Direction of Effects in Multiple Linear Regression Models

Detecting heterogeneity in the causal direction of dependence: A model-based recursive partitioning approach

Methods of causal discovery and direction of dependence to evaluate causal properties of variable relations have experienced rapid development. The majority of causal discovery methods, however, relies on the assumption of causal effect homogeneity, that is, the identified causal structure is expected to hold for the entire population. Because causal mechanisms can vary across subpopulations, we propose combining methods of model-based recursive partitioning and non-Gaussian causal discovery to identify such subpopulations. The resulting algorithm can discover subpopulations with potentially varying magnitude and causal direction of effects under mild parameter inequality assumptions. Feasibility conditions are described and results from synthetic data experiments are presented suggesting that large effects and large sample sizes are beneficial for detecting causally competing subgroups with acceptable statistical performance. In a real-world data example, the extraction of meaningful subgroups that differ in the causal mechanism underlying the development of numerical cognition is illustrated. Potential extensions and recommendations for best practice applications are discussed.

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

In this study, we explored whether satisfaction with government management, perception of risk, and gratitude influenced public anxiety during the COVID-19 pandemic in China. Using a cross-sectional, anonymous and confidential online survey, a nationwide sample of Chinese adults (N = 876) was targeted between March 25-March 30, 2020, a period in which newly confirmed cases significantly declined in China. The anxiety level was decreased as compared to that assessed during the peak period. Multiple parallel mediation modeling demonstrated that risk perception and gratitude partially mediated the relationship between satisfaction with government management and public anxiety. Increasing satisfaction and gratitude, as well as reducing risk perception contribute to the public's mental health. The results may shed light on the positive factors for psychological well-being during the COVID-19 pandemic and may aid potential strategies for the policy maker, the public, and the clinic to regulate negative emotions or future emerging infectious diseases.

Direction Dependence Analysis in the Presence of Confounders: Applications to Linear Mediation Models Using Observational Data

Statistical methods to identify mis-specifications of linear regression models with respect to the direction of dependence (i.e. whether x→y or y→x better approximates the data-generating mechanism) have received considerable attention. Direction dependence analysis (DDA) constitutes such a statistical tool and makes use of higher-moment information of variables to derive statements concerning directional model mis-specifications in observational data. Previous studies on direction of dependence mainly focused on statistical inference and guidelines for the selection from the two directionally competing candidate models (x→y versus y→x) while assuming the absence of unobserved common causes. The present study describes properties of DDA when confounders are present and extends existing DDA methodology by incorporating the confounder model as a possible explanation. We show that all three explanatory models can be uniquely identified under standard DDA assumptions. Further, we discuss the proposed approach in the context of testing competing mediation models and evaluate an organizational model proposing a mediational relation between school leadership and student achievement via school safety using observational data from an urban school district. Overall, DDA provides strong empirical support that school safety has indeed a causal effect on student achievement but suggests that important confounders are present in the school leadership-safety relation.

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

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.

Locating Event-Based Causal Effects: A Configural Perspective

Statistical models for the analysis of hypotheses that are compatible with direction dependence were originally specified based on the linear model. In these models, relations among variables reflected directional or causal hypotheses. In a number of causal theories, however, effects are defined as resulting from causes that did versus did not occur. To accommodate this type of theory, the present article proposes analyzing directional or causal hypotheses at the level of configurations. Causes thus have the effect that, in a particular sector of the data space, the density of cases increases or decreases. With reference to log-linear models of direction dependence, this article specifies base models for the configural analysis of directional or causal hypotheses. In contrast to standard configural analysis, the models are applied in a confirmatory context. Specific direction dependence hypotheses are analyzed. In a simulation study, it is shown that the proposed methods have good power to identify the sectors in the data space in which density exceeds or falls below expectation. In a data example, it is shown that the evolutionary hypothesis that body size determines brain size is confirmed in particular for higher vertebrates.

Direction of dependence in measurement error models

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.

Evidence that psychopathology symptom networks have limited replicability

Network analysis is quickly gaining popularity in psychopathology research as a method that aims to reveal causal relationships among individual symptoms. To date, 4 main types of psychopathology networks have been proposed: (a) association networks, (b) regularized concentration networks, (c) relative importance networks, and (d) directed acyclic graphs. The authors examined the replicability of these analyses based on symptoms of major depression and generalized anxiety between and within 2 highly similar epidemiological samples (i.e., the National Comorbidity Survey-Replication [n = 9282] and the National Survey of Mental Health and Wellbeing [n = 8841]). Although association networks were stable, the 3 other types of network analysis (i.e., the conditional independence networks) had poor replicability between and within methods and samples. The detailed aspects of the models-such as the estimation of specific edges and the centrality of individual nodes-were particularly unstable. For example, 44% of the symptoms were estimated as the "most influential" on at least 1 centrality index across the 6 conditional independence networks in the full samples, and only 13-21% of the edges were consistently estimated across these networks. One of the likely reasons for the instability of the networks is the predominance of measurement error in the assessment of individual symptoms. The authors discuss the implications of these findings for the growing field of psychopathology network research, and conclude that novel results originating from psychopathology networks should be held to higher standards of evidence before they are ready for dissemination or implementation in the field. (PsycINFO Database Record

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Direction-dependence analysis

The concept of direction dependence has attracted growing attention due to its potential to help decide which of two competing linear regression models ( X → Y or Y → X) is more likely to reflect the correct causal flow. Several tests have been proposed to evaluate hypotheses compatible with direction dependence. In this issue, Thoemmes (2015) reports results of an empirical evaluation of direction-dependence tests using real-world data sets with known causal ordering and concludes that the tests (known to perform excellent in simulation studies) perform poorly in the real-world setting. The present article aims at answering the question how this is possible. First, we review potential conceptual issues associated with Thoemmes’ (2015) approach. We argue that direction dependence is best conceptualized as a confirmatory approach to test focused directional theories. Thoemmes’ (2015) evaluation is based on an exploratory use of direction dependence. It implicitly follows the tradition of causal search algorithms. Second, we discuss potential statistical issues associated with Thoemmes’ (2015) selection schemes used to decide whether a variable pair is suitable for direction-dependence analysis. Based on these issues, new tests of direction dependence as well as new guidelines for confirmatory direction-dependence analysis are proposed. An empirical example is given to illustrate the application of these guidelines.