Causal Mediation Analysis

Statistical mediation and moderation have most prominently been distinguished by Baron and Kenny (1986). More complex models that combine both of these effects have recently received increased attention, namely mediated moderation and moderated mediation (e.g., Muller, Judd, & Yzerbyt, 2005). Presently the focus is on a three variable model that is often claimed to represent an instance of moderated mediation or mediated moderation. More specifically, in this model a single variable is considered to simultaneously mediate and moderate the same effect.
We show that this specific model however cannot be considered either an instance of mediated moderation nor of moderated mediation. Also, we argue that this particular model is a priori misspecified. A data pattern that seems to agree with this model is recognized as plausible, but it indicates that the model must be modified in one of two ways to be methodologically sound. We conclude by recommending to not use this three variable model and to consider evidence that seemingly agrees with it as evidence that the three variable model is inadequate.

Mediation analysis aims at evaluating the causal mechanisms through which a treatment or intervention affects an outcome of interest. The goal is to  disentangle the total treatment effect into an indirect effect operating through one or several observed intermediate variables, the so-called mediators, as well as a direct effect reflecting any impact not captured by the observed mediator(s). This paper reviews methodological advancements with a particular focus on applications in economics. It defines the parameters of interest, covers various identification strategies, e.g. based on control variables or instruments, and presents sensitivity checks. Furthermore, it discusses several extensions of the standard mediation framework, such as multivalued treatments, mismeasured mediators, and outcome attrition.

The hypothesis of this study is twofold and states that parental socioeconomic status has an effect on the soft drink consumption of the child, and that this effect is mediated by the soft drink related parenting practices. One thousand six hundred and thirty-nine parents of 2.5-7 year old children from 34 Flemish pre-primary and primary schools, completed a self-administered questionnaire on sociodemographic characteristics, soft drink consumption and soft drink related parenting practices. Causal mediation analyses showed an effect of socioeconomic status on soft drink consumption of the child: children from high socioeconomic status consume 0.42 times the amount of soft drinks of children from lower socioeconomic status. Interestingly, this effect is almost entirely mediated by three soft drink parenting practices: soft drinks served at meals, the child can take soft drink whenever he or she wants and having soft drinks at home.

Hypotheses about psychological processes are often tested using traditional mediation analysis. This analysis relies onmeasurement of a transmitting variable. Conducting this analysis has become almost synonymous with examining processhypotheses. An alternative strategy to mediation analysis (the Testing-a-Process-hypothesis-by-an-Interaction Strategy, TPIS) isillustrated here. TPIS is based on a fully experimental design whereby a hypothesized process is tested by an interaction betweenthe hypothesized cause of an effect and a contextual variable. In the interaction term, the contextual variable allows comparisonof the causal effect observed when the process is uninterrupted to the effect observed when the process is interrupted. Thus, TPIS translatesatheoreticalprocesshypothesis intoastatisticalinteractionhypothesisthatusesafully experimental designtodirectlyexamine the hypothesized process.

Objectives: To test whether normative and non-normative forms of obligation to obey the police are empirically distinct and to assess whether they exhibit different dynamics in terms of the downstream effects of police-citizen contact. To draw an empirically informed conclusion as to whether police legitimacy can be partly defined as a normatively grounded form of obligation to obey the police. Methods: The Scottish Community Engagement Trial of procedurally just policing had a putative but unexpectedly negative causal effect. To help extract value from the study we use a natural effect model for causally ordered mediators to assess causal pathways that include-but also extend beyond-the experimental treatment to procedural justice. Results: Confirmatory factor analysis indicates that normative and non-normative forms of obligation are empirically distinct. Causal mediation analysis suggests that normative obligation to obey the police is sensitive to subjectively experienced procedurally just or unjust police behaviour and influences cooperation with the police and traffic law compliance in a way that is consistent with procedural justice theory (PJT). Non-normative obligation to obey the police is 'sticky' and unresponsive: it does not transmit the impact of the contact on either cooperation or compliance with traffic laws, and it is weakly and negatively correlated with normative obligation to obey the police (despite having moderately strong negative correlations with procedural justice and personal sense of power). Conclusions: Scholars have argued that criminologists have conflated normative and non-normative forms of felt obligation to obey police commands and that obligation should consequently be treated as an outcome of legitimacy rather than a constituent part of legitimacy. Findings indicate that legitimacy can reasonably be defined partly as normative obligation in the Scottish road-user context, so long as it is measured properly. More research into the dynamics of non-normative obligation to obey the police is needed.

