Identification and Sensitivity Analysis for Average Causal Mediation Effects with Time-Varying Treatments and Mediators: Investigating the Underlying Mechanisms of Kindergarten Retention Policy

Considering that causal mechanisms unfold over time, it is important to investigate the mechanisms over time, taking into account the time-varying features of treatments and mediators. However, identification of the average causal mediation effect in the presence of time-varying treatments and mediators is often complicated by time-varying confounding. This article aims to provide a novel approach to uncovering causal mechanisms in time-varying treatments and mediators in the presence of time-varying confounding. We provide different strategies for identification and sensitivity analysis under homogeneous and heterogeneous effects. Homogeneous effects are those in which each individual experiences the same effect, and heterogeneous effects are those in which the effects vary over individuals. Most importantly, we provide an alternative definition of average causal mediation effects that evaluates a partial mediation effect; the effect that is mediated by paths other than through an intermediate confounding variable. We argue that this alternative definition allows us to better assess at least a part of the mediated effect and provides meaningful and unique interpretations. A case study using ECLS-K data that evaluates kindergarten retention policy is offered to illustrate our proposed approach.     

Commentary: Using Potential Outcomes to Understand Causal Mediation Analysis

In this commentary, we demonstrate how the potential outcomes framework can help understand the key identification assumptions underlying causal mediation analysis. We show that this framework can lead to the development of alternative research design and statistical analysis strategies applicable to the longitudinal data settings considered by Maxwell, Cole, and Mitchell (2011).     

A Class of Distribution-Free Models for Longitudinal Mediation Analysis

Mediation analysis constitutes an important part of treatment study to identify the mechanisms by which an intervention achieves its effect. Structural equation model (SEM) is a popular framework for modeling such causal relationship. However, current methods impose various restrictions on the study designs and data distributions, limiting the utility of the information they provide in real study applications. In particular, in longitudinal studies missing data is commonly addressed under the assumption of missing at random (MAR), where current methods are unable to handle such missing data if parametric assumptions are violated. In this paper, we propose a new, robust approach to address the limitations of current SEM within the context of longitudinal mediation analysis by utilizing a class of functional response models (FRM). Being distribution-free, the FRM-based approach does not impose any parametric assumption on data distributions. In addition, by extending the inverse probability weighted (IPW) estimates to the current context, the FRM-based SEM provides valid inference for longitudinal mediation analysis under the two most popular missing data mechanisms; missing completely at random (MCAR) and missing at random (MAR). We illustrate the approach with both real and simulated data.     

Mediation analysis with structural equation models: Combining theory,design, and statistics

Statistical tests of indirect effects can hardly distinguish between genuine and spurious mediation effects. The present research demonstrates, however, that mediation analysis can be improved by combining a significance test of the indirect effect with assessing the fit of causal models. Testing only the indirect effect can be misleading, because significant results may also be obtained when the underlying causal model is different from the mediation model. We use simulated data to demonstrate that additionally assessing the fit of causal models with structural equation models can be used to exclude subsets of models that are incompatible with the observed data. The results suggest that combining structural equation modeling with appropriate research design and theoretically stringent mediation analysis can improve scientific insights. Finally, we discuss limitations of the structural equation modeling approach, and we emphasize the importance of non‐statistical methods for scientific discovery.     

On the (In)Validity of Tests of Simple Mediation: Threats and Solutions

Mediation analysis is a popular framework for identifying underlying mechanisms in social psychology. In the context of simple mediation, we review and discuss the implications of three facets of mediation analysis: (a) conceptualization of the relations between the variables, (b) statistical approaches, and (c) relevant elements of design. We also highlight the issue of equivalent models that are inherent in simple mediation. The extent to which results are meaningful stem directly from choices regarding these three facets of mediation analysis. We conclude by discussing how mediation analysis can be better applied to examine causal processes, highlight the limits of simple mediation, and make recommendations for better practice.     

Assessing Omitted Confounder Bias in Multilevel Mediation Models

To draw valid inference about an indirect effect in a mediation model, there must be no omitted confounders. No omitted confounders means that there are no common causes of hypothesized causal relationships. When the no-omitted-confounder assumption is violated, inference about indirect effects can be severely biased and the results potentially misleading. Despite the increasing attention to address confounder bias in single-level mediation, this topic has received little attention in the growing area of multilevel mediation analysis. A formidable challenge is that the no-omitted-confounder assumption is untestable. To address this challenge, we first analytically examined the biasing effects of potential violations of this critical assumption in a two-level mediation model with random intercepts and slopes, in which all the variables are measured at Level 1. Our analytic results show that omitting a Level 1 confounder can yield misleading results about key quantities of interest, such as Level 1 and Level 2 indirect effects. Second, we proposed a sensitivity analysis technique to assess the extent to which potential violation of the no-omitted-confounder assumption might invalidate or alter the conclusions about the indirect effects observed. We illustrated the methods using an empirical study and provided computer code so that researchers can implement the methods discussed.     

