dissertation on mediation

• Search Menu
• Advance articles
• Books for Review
• Author Guidelines
• Submission Site
• Open Access
• About Industrial Law Journal
• Editorial Board
• Advertising and Corporate Services
• Journals Career Network
• Self-Archiving Policy
• Dispatch Dates
• Journals on Oxford Academic
• Books on Oxford Academic

• < Previous

The Role of Mediation: A Critical Analysis of the Changing Nature of Dispute Resolution in the Workplace

• Article contents
• Figures & tables
• Supplementary Data

Tony Bennett, The Role of Mediation: A Critical Analysis of the Changing Nature of Dispute Resolution in the Workplace, Industrial Law Journal , Volume 41, Issue 4, December 2012, Pages 479–480, https://doi.org/10.1093/indlaw/dws033

• Permissions Icon Permissions

1. INTRODUCTION

Mediation is a model of dispute resolution, it is argued, which lends itself particularly well to situations where the parties have become entrenched in their positions. From a practical perspective, it is a method of resolving workplace disputes that, it is further argued, seeks to avoid a more formal and often more confrontational route, such as grievance and discipline procedures, and rather than attribute blame looks to rebuild damaged relationships for the future. 1

Mediation is also closely linked with government strategy and policy on employee relations. Under the last Labour administration, the Employment Act 2002 (Dispute Resolution) Regulations 2004 were established with the intention of promoting ‘best practice’ and halting the rising number of employment disputes. When the regulations not only failed to stem the rising number of disputes, but were linked to further rapid increases, 2 the Government commissioned further research to consider alternatives. The Gibbons report signalled the UK Government’s intention to repeal the 2004 regulations and increase the use of mediation as a dispute resolution strategy to reduce ‘the burden’ on the employment tribunal system. 3

Email alerts

Citing articles via.

• Recommend to your Library

Affiliations

• Online ISSN 1464-3669
• Print ISSN 0305-9332
• Copyright © 2024 Industrial Law Society
• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Institutional account management
• Rights and permissions
• Get help with access
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

CONCEPTUAL ANALYSIS article

On the interpretation and use of mediation: multiple perspectives on mediation analysis.

• 1 Department of Psychology, Ohio State University, Columbus, OH, United States
• 2 Division of Epidemiology, College of Public Health, Ohio State University, Columbus, OH, United States
• 3 Department of Psychology, KU Leuven, Leuven, Belgium

Mediation analysis has become a very popular approach in psychology, and it is one that is associated with multiple perspectives that are often at odds, often implicitly. Explicitly discussing these perspectives and their motivations, advantages, and disadvantages can help to provide clarity to conversations and research regarding the use and refinement of mediation models. We discuss five such pairs of perspectives on mediation analysis, their associated advantages and disadvantages, and their implications: with vs. without a mediation hypothesis, specific effects vs. a global model, directness vs. indirectness of causation, effect size vs. null hypothesis testing, and hypothesized vs. alternative explanations. Discussion of the perspectives is facilitated by a small simulation study. Some philosophical and linguistic considerations are briefly discussed, as well as some other perspectives we do not develop here.

Introduction

Without respect to a given statistical model, mediation processes are framed in terms of intermediate variables between an independent variable and a dependent variable, with a minimum of three variables required in total: X , M , and Y , where X is the independent variable (IV), Y is the dependent variable (DV), and M is the (hypothesized) mediator variable that is supposed to transmit the causal effect of X to Y . The total effect of X on Y is referred to as the total effect ( TE ), and that effect is then partitioned into a combination of a direct effect (DE) of X on Y , and an indirect effect ( IE ) of X on Y that is transmitted through M . In other words, the relationship between X and Y is decomposed into a direct link and an indirect link.

