Experimental Power for Indirect Effects in Group-randomized Studies with Group-level Mediators

Mediation analyses have provided a critical platform to assess the validity of theories of action across a wide range of disciplines. Despite widespread interest and development in these analyses, literature guiding the design of mediation studies has been largely unavailable. Like studies focused on the detection of a total or main effect, an important design consideration is the statistical power to detect indirect effects if they exist. Understanding the sensitivity to detect indirect effects is exceptionally important because it directly influences the scale of data collection and ultimately governs the types of evidence group-randomized studies can bring to bear on theories of action. However, unlike studies concerned with the detection of total effects, literature has not established power formulas for detecting multilevel indirect effects in group-randomized designs. In this study, we develop closed-form expressions to estimate the variance of and the power to detect indirect effects in group-randomized studies with a group-level mediator using two-level linear models (i.e., 2-2-1 mediation). The results suggest that when carefully planned, group-randomized designs may frequently be well positioned to detect mediation effects with typical sample sizes. The resulting power formulas are implemented in the R package PowerUpR and the PowerUp!-Mediator software (causalevaluation.org).     

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.     

基于不对称区间估计的有调节的中介模型检验

有调节的中介模型是中介过程受到调节变量影响的模型。评介了基于Bootstrap不对称置信区间和贝叶斯不对称可靠区间进行有调节的中介模型检验的3种方法, 包括亚组分析法、差异分析法和系数乘积法。模拟研究发现, 偏差校正的百分位Bootstrap置信区间和无先验信息的贝叶斯可靠区间在有调节的中介模型检验中表现相当, 都优于百分位Bootstrap置信区间的表现。建议使用系数乘积法进行第一阶段或第二阶段被调节的中介模型检验, 使用差异分析法进行两阶段被调节的中介模型检验, 并用一个实际例子演示如何用不对称区间估计检验有调节的中介模型。随后评述了3种有调节的中介模型检验方法在国内心理学的应用现状, 并展望了检验的拓展方向。     

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.     

BANOVA: Bayesian Analysis of Experiments in Consumer Psychology

This article introduces a Bayesian extension of ANOVA for the analysis of experimental data in consumer psychology. The approach, called BANOVA (Bayesian ANOVA), addresses some common challenges that consumer psychologists encounter in their experimental work, and is specifically suited for the analysis of repeated measures designs. There appears to be a recent surge in interest in those designs based on the recognition that they are sensitive to individual differences in response to experimental treatments and that they offer advantages for assessing causal mediating mechanisms, even at the individual level. BANOVA enables the analysis of repeated measures data derived from mixed within–between‐subjects experiments with Normal and nonNormal‐dependent variables and accommodates unobserved individual differences. It allows for the calculation of effect sizes, planned comparisons, simple effects, spotlight and floodlight analyses, and includes a wide range of mediation, moderation, and moderated mediation analyses. An R software package implements these analyses, and aims to provide a one‐stop shop for the analysis of experiments in consumer psychology. The package is illustrated through applications to a number of data sets from previously published studies.     

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。     

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.     

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.     

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.     

A Bayesian Approach for Estimating Mediation Effects With Missing Data

Methodologists have developed mediation analysis techniques for a broad range of substantive applications, yet methods for estimating mediating mechanisms with missing data have been understudied. This study outlined a general Bayesian missing data handling approach that can accommodate mediation analyses with any number of manifest variables. Computer simulation studies showed that the Bayesian approach produced frequentist coverage rates and power estimates that were comparable to those of maximum likelihood with the bias-corrected bootstrap. We share an SAS macro that implements Bayesian estimation and use 2 data analysis examples to demonstrate its use.     

基于结构方程模型的多重中介效应分析

多重中介模型是指存在多个中介变量的模型。多重中介模型可以分析特定中介效应、总的中介效应和对比中介效应。指出了目前多重中介模型分析普遍存在的问题,包括分析不完整、使用Sobel检验带来的局限。建议通过增加辅助变量的方法进行完整的多重中介效应分析,使用偏差校正的Bootstrap方法进行中介检验。总结出一个多重中介SEM分析流程,并有示例和相应的MPLUS程序。随后展望了辅助变量和中介效应检验方法的发展方向。     

基于两水平被试内设计的中介效应分析方法

在心理学和其他社科研究领域,通常的中介效应分析都基于被试间设计,研究者对于如何分析基于被试内设计的中介效应往往并不清楚。本文阐述了两水平被试内设计的中介效应分析方法(依次检验法和路径分析法),综合各方法优缺点给出一个分析流程,并用应用研究实例演示如何分析两水平被试内中介效应,最后展望了基于被试内设计的中介效应分析研究的拓展方向。     

三类多层中介效应分析方法比较

比较了贝叶斯法、Monte Carlo法和参数Bootstrap法在2-1-1多层中介分析中的表现。结果发现：1)有先验信息的贝叶斯法的中介效应点估计和区间估计都最准确;2)无先验信息的贝叶斯法、Monte Carlo法、偏差校正和未校正的参数Bootstrap法的中介效应点估计和区间估计表现相当,但Monte Carlo法在第Ⅰ类错误率和区间宽度指标上表现略优于其他三种方法,偏差校正的Bootstrap法在统计检验力上表现略优于其他三种方法,但在第Ⅰ类错误率上表现最差;结果表明,当有先验信息时,推荐使用贝叶斯法;当先验信息不可得时,推荐使用Monte Carlo法。     

Testing mediation effects in cross-classified multilevel data

In this article, we propose an approach to test mediation effects in cross-classified multilevel data in which the initial cause is associated with one crossed factor, the mediator is associated with the other crossed factor, and the outcome is associated with Level-1 units (i.e., the 2^(A)?2^(B)?1 design). Multiple-membership models and cross-classified random effects models are used to estimate the indirect effects. The method is illustrated using real data from the Early Childhood Longitudinal Study–Kindergarten Cohort (1998). The results from the simulation study show that the proposed method can produce a consistent estimate of the indirect effect and reliable statistical inferences, given an adequate sample size.     