This paper suggests a causal framework for disentangling individual level treatment effects and interference effects, i.e., general equilibrium, spillover, or interaction effects related to treatment distribution. Thus, the framework allows for a relaxation of the Stable Unit Treatment Value Assumption (SUTVA), which assumes away any form of treatment-dependent interference between study participants. Instead, we permit interference effects within aggregate units, for example, regions or local labor markets, but need to rule out interference effects between these aggregate units. Borrowing notation from the causal mediation literature, we define a range of policy-relevant effects and formally discuss identification based on randomization, selection on observables, and difference-indifferences. We also present an application to a policy intervention extending unemployment benefit durations in selected regions of Austria that arguably affected ineligibles in treated regions through general equilibrium effects in local labor markets. IfW Kiel, IZA ([email protected]). Financial support by Deutsche Forschungsgemeinschaft through CRC TRR 190 is gratefully acknowledged. We thank Josef Zweimüller for his support with the empirical application. Joachim Winter provided helpful comments on the draft.

In defending the scientific legitimacy of ceteris paribus qualified causal generalizations, we situate and specify the reference of the ceteris paribus proviso within a fundamental causal framework consisting of causal agents, pathways of influence, mediators, moderators, and causal consequences. In so doing, we provide an explication of the reference and utility of the ceteris paribus proviso in terms of mediators and moderators as these constitute the range of factors that can impinge on the relation between cause and effect. We argue that the conceptual causal roadmap embodied by the ceteris paribus qualification serves as a schematic template for the ongoing identification of causally relevant factors and plays an indispensable heuristic role in advancing scientific inquiry into causal relations. We then provide guidelines for differentiating between acceptable and unacceptable uses of ceteris paribus and describe how mediators and moderators conceptually encompassed by the ceteris paribus proviso can be employed in evaluating the meaning and acceptability of proposed ceteris paribus causal generalizations, as well serve as a guide to investigators in the process of designing studies to identify a causal agent, mediators, moderators, pathways of influence, and causal consequences.

Keywords: Ceteris Paribus; causal generalizations; causal explanation; mediation, moderation

This paper considers the evaluation of direct and indirect treatment effects, also known as mediation analysis, when outcomes are only observed for a subpopulation due to sample selection or outcome attrition. For identification, we combine sequential conditional independence assumptions on the assignment of the treatment and the mediator, i.e. the variable through which the indirect effect operates, with either selection on observables/missing at random or instrumental variable assumptions on the outcome attrition process. We derive expressions for the effects of interest that are based on inverse probability weighting by specific treatment, mediator, and/or selection propensity scores. We also provide a brief simulation study and an empirical illustration based on U.S. Project STAR data that assesses the direct effect and indirect effect (via absenteeism) of smaller kindergarten classes on math test scores.

Mechanisms explaining the negative effects of parental divorce on children's attainment have long been conjectured and assessed. Yet few studies of parental divorce have carefully attended to the assumptions and methods necessary to estimate causal mediation effects. Applying a causal framework to linked U.S. panel data, we assess the degree to which parental divorce limits children's education among whites and nonwhites and whether observed lower levels of educational attainment are explained by postdivorce family conditions and children's skills. Our analyses yield three key findings. First, the negative effect of divorce on educational attainment, particularly college, is substantial for white children; by contrast, divorce does not lower the educational attainment of nonwhite children. Second, declines in family income explain as much as one-to two-thirds of the negative effect of parental divorce on white children's education. Family instability also helps explain the effect, particularly when divorce occurs in early childhood. Children's psychosocial skills explain about one-fifth of the effect, whereas children's cognitive skills play a minimal role. Third, among nonwhites, the minimal total effect on education is explained by the offsetting influence of postdivorce declines in family income and stability alongside increases in children's psychosocial and cognitive skills.

