Covariate selection in causal learning under non-Gaussianity

Understanding causal mechanisms is a central goal in the behavioral, developmental, and social sciences. When estimating and probing causal effects using observational data, covariate adjustment is a crucial element to remove dependencies between focal predictors and the error term. Covariate selection, however, constitutes a challenging task because availability alone is not an adequate criterion to decide whether a covariate should be included in the statistical model. The present study introduces a non-Gaussian method for covariate selection and provides a forward selection algorithm for linear models (i.e., non-Gaussian forward selection; nGFS) to select appropriate covariates from a set of potential control variables to avoid inconsistent and biased estimators of the causal effect of interest. Further, we demonstrate that the forward selection algorithm has properties compatible with principles of direction of dependence, i.e., probing whether the causal target model is correctly specified with respect to the causal direction of effects. Results of a Monte Carlo simulation study suggest that the selection algorithm performs well, in particular when sample sizes are large (i.e., n ≥ 250) and data strongly deviate from Gaussianity (e.g., distributions with skewness beyond 1.5). An empirical example is given for illustrative purposes.

Job insecurity and performance in public and private sectors: a moderated mediation model

Purpose

The purpose of this study was to extend our knowledge of the relationship between quantitative and qualitative job insecurity and performance. On the basis of stress theories, we hypothesised that qualitative job insecurity (QLJI) would mediate the negative effect of quantitative job insecurity (QTJI) on two different indicators of performance: task performance (TP) and counterproductive work behaviours (CPWBs). In addition, the authors hypothesised that the effect of QTJI on QLJI would be moderated by the economic sector (public vs private) in which employees worked. Therefore, the authors empirically tested a moderated mediation model via PROCESS.

Design/methodology/approach

Participants were 431 employees from various Italian organisations. Data were collected using a self-report questionnaire measuring QTJI, QLJI, TP and CPWBs.

Findings

The results indicated that economic sector moderated the relationship between quantitative and QLJI. Both quantitative and QLJI were related to performance outcomes. Furthermore, QLJI mediated the effect of QTJI on TP and CPWB. However, this mediation was particularly apparent among employees in the private sector, supporting our hypothesised moderated mediation model.

Practical implications

The results suggest that managers of private and public organisations need to apply different policies to reduce the impact of job insecurity on CPWBs and increase the TP of their employees.

Originality/value

This study attempted to examine the job insecurity–performance relationship in more depth. For the first time, the effects of both job insecurity dimensions on performance were simultaneously investigated, with economic sector as a moderator and QLJI as a mediator.

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.

Testing the Causal Direction of Mediation Effects in Randomized Intervention Studies

In a recent update of the standards for evidence in research on prevention interventions, the Society of Prevention Research emphasizes the importance of evaluating and testing the causal mechanism through which an intervention is expected to have an effect on an outcome. Mediation analysis is commonly applied to study such causal processes. However, these analytic tools are limited in their potential to fully understand the role of theorized mediators. For example, in a design where the treatment x is randomized and the mediator (m) and the outcome (y) are measured cross-sectionally, the causal direction of the hypothesized mediator-outcome relation is not uniquely identified. That is, both mediation models, x → m → y or x → y → m, may be plausible candidates to describe the underlying intervention theory. As a third explanation, unobserved confounders can still be responsible for the mediator-outcome association. The present study introduces principles of direction dependence which can be used to empirically evaluate these competing explanatory theories. We show that, under certain conditions, third higher moments of variables (i.e., skewness and co-skewness) can be used to uniquely identify the direction of a mediator-outcome relation. Significance procedures compatible with direction dependence are introduced and results of a simulation study are reported that demonstrate the performance of the tests. An empirical example is given for illustrative purposes and a software implementation of the proposed method is provided in SPSS.

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.

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.