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.     

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.     

Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: new procedures and recommendations

The authors propose new procedures for evaluating direct, indirect, and total effects in multilevel models when all relevant variables are measured at Level 1 and all effects are random. Formulas are provided for the mean and variance of the indirect and total effects and for the sampling variances of the average indirect and total effects. Simulations show that the estimates are unbiased under most conditions. Confidence intervals based on a normal approximation or a simulated sampling distribution perform well when the random effects are normally distributed but less so when they are nonnormally distributed. These methods are further developed to address hypotheses of moderated mediation in the multilevel context. An example demonstrates the feasibility and usefulness of the proposed methods.     

Multilevel mediation analysis: The effects of omitted variables in the 1–1–1 model

Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1–1–1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c – c′) are equivalent at the between‐ and within‐cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within‐cluster ab and c – c′ no longer holds. Correlation between random slopes implies that the within‐cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.     

Quantile Mediation Models: A Comparison of Methods for Assessing Mediation Across the Outcome Distribution

Recent introduction of quantile regression methods to analysis of epidemiologic data suggests that traditional mean regression approaches may not suffice for some health outcomes such as Body Mass Index (BMI). In the same vein, the traditional mean-based approach to mediation modeling may not be sufficient to capture the potentially different mediating effects of behavioral interventions across the outcome distribution. By combining methods for estimating conditional quantiles with traditional mediation modeling techniques, mediation effects can be estimated for any quantile of the outcome distribution (so-called quantile mediation effects). Estimation and inference techniques for quantile mediation effects are compared through simulation studies, and recommendations are given. The quantile mediation methods are further compared with the traditional mean-based regression approaches to mediation analysis through analysis of data from Healthy Places, a trial that is examining the effects of the community–built environment on resident obesity risk. We found the magnitudes of indirect (mediating) effects of walkability on BMI and waist circumference were substantially larger for the upper quantiles compared with the median or mean. Results suggest that restricting the examination of mediation to the mean of the outcome distribution provides an incomplete picture of proposed mediating mechanisms and in some cases may miss important mediational relationships to outcomes.     

Statistical mediation analysis with a multicategorical independent variable

Virtually all discussions and applications of statistical mediation analysis have been based on the condition that the independent variable is dichotomous or continuous, even though investigators frequently are interested in testing mediation hypotheses involving a multicategorical independent variable (such as two or more experimental conditions relative to a control group). We provide a tutorial illustrating an approach to estimation of and inference about direct, indirect, and total effects in statistical mediation analysis with a multicategorical independent variable. The approach is mathematically equivalent to analysis of (co)variance and reproduces the observed and adjusted group means while also generating effects having simple interpretations. Supplementary material available online includes extensions to this approach and Mplus, SPSS, and SAS code that implements it.     

Moving Forward Indirectly: Reanalyzing the validity of employment interviews with indirect range restriction methodology

This study provides updated estimates of the criterion‐related validity of employment interviews, incorporating indirect range restriction methodology. Using a final dataset of 92 coefficients (N = 7,389), we found corrected estimates by structural level of .20 (Level 1), .46 (Level 2), .71 (Level 3), and .70 (Level 4). The latter values are noticeably higher than in previous interview meta‐analyses where the assumption was made that all restriction was direct. These results highlight the importance of considering indirect range restriction in selection. However, we found a number of studies involving both indirect and direct restriction, which calls into question the viability of assuming all restriction is now indirect. We found preliminary empirical support for correction of one of these multiple restriction patterns, indirect then direct.     

An overview of applied robust methods

Data in social sciences are typically non-normally distributed and characterized by heavy tails. However, most widely used methods in social sciences are still based on the analyses of sample means and sample covariances. While these conventional methods continue to be used to address new substantive issues, conclusions reached can be inaccurate or misleading. Although there is no ‘best method’ in practice, robust methods that consider the distribution of the data can perform substantially better than the conventional methods. This article gives an overview of robust procedures, emphasizing a few that have been repeatedly shown to work well for models that are widely used in social and behavioural sciences. Real data examples show how to use the robust methods for latent variable models and for moderated mediation analysis when a regression model contains categorical covariates and product terms. Results and logical analyses indicate that robust methods yield more efficient parameter estimates, more reliable model evaluation, more reliable model/data diagnostics, and more trustworthy conclusions when conducting replication studies. R and SAS programs are provided for routine applications of the recommended robust method.     

Distinguishing Direct and Indirect Effects of Executive Functions on Reading Comprehension in Adolescents

This study investigated direct and indirect effects of executive functions on reading comprehension in adolescents (N?=?87, M?=?14.0?years, SD?=?1.5) by testing for parallel mediation of effects of working memory, task-switching, and inhibitory control via decoding and text recall/inference. Working memory showed direct and indirect effects on passage comprehension, the latter mediated by text recall/inference. Task-switching was associated with decoding but its relation to passage comprehension was not significant. Inhibitory control showed indirect effects on passage comprehension via decoding and text recall/inference. Results indicate overlapping but distinct contributions of executive functions to reading skills.     

