to determine the direction of dependence in reversible linear regression models (e.g., x→y vs. y→x), have experienced rapid development within the last decade. However, previous research largely rested on the assumption that the true predictor is measured without measurement error. The present paper extends the direction dependence principle to measurement error models. First, we discuss asymmetric representations of the reliability coefficient in terms of higher moments of variables and the attenuation of skewness and excess kurtosis due to measurement error. Second, we identify conditions where direction dependence decisions are biased due to measurement error and suggest method of moments (MOM) estimation as a remedy. Third, we address data situations in which the true outcome exhibits both regression and measurement error, and propose a sensitivity analysis approach to determining the robustness of direction dependence decisions against unreliably measured outcomes. Monte Carlo simulations were performed to assess the performance of MOM-based direction dependence measures and their robustness to violated measurement error assumptions (i.e., non-independence and non-normality). An empirical example from subjective well-being research is presented. The plausibility of model assumptions and links to modern causal inference methods for observational data are discussed.
确定回归线方向的方法，即确定可逆线性回归模型中依赖关系的方向（例如，x→y 与 y→x），在过去十年中得到了迅速发展。然而，以往的研究很大程度上基于真实预测变量的测量不存在测量误差这一假设。本文将方向依赖原理扩展到测量误差模型。首先，我们根据变量的高阶矩以及测量误差导致的偏度和超额峰度的衰减来讨论可靠性系数的非对称表示。其次，我们确定了由于测量误差导致方向依赖决策存在偏差的条件，并提出矩估计法（MOM）作为一种补救措施。第三，我们处理真实结果同时存在回归和测量误差的数据情况，并提出一种敏感性分析方法，以确定方向依赖决策对不可靠测量结果的稳健性。进行了蒙特卡罗模拟，以评估基于矩估计法的方向依赖度量的性能及其对违反测量误差假设（即非独立性和非正态性）的稳健性。给出了一个来自主观幸福感研究的实证例子。讨论了模型假设的合理性以及与观测数据现代因果推断方法的联系。
