Direction of dependence in measurement error models

• Published in: British journal of mathematical & statistical psychology Vol. 71; no. 1; pp. 117 - 145
• Main Authors: Wiedermann, Wolfgang, Merkle, Edgar C., Eye, Alexander
• Format: Journal Article
• Language: English
• Published: England British Psychological Society 01.02.2018
• Subjects: Attenuation; Computer Simulation; Decision analysis; Decisions; Dependence; direction dependence; Economic models; Empirical analysis; Error analysis; Error detection; Kurtosis; Linear Models; linear regression; measurement error; Measurement methods; Method of moments; Models, Statistical; Monte Carlo Method; non‐normality; Normality; R&D; Regression analysis; Regression models; Reproducibility of Results; Research & development; Robustness; Sensitivity analysis; Well being; linear regression; measurement error; method of moments; direction dependence; non-normality; sensitivity analysis
• ISSN: 0007-1102; 2044-8317; 2044-8317
• DOI: 10.1111/bmsp.12111

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.