有调节的多层中介效应分析

多层中介和多层调节效应分析在社科领域已常有应用,但如果将多层中介和调节整合在一起,可以产生2（多层中介类型）×2（调节变量的层次）×3（调节的中介路径）共12种有调节的多层中介模型。面对有调节的多层中介效应分析,研究者往往束手无策。详述了基于多层线性模型的12种有调节的多层中介的分析方法和基于多层结构方程模型的4类有调节的多层中介分析方法,包括正交分割法,随机系数预测法,潜调节结构方程法和贝叶斯合理值法。这四类方法的核心议题在于如何处理潜调节项。当样本量足够大时,建议选择潜调节结构方程法;当样本量不足时,建议选择贝叶斯合理值法。随后用一个实际例子演示如何进行有调节的多层中介效应分析并有相应的Mplus程序。最后展望了有调节的多层中介效应分析研究的拓展方向。     

Bias in cross-sectional analyses of longitudinal mediation

Most empirical tests of mediation utilize cross-sectional data despite the fact that mediation consists of causal processes that unfold over time. The authors considered the possibility that longitudinal mediation might occur under either of two different models of change: (a) an autoregressive model or (b) a random effects model. For both models, the authors demonstrated that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters even under the ideal conditions when mediation is complete. In longitudinal models where variable M completely mediates the effect of X on Y, cross-sectional estimates of the direct effect of X on Y, the indirect effect of X on Y through M, and the proportion of the total effect mediated by M are often highly misleading.     

On Muddled Reasoning and Mediation Modeling

The hope of mediation modeling is that psychologists can go beyond tests of association to truly uncover mechanisms of change. We argue this hope can be realized only if psychologists make important distinctions regarding causality and inference. From the perspective of Aristotelian philosophy, mediation models are sequences of efficient causes, and psychologists should therefore seek to identify those persons who can be traced through the entire sequence successfully. By reanalyzing data from two mediation studies we demonstrate that contemporary, aggregate methods of analysis are not suitable for this task because they are instead focused on making inferences about population parameters. In both studies alternative, person-centered methods revealed that majorities of participants were not traceable through the statistically significant mediation models.     

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。     

真实型领导对员工工作投入影响的多重中介效应模型

为了考察真实型领导影响员工工作投入的内在作用机制,采用真实型领导行为量表、职业认同量表、情感承诺量表、组织支持感量表和工作投入量表对308名企业员工进行施测,结果发现：（1）真实型领导通过职业认同、情感承诺和组织支持感的间接作用对员工的工作投入产生影响;（2）职业认同、情感承诺和组织支持感在真实型领导影响员工工作投入的过程中起完全中介作用。     

Mediation Analysis in Social Psychology: Current Practices and New Recommendations

A key aim of social psychology is to understand the psychological processes through which independent variables affect dependent variables in the social domain. This objective has given rise to statistical methods for mediation analysis. In mediation analysis, the significance of the relationship between the independent and dependent variables has been integral in theory testing, being used as a basis to determine (1) whether to proceed with analyses of mediation and (2) whether one or several proposed mediator(s) fully or partially accounts for an effect. Synthesizing past research and offering new arguments, we suggest that the collective evidence raises considerable concern that the focus on the significance between the independent and dependent variables, both before and after mediation tests, is unjustified and can impair theory development and testing. To expand theory involving social psychological processes, we argue that attention in mediation analysis should be shifted towards assessing the magnitude and significance of indirect effects.     

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。     

Testing indirect effect with a complete or incomplete dichotomous mediator

Past methodological research on mediation analysis mainly focused on situations where all variables were complete and continuous. When issues of categorical data occur combined with missing data, more methodological considerations are involved. Specifically, appropriate decisions need to be made on estimation methods of the indirect effects and on confidence intervals for testing the indirect effects with accommodations of missing data. We compare strategies that address these issues based on a model with a dichotomous mediator, aiming to provide guidelines for researchers facing such challenges in practice.     

Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models

Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.     

The Combined Effects of Measurement Error and Omitting Confounders in the Single-Mediator Model

Mediation analysis requires a number of strong assumptions be met in order to make valid causal inferences. Failing to account for violations of these assumptions, such as not modeling measurement error or omitting a common cause of the effects in the model, can bias the parameter estimates of the mediated effect. When the independent variable is perfectly reliable, for example when participants are randomly assigned to levels of treatment, measurement error in the mediator tends to underestimate the mediated effect, while the omission of a confounding variable of the mediator-to-outcome relation tends to overestimate the mediated effect. Violations of these two assumptions often co-occur, however, in which case the mediated effect could be overestimated, underestimated, or even, in very rare circumstances, unbiased. To explore the combined effect of measurement error and omitted confounders in the same model, the effect of each violation on the single-mediator model is first examined individually. Then the combined effect of having measurement error and omitted confounders in the same model is discussed. Throughout, an empirical example is provided to illustrate the effect of violating these assumptions on the mediated effect.     

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.