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.     

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。     

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.     

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。     

The Performance of Methods to Test Upper-Level Mediation in the Presence of Nonnormal Data

A Monte Carlo study compared the statistical performance of standard and robust multilevel mediation analysis methods to test indirect effects for a cluster randomized experimental design under various departures from normality. The performance of these methods was examined for an upper-level mediation process, where the indirect effect is a fixed effect and a group-implemented treatment is hypothesized to impact a person-level outcome via a person-level mediator. Two methods—the bias-corrected parametric percentile bootstrap and the empirical-M test—had the best overall performance. Methods designed for nonnormal score distributions exhibited elevated Type I error rates and poorer confidence interval coverage under some conditions. Although preliminary, the findings suggest that new mediation analysis methods may provide for robust tests of indirect effects.     

Distribution of the product confidence limits for the indirect effect: Program PRODCLIN

This article describes a program, PRODCLIN (distribution of the PRODuct Confidence Limits for INdirect effects), written for SAS, SPSS, and R, that computes confidence limits for the product of two normal random variables. The program is important because it can be used to obtain more accurate confidence limits for the indirect effect, as demonstrated in several recent articles (MacKinnon, Lockwood, & Williams, 2004; Pituch, Whittaker, & Stapleton, 2005). Tests of the significance of and confidence limits for indirect effects based on the distribution of the product method have more accurate Type I error rates and more power than other, more commonly used tests. Values for the two paths involved in the indirect effect and their standard errors are entered in the PRODCLIN program, and distribution of the product confidence limits are computed. Several examples are used to illustrate the PRODCLIN program. The PRODCLIN programs in rich text format may be downloaded from www.psychonomic.org/archive.     

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.     

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.     

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.     

An open-source LabVIEW application toolkit for phasic heart rate analysis in psychophysiological research

The cardiovascular system has been extensively measured in a variety of research and clinical domains. Despite technological and methodological advances in cardiovascular science, the analysis and evaluation of phasic changes in heart rate persists as a way to assess numerous psychological concomitants. Some researchers, however, have pointed to constraints on data analysis when evaluating cardiac activity indexed by heart rate or heart period. Thus, an off-line application toolkit for heart rate analysis is presented. The program, written with National Instruments’ LabVIEW, incorporates a variety of tools for off-line extraction and analysis of heart rate data. Current methods and issues concerning heart rate analysis are highlighted, and how the toolkit provides a flexible environment to ameliorate common problems that typically lead to trial rejection is discussed. Source code for this program may be downloaded from the Psychonomic Society Web archive atwww.psychonomic.org/archive/.     

Four applications of permutation methods to testing a single-mediator model

Four applications of permutation tests to the single-mediator model are described and evaluated in this study. Permutation tests work by rearranging data in many possible ways in order to estimate the sampling distribution for the test statistic. The four applications to mediation evaluated here are the permutation test of ab, the permutation joint significance test, and the noniterative and iterative permutation confidence intervals for ab. A Monte Carlo simulation study was used to compare these four tests with the four best available tests for mediation found in previous research: the joint significance test, the distribution of the product test, and the percentile and bias-corrected bootstrap tests. We compared the different methods on Type I error, power, and confidence interval coverage. The noniterative permutation confidence interval for ab was the best performer among the new methods. It successfully controlled Type I error, had power nearly as good as the most powerful existing methods, and had better coverage than any existing method. The iterative permutation confidence interval for ab had lower power than do some existing methods, but it performed better than any other method in terms of coverage. The permutation confidence interval methods are recommended when estimating a confidence interval is a primary concern. SPSS and SAS macros that estimate these confidence intervals are provided.     

A Web-Based Archive of Norms,Stimuli, and Data

A new public archive of norms, stimuli, data, and source code,www.psychonomic.org/archive, is at the service of researchers and students in experimental psychology. The archive has received contributions from more than 60 researchers. The August and November 2004 issues ofBehavior Research Methods, Instruments, & Computers comprise articles related to the inaugural contents of the archive, which will henceforth accept contributions related to articles published in all Psychonomic Society journals.     

Does Career Success Make You Happy? The Mediating Role of Multiple Subjective Success Evaluations

We hypothesize that career success assessed as objective career achievements (income and responsibility status) has an indirect positive association with life satisfaction that is channeled through multiple subjective success evaluations. These are based on (a) social comparisons (comparison with others, other-referent success evaluation) and (b) individual standards (satisfaction with career achievements, self-referent success evaluations). We tested our reasoning in a 2-year prospective study with N = 990 professionals. Controlling for gender, family status, and workload, the results of two mediation models that draw on all information from two measurement points supported our reasoning. We found indirect positive associations between career success and life satisfaction (H1) channeled through both other-referent (H2) and self-referent (H3) subjective success evaluation. In both mediation models, we found partial mediation, and the remaining direct path from career success to life satisfaction was negative. We conclude that career success has mixed effects on a person’s life satisfaction: The net effect of positive indirect and negative direct effects is positive, but not large. We discuss the significance of these findings for theorizing about the influence of the work domain on life satisfaction as well as for conceptual issues in the analysis of mediators and moderators of the career success life satisfaction association.     

中介效应的检验方法和效果量测量:回顾与展望

通过中介效应检验方法之间的比较和效果量指标之间的比较,建议放弃将总效应c显著作为中介效应检验的前提条件,放弃基于直接效应c'显著性的完全和部分中介的提法,推荐使用偏差校正的百分位Bootstrap法直接对中介效应ab进行检验,使用κ²、R_med²等中介效果量指标并报告效果量的置信区间。作为示例,用R软件的MBESS软件包对某消防员饮食健康调查进行了中介效应检验和效果量测量。随后展望了中介效应检验方法和效果量测量的拓展方向。     

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.     

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.     

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.     

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。