A Regression Framework for Causal Mediation Analysis with Applications to Behavioral Science

We introduce and extend the classical regression framework for conducting mediation analysis from the fit of only one model. Using the essential mediation components (EMCs) allows us to estimate causal mediation effects and their analytical variance. This single-equation approach reduces computation time and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations. Additionally, we extend this framework to non-nested mediation systems, provide a joint measure of mediation for complex mediation hypotheses, propose new visualizations for mediation effects, and explain why estimates of the total effect may differ depending on the approach used. Using data from social science studies, we also provide extensive illustrations of the usefulness of this framework and its advantages over traditional approaches to mediation analysis. The example data are freely available for download online and we include the R code necessary to reproduce our results.     

Flexible Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula

In the social sciences, mediation analysis has typically been formulated in the context of linear models using the Baron &; Kenny (1986) Baron, R. M. and Kenny, D. A. 1986. The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51: 1173–1182. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] approach. Extensions to nonlinear models have been considered but lack formal justification. By placing mediation analysis within the counterfactual framework of causal inference one can define causal mediation effects in a way that is not tied to a specific statistical model and identify them under certain no unmeasured confounding assumptions. Corresponding estimation procedures using parametric or nonparametric models, based on the so-called mediation formula, have recently been proposed in the psychological literature and made accessible through the R-package mediation. A number of limitations of the latter approach are discussed and a more flexible approach using natural effects models is proposed as an alternative. The latter builds on the same counterfactual framework but enables interpretable and parsimonious modeling of direct and mediated effects and facilitates tests of hypotheses that would otherwise be difficult or impossible to test. We illustrate the approach in a study of individuals who ended a romantic relationship and explore whether the effect of attachment anxiety during the relationship on unwanted pursuit behavior after the breakup is mediated by negative affect during the breakup.     

Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation

It is well known from the mediation analysis literature that the identification of direct and indirect effects relies on strong no unmeasured confounding assumptions of no unmeasured confounding. Even in randomized studies the mediator may still be correlated with unobserved prognostic variables that affect the outcome, in which case the mediator's role in the causal process may not be inferred without bias. In the behavioural and social science literature very little attention has been given so far to the causal assumptions required for moderated mediation analysis. In this paper we focus on the index for moderated mediation, which measures by how much the mediated effect is larger or smaller for varying levels of the moderator. We show that in linear models this index can be estimated without bias in the presence of unmeasured common causes of the moderator, mediator and outcome under certain conditions. Importantly, one can thus use the test for moderated mediation to support evidence for mediation under less stringent confounding conditions. We illustrate our findings with data from a randomized experiment assessing the impact of being primed with social deception upon observer responses to others’ pain, and from an observational study of individuals who ended a romantic relationship assessing the effect of attachment anxiety during the relationship on mental distress 2 years after the break‐up.     

What mediation analysis can (not) do

The present article is concerned with a common misunderstanding in the interpretation of statistical mediation analyses. These procedures can be sensibly used to examine the degree to which a third variable (Z) accounts for the influence of an independent (X) on a dependent variable (Y) conditional on the assumption that Z actually is a mediator. However, conversely, a significant mediation analysis result does not prove that Z is a mediator. This obvious but often neglected insight is substantiated in a simulation study. Using different causal models for generating Z (genuine mediator, spurious mediator, correlate of the dependent measure, manipulation check) it is shown that significant mediation tests do not allow researchers to identify unique mediators, or to distinguish between alternative causal models. This basic insight, although well understood by experts in statistics, is persistently ignored in the empirical literature and in the reviewing process of even the most selective journals.     

An Internal Limit of the Structural Analysis of Causation

Structural models of systems of causal connections have become a common tool in the analysis of the concept of causation. In the present paper I offer a general argument to show that one of the most powerful definitions of the concept of actual cause, provided within the structural models framework, is not sufficient to grant a full account of our intuitive judgements about actual causation, so that we are still waiting for a comprehensive definition. This is done not simply by focusing on a set of case studies, but by arguing that our intuitions about two different kinds of causal patterns, i.e., overdetermination and counterdetermination, cannot be addressed using that definition.     

Estimating Complex Measurement and Growth Models Using the R Package PLmixed

Measurement models, such as factor analysis and item response theory models, are commonly implemented within educational, psychological, and behavioral science research to mitigate the negative effects of measurement error. These models can be formulated as an extension of generalized linear mixed models within a unifying framework that encompasses various kinds of multilevel models and longitudinal models, such as partially nonlinear latent growth models. We introduce the R package PLmixed, which implements profile maximum likelihood estimation to estimate complex measurement and growth models that can be formulated within the general modeling framework using the existing R package lme4 and function optim. We demonstrate the use of PLmixed through two examples before concluding with a brief overview of other possible models.     

基于阶层线性理论的多层级中介效应

本文介绍了三种常见的多层级中介效应模型, 并根据阶层线性理论和依次检验回归系数的方法, 详述了多层级中介效应的检验步骤以及中介效应量的估计方法, 在2-1-1和1-1-1中介效应模型中, 推荐采用对层1自变量按组均值中心化, 同时将组均值置于层2截距方程式的中心化方法, 以实现组间和组内中介效应的有效分离。本文还展望了多层级中介效应模型的拓展方向, 即多层级调节性中介模型和多层级结构方程模型; 以及检验方法的拓展, 即Sobel检验和置信区间检验。     

有调节的中介模型检验方法：竞争还是替补?