类别变量的中介效应分析

在心理学和其他社科研究领域,研究者能熟练地进行连续变量的中介效应分析,但面对自变量、中介变量或(和)因变量为类别变量的中介效应分析,研究者往往束手无策。在阐述类别自变量中介分析方法的基础上,我们建议使用整体和相对中介相结合的类别自变量中介分析方法,并给出了分析流程。以二分因变量为例,讨论了中介变量或(和)因变量为类别变量的中介分析方法的发展过程(即尺度统一的过程),建议通过检验Za×Zb的显著性来判断中介效应的显著性。用二个实际例子演示如何进行类别变量的中介效应分析。最后展望了类别变量的中介效应分析研究的拓展方向。     

纵向数据的中介效应分析

目前中介效应检验主要是基于截面数据,但许多时候截面数据的中介分析不适合进行因果推断,因而需要收集历时性的纵向数据,进行纵向数据的中介分析。评介了基于交叉滞后面板模型、多层线性模型和潜变量增长模型的纵向数据的中介分析方法及其四个发展。第一,中介效应随时间变化,如连续时间模型、多层时变系数模型。第二,中介效应随个体变化,如随机效应的交叉滞后面板模型和多层自回归模型。第三,中介模型的整合,如交叉滞后面板模型与多层线性模型整合为多层自回归模型。第四,中介检验方法的发展,建议使用Monte Carlo、Bootstrap和贝叶斯法进行纵向数据的中介分析。总结出一个纵向数据的中介分析流程并给出相应的Mplus程序。随后展望了纵向数据的中介分析的拓展方向。     

Bayesian Model Averaging for Propensity Score Analysis

This article considers Bayesian model averaging as a means of addressing uncertainty in the selection of variables in the propensity score equation. We investigate an approximate Bayesian model averaging approach based on the model-averaged propensity score estimates produced by the R package BMA but that ignores uncertainty in the propensity score. We also provide a fully Bayesian model averaging approach via Markov chain Monte Carlo sampling (MCMC) to account for uncertainty in both parameters and models. A detailed study of our approach examines the differences in the causal estimate when incorporating noninformative versus informative priors in the model averaging stage. We examine these approaches under common methods of propensity score implementation. In addition, we evaluate the impact of changing the size of Occam’s window used to narrow down the range of possible models. We also assess the predictive performance of both Bayesian model averaging propensity score approaches and compare it with the case without Bayesian model averaging. Overall, results show that both Bayesian model averaging propensity score approaches recover the treatment effect estimates well and generally provide larger uncertainty estimates, as expected. Both Bayesian model averaging approaches offer slightly better prediction of the propensity score compared with the Bayesian approach with a single propensity score equation. Covariate balance checks for the case study show that both Bayesian model averaging approaches offer good balance. The fully Bayesian model averaging approach also provides posterior probability intervals of the balance indices.     

Potential Mediators in Parenting and Family Intervention: Quality of Mediation Analyses

Parenting and family interventions have repeatedly shown effectiveness in preventing and treating a range of youth outcomes. Accordingly, investigators in this area have conducted a number of studies using statistical mediation to examine some of the potential mechanisms of action by which these interventions work. This review examined from a methodological perspective in what ways and how well the family-based intervention studies tested statistical mediation. A systematic search identified 73 published outcome studies that tested mediation for family-based interventions across a wide range of child and adolescent outcomes (i.e., externalizing, internalizing, and substance-abuse problems; high-risk sexual activity; and academic achievement), for putative mediators pertaining to positive and negative parenting, family functioning, youth beliefs and coping skills, and peer relationships. Taken as a whole, the studies used designs that adequately addressed temporal precedence. The majority of studies used the product of coefficients approach to mediation, which is preferred, and less limiting than the causal steps approach. Statistical significance testing did not always make use of the most recently developed approaches, which would better accommodate small sample sizes and more complex functions. Specific recommendations are offered for future mediation studies in this area with respect to full longitudinal design, mediation approach, significance testing method, documentation and reporting of statistics, testing of multiple mediators, and control for Type I error.     

Data Analytic Advances That Bridge the Scientist-Practitioner Gap

In this commentary, I advance the view that the scientist-practitioner gap is partly due to the research designs commonly used in psychotherapy research. Specifically, I believe that randomized controlled trials, which are important for establishing treatment efficacy and as leverage when making the case for the value of psychotherapy in relation to various stakeholders, are limited for further development of clinical theories. Instead, I find recent advances in cross-lagged panel modeling to be both clinically intuitive and stronger for causal inference than most other nonexperimental designs. In addition to discussing causal inference and clinical interpretation of cross-lagged panel models, I discuss the potential of improving mediation analysis, personalization of research, and studying issues of clinical timing. Finally, I briefly discuss some limitations of cross-lagged panel models. It is my belief that the use of these data analytic advances can make empirical research better live up to the innovations in Beck’s work.