It is standard in consumer price theory to decompose the price effect into two additive components: the
income effect and the substitution effect. Here I show that all three effects can be interpreted causally. I do
so using recently developed causal mediation techniques for decomposing a total effect of X on Y into pathspecific
effects. Within the formal framework provided by these techniques, the additive decomposition is a
special case of a more general decomposition that allows for interaction between a model’s variables. The
broader framework enables one to define a wider range of counterfactuals than does the standard theory,
but does not license the econometric derivation of the substitution effect from the income effect and the
price effect, or the derivation of the income effect from the substitution effect and the price effect.

In the debate about the influence of religion on voting, the behavioral dimension is often analyzed, especially church attendance. In this debate, churchgoers are considered to be more exposed to the political messages of their religious leaders. Following this perspective, we tested the hypothesis that church attendance was a mechanism through which the evangelical religion influenced the vote for Bolsonaro in 2018. The results show that approximately 16% of the effect of being evangelical on the vote for Bolsonaro is explained by this mechanism. To achieve this result, we use the mediation model for qualitative observational data. The database used is the Latin America Public Opinion Project (LAPOP) 2019.

Causal mediation analysis aims at disentangling a treatment effect into an indirect mechanism operating through an intermediate outcome or mediator, as well as the direct effect of the treatment on the outcome of interest. However, the evaluation of direct and indirect effects is frequently complicated by non-ignorable selection into the treatment and/or mediator, even after controlling for observables, as well as sample selection/outcome attrition. We propose a method for bounding direct and indirect effects in the presence of such complications using a method that is based on a sequence of linear programming problems. Considering inverse probability weighting by propensity scores, we compute the weights that would yield identification in the absence of complications and perturb them by an entropy parameter reflecting a specific amount of propensity score misspecification to set-identify the effects of interest. We apply our method to data from the National Longitudinal Survey of Youth 1979 to derive bounds on the explained and unexplained components of a gender wage gap decomposition that is likely prone to non-ignorable mediator selection and outcome attrition.

This paper combines causal mediation analysis with double machine learning to control for observed confounders in a data-driven way under a selection-on-observables assumption in a high-dimensional setting. We consider the average indirect effect of a binary treatment operating through an intermediate variable (or mediator) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. Estimation is based on efficient score functions, which possess a multiple robustness property w.r.t. misspecifications of the outcome, mediator, and treatment models. This property is key for selecting these models by double machine learning, which is combined with data splitting to prevent overfitting in the estimation of the effects of interest. We demonstrate that the direct and indirect effect estimators are asymptotically normal and root-n consistent under specific regularity conditions and investigate the finite sample properties of the suggested methods in a...

This article describes the RMediation package, which offers various methods for building confidence intervals (CIs) for mediated effects. The mediated effect is the product of two regression coefficients. The distribution-of-the-product method has the best statistical performance of existing methods for building CIs for the mediated effect. RMediation produces CIs using methods based on the distribution of product, Monte Carlo simulations, and an asymptotic normal distribution. Furthermore, RMediation generates percentiles, quantiles, and the plot of the distribution and CI for the mediated effect. An existing program, called PRODCLIN, published in Behavior Research Methods, has been widely cited and used by researchers to build accurate CIs. PRODCLIN has several limitations: The program is somewhat cumbersome to access and yields no result for several cases. RMediation described herein is based on the widely available R software, includes several capabilities not available in PRODCLIN, and provides accurate results that PRODCLIN could not.