Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS

Abstract

In nonexperimental data, at least three possible explanations exist for the association of two variables x and y: (1) x is the cause of y, (2) y is the cause of x, or (3) an unmeasured confounder is present. Statistical tests that identify which of the three explanatory models fits best would be a useful adjunct to the use of theory alone. The present article introduces one such statistical method, direction dependence analysis (DDA), which assesses the relative plausibility of the three explanatory models on the basis of higher-moment information about the variables (i.e., skewness and kurtosis). DDA involves the evaluation of three properties of the data: (1) the observed distributions of the variables, (2) the residual distributions of the competing models, and (3) the independence properties of the predictors and residuals of the competing models. When the observed variables are nonnormally distributed, we show that DDA components can be used to uniquely identify each explanatory model. Statistical inference methods for model selection are presented, and macros to implement DDA in SPSS are provided. An empirical example is given to illustrate the approach. Conceptual and empirical considerations are discussed for best-practice applications in psychological data, and sample size recommendations based on previous simulation studies are provided.

Perceived Stress, Stigma, Traumatic Stress Levels and Coping Responses amongst Residents in Training across Multiple Specialties during COVID-19 Pandemic—A Longitudinal Study

“…Compared with baseline, responses from timepoint 2 indicated that use of problem solving and use of social support as coping strategies were negative and positive predictors of traumatic stress, respectively (see Table 3 ). In order to further clarify the relationship between social support and traumatic stress, we employed DDA [ 15 ]. We hypothesized that greater traumatic stress would lead to more frequent use of social support seeking as a coping mechanism (IES-R €→ Social support), while controlling for gender, seniority, living arrangements, marital status, exposure to patients with respiratory symptoms, and deployment to high-risk areas (NCID).…”

“…We also employed linear regression analyses to examine the predictors of PSS, IES-R, and HWSS at each timepoint, while controlling for gender, seniority, marital status, living arrangement, exposure to patients with respiratory symptoms, and deployment to high-risk areas (NCID). Direction Dependence Analysis (DDA [ 15 ]) was then used to further clarify the direction of relationship between the predictors and outcome variables. DDA allows us to evaluate the theory of one-directional relationships between variables (e.g., x → y) as compared to other directional alternatives (e.g., y → x) using skewness and kurtosis of the data [ 15 ].…”

“…Direction Dependence Analysis (DDA [ 15 ]) was then used to further clarify the direction of relationship between the predictors and outcome variables. DDA allows us to evaluate the theory of one-directional relationships between variables (e.g., x → y) as compared to other directional alternatives (e.g., y → x) using skewness and kurtosis of the data [ 15 ]. The theory (x → y) is supported when the distribution of variable y is closer to normality than x, the residual distribution of x → y is closer to normality than that of y → x, and the independence assumption of residuals and predictor holds for x → y while at the same time being violated for y → x [ 15 ].…”

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

“…In other words, the approach presented here assumes that variables are nonnormally distributed. Higher-than-second moment information of variables has been used in the past in the development of causal discovery algorithms (Mooij, Peters, Janzing, Zscheischler, & Schölkopf, 2016;Shimizu, Hoyer, Hyvärinen, & Kerminen, 2006;Shimizu et al, 2011), confirmatory methods to test the direction of dependence in linear models (Wiedermann & Li, 2018;Wiedermann & von Eye, 2015), estimation algorithms in independent component analysis (Hyvärinen, Karhunen, & Oja, 2001), and search algorithms for covariate selection in linear models (Entner, Hoyer, & Spirtes, 2012). In the present study, we discuss similar principles for the development of unconfoundedness tests in mediation analysis and evaluate their performance in detecting potential confounders in mediator-outcome relations with randomized treatment.…”

Back to the future: Considerations in use and reporting of the retrospective pretest

“…For example, the need to justify one’s effort, or to appear to oneself or the evaluator to have improved over time, could cause people to maximize the difference between posttest and retrospective pretest ratings when those rating scales are presented together. Statistical techniques such as stochastic frontier analyses (Rosenman et al, 2011) and directional dependence analysis (Pornprasertmanit & Little, 2012; von Eye & DeShon, 2012; Wiedermann & Li, 2018; Wiedermann & von Eye, 2015) provide methods to determine whether and to what degree such confounds are present at each measurement point.…”