在心理和其他社科研究领域, 经常遇到中介和调节变量。模型的变量多于3个时, 可能同时包含中介和调节变量, 一种常见的模型是有调节的中介模型。本文检视文献上各种检验有调节的中介模型的方法, 理清方法之间是竞争关系(分清优劣)还是替补关系(分清先后), 在此基础上总结出检验有调节的中介模型的步骤, 并用一个实例进行演示。文中也讨论了有调节的中介模型与有中介的调节模型的联系与区别。     

Bayes nets and babies: infants' developing statistical reasoning abilities and their representation of causal knowledge

A fundamental assumption of the causal graphical model framework is the Markov assumption, which posits that learners can discriminate between two events that are dependent because of a direct causal relation between them and two events that are independent conditional on the value of another event(s). Sobel and Kirkham (2006) demonstrated that 8-month-old infants registered conditional independence information among a sequence of events; infants responded according to the Markov assumption in such a way that was inconsistent with models that rely on simple calculations of associative strength. The present experiment extends these findings to younger infants, and demonstrates that such responses potentially develop during the second half of the first year of life. These data are discussed in terms of a developmental trajectory between associative mechanisms and causal graphical models as representations of infants' causal and statistical learning.     

Nonlinear Predictive Models for Multiple Mediation Analysis: With an Application to Explore Ethnic Disparities in Anxiety and Depression Among Cancer Survivors

Mediation analysis allows the examination of effects of a third variable (mediator/confounder) in the causal pathway between an exposure and an outcome. The general multiple mediation analysis method (MMA), proposed by Yu et al., improves traditional methods (e.g., estimation of natural and controlled direct effects) to enable consideration of multiple mediators/confounders simultaneously and the use of linear and nonlinear predictive models for estimating mediation/confounding effects. Previous studies find that compared with non-Hispanic cancer survivors, Hispanic survivors are more likely to endure anxiety and depression after cancer diagnoses. In this paper, we applied MMA on MY-Health study to identify mediators/confounders and quantify the indirect effect of each identified mediator/confounder in explaining ethnic disparities in anxiety and depression among cancer survivors who enrolled in the study. We considered a number of socio-demographic variables, tumor characteristics, and treatment factors as potential mediators/confounders and found that most of the ethnic differences in anxiety or depression between Hispanic and non-Hispanic white cancer survivors were explained by younger diagnosis age, lower education level, lower proportions of employment, less likely of being born in the USA, less insurance, and less social support among Hispanic patients.     

Computation and Causation

The computer's effect on our understanding of causation has been enormous. By the mid-1980s, philosophical and social-scientific work on the topic had left us with (1) no reasonable reductive account of causation and (2) a class of statistical causal models tied to linear regression. At this time, computer scientists were attacking the problem of equipping robots with models of the external that included probabilistic portrayals of uncertainty. To solve the problem of efficiently storing such knowledge, they introduced Bayes Networks and directed graphs. By attaching a causal interpretation to Bayes Networks, the philosophy of causation changed dramatically. We are now able to be extremely general about how causal structure connects to data, and systematic about when causal structures are empirically indistinguishable. In this essay I try to motivate and describe this synthesis.     

Effect size measures for mediation models: quantitative strategies for communicating indirect effects

The statistical analysis of mediation effects has become an indispensable tool for helping scientists investigate processes thought to be causal. Yet, in spite of many recent advances in the estimation and testing of mediation effects, little attention has been given to methods for communicating effect size and the practical importance of those effect sizes. Our goals in this article are to (a) outline some general desiderata for effect size measures, (b) describe current methods of expressing effect size and practical importance for mediation, (c) use the desiderata to evaluate these methods, and (d) develop new methods to communicate effect size in the context of mediation analysis. The first new effect size index we describe is a residual-based index that quantifies the amount of variance explained in both the mediator and the outcome. The second new effect size index quantifies the indirect effect as the proportion of the maximum possible indirect effect that could have been obtained, given the scales of the variables involved. We supplement our discussion by offering easy-to-use R tools for the numerical and visual communication of effect size for mediation effects.     

Generalized bilinear models

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.     

Quantifying and Testing Indirect Effects in Simple Mediation Models When the Constituent Paths Are Nonlinear

Most treatments of indirect effects and mediation in the statistical methods literature and the corresponding methods used by behavioral scientists have assumed linear relationships between variables in the causal system. Here we describe and extend a method first introduced by Stolzenberg (1980) Stolzenberg, R. M. 1980. The measurement and decomposition of causal effects in nonlinear and nonadditive models.. Sociological Methodology, 11: 459–488. [Crossref] , [Google Scholar] for estimating indirect effects in models of mediators and outcomes that are nonlinear functions but linear in their parameters. We introduce the concept of the instantaneous indirect effect of X on Y through M and illustrate its computation and describe a bootstrapping procedure for inference. Mplus code as well as SPSS and SAS macros are provided to facilitate the adoption of this approach and ease the computational burden on the researcher.