Confounder detection in linear mediation models: Performance of kernel-based tests of independence

Abstract

It is well-known that the identification of direct and indirect effects in mediation analysis requires strong unconfoundedness assumptions. Even when the predictor is under experimental control, unconfoundedness assumptions must be imposed on the mediator-outcome relation in order to guarantee valid indirect-effect identification. Researchers are therefore advised to test for unconfoundedness when estimating mediation effects. Significance tests to evaluate unconfoundedness usually rely on an instrumental variable (IV)-that is, a variable that is nonindependent of the explanatory variable and, at the same time, independent of all exogenous factors that affect the outcome when the explanatory variable is held constant. Because IVs may be hard to come by, the present study shows that confounders of the mediator-outcome relation can be detected without making use of IVs when variables are nonnormal. We show that kernel-based tests of independence are able to detect confounding under nonnormality. Results from a simulation study are presented that suggest that these tests perform well in terms of Type I error protection and statistical power, independent of the distribution or measurement level of the confounder. A real-world data example from the Job Search Intervention Study (JOBS II) illustrates how the presented approach can be used to minimize the risk of obtaining biased indirect-effect estimates. The data requirements and role of unconfoundedness tests as diagnostic tools are discussed. A Monte Carlo-based power analysis tool for sample size planning is also provided.

The Relationship of Fear of Death Between Neuroticism and Anxiety During the Covid-19 Pandemic

“…This procedure was also taken into consideration as different confounders might occur, but it also to previously examine and avoid collinearity across variables. This involved procedures such as evaluating outliers or the independence of linearly uncorrelated residuals as depicted in previous literature (25). The statistical analysis for the mediation model was performed using SPSS 22 (IBM) under the Process macro for SPSS (26) to test the hypothesis that death fear mediates the effect of personality on anxiety.…”

Risk perception and gratitude mediate the negative relationship between COVID-19 management satisfaction and public anxiety

“…Next, Direction Dependence Analysis (DDA) was applied to evaluate the most probable causal direction between variables using the SPSS add-ons (publicly available at https://www.ddaproject.com ). The DDA was developed to determine causal relationships 61 – 63 and has been used effectively in previous studies 64 – 66 . Specifically, the DDA consists of three components and the target model (e.g.…”

“…com). The DDA was developed to determine causal relationships [61][62][63] and has been used effectively in previous studies [64][65][66] . Specifically, the DDA consists of three components and the target model (e.g.…”

One Step at a Time: A Statistical Approach for Distinguishing Mediators, Confounders, and Colliders using Direction Dependence Analysis (DDA)

“…Formal statistical tests for independence that are based on the HSIC (i.e., 𝐻𝐻 0 : 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 = 0) are also available. In the current study, we apply the asymptotic (gamma-approximated) HSIC test with median heuristic bandwidths (Gretton et al, 2008) as recommended by simulation results from Wiedermann and Li (2019). Selection of causal models I, II and III can be made by conducting HSIC-based independence tests.…”

“…We evaluated four sample sizes in the simulation: 500, 1000, 2000, and 5000. The levels of sample size were selected to reflect a range of small to large samples appropriate for DDA, as previous studies have shown that the HSIC test may require sample sizes in excess of n ≥ 800 to achieve sufficient power (Wiedermann & Li, 2019).…”