While the conceptual model of mediation is straight-forward, applying it is much less so ( Bullock et al., 2010 ). There are multiple schools of thought and discussions regarding mediation that provide detailed arguments and criteria regarding mediation claims for specific models or sets of assumptions (e.g., Baron and Kenny, 1986 ; Kraemer et al., 2002 ; Jo, 2008 ; Pearl, 2009 ; Imai et al., 2010 ). As still further evidence of the difficulty of making mediation claims, parameter bias, and sensitivity have emerged as common concerns (e.g., Sobel, 2008 ; Imai et al., 2010 ; VanderWeele, 2010 ; Fritz et al., 2016 ), as has statistical power for testing both indirect (e.g., Shrout and Bolger, 2002 ; Fritz and MacKinnon, 2007 ; Preacher and Hayes, 2008 ) and total effects ( Kenny and Judd, 2014 ; Loeys et al., 2015 ; O'Rourke and MacKinnon, 2015 ).

Relatively untouched is that there are cross-cutting concerns related to the fact that what is considered appropriate for a mediation claim depends not only on statistical and theoretical criteria, but also on the experience, assumptions, needs, and general point of view of a researcher. Some perspectives may be more often correct than others (e.g., more tenable assumptions, better clarification of what constitutes a mediator, etc.), but all perspectives and models used by researchers are necessarily incomplete and unable to fully capture all considerations necessary for conducting research, leaving some approaches ill-suited for certain tasks. This is in line with a recent article by Gelman and Hennig (2017) , who note that while the tendency in the literature is to find and formulate one best approach based on seemingly objective criteria there is nonetheless unavoidable subjectivity involved in any statistical decision. Researchers always view only a subset of reality, and rather than denying this it is advantageous—even necessary—to embrace that there are multiple perspectives relevant to any statistical discussion.

The aim of the article is not to propose new approaches or to criticize existing approaches, but to explain that the existence and use of multiple perspectives is both useful and sensible for mediation analysis. We use the term mediation in the general sense that a mediation model explains values of Y as indirectly caused by values of X , without favoring any specific statistical model or set of identifying assumptions. The three variables may be exhaustive, or a subset of much larger set of variables. As we discuss, there can be value in different and divergent considerations and convergence is not required or uniformly advantageous. Our points here are more general than any specific statistical model (and their IE, DE , and TE estimates and tests), but there are a few points that require we first review simple mediation models as estimated by ordinary least squares linear regression. We will then take the concept of mediation to an extreme with a time-series example, using the example to illustrate and discuss the various perspectives, not as a representative case but to clarify some issues.

Mediation with Linear Regression

Within a regression framework, the population parameters a, b, c , and c ′ (Figures 1 , 2 ) are estimated not with a single statistical model, but rather a set of either two or three individual regression models. We say two or three because the first, Model 1, is somewhat controversial and is not always necessary ( Kenny and Judd, 2014 ). This model yields the sample regression weight c as an estimate of the TE:

Models 2 and 3 are used to estimate the DE and IE . Specifically, the DE is presented as the path from X to Y , c ′. The IE is estimated by the product of the path from X to M (Model 2) and the path from M to Y (Model 3), i.e., the product of the regression weights a and b . The equations for these two models are as follows:

Together, these two models yield the direct effect, c ′, as well as the indirect effect ab . Further, the summation of these two effects is equal to the total effect, i.e., c = c ′+ ab . Assuming no missing data and a saturated model (as in the case of Equations 2 and 3) this value of c is equal to that provided by Model 1.

Figure 1 . Effect of X and Y without considering mediation.

Figure 2 . Effect of X on Y including mediation.

The total effect can then be inferred in two different ways, either based on Figure 1 (Model 1) or on Figure 2 (a combination of Models 2 and 3), but as we will discuss there are important conceptual differences between these two numerically identical total effects. We will refer to the TE associated with Figure 1 as TE 1 , and the TE associated with Figure 2 as TE 2 .

A Time Series Example

To take the concept of mediation to an extreme, imagine a stationary autoregressive process for T equidistant time points (e.g., T consecutive days) with a lag of 1 as in the most simple autoregressive time series model, i.e., AR (1). In such a model the expected correlation between consecutive observations is stable (stationary), and the model is equivalent with a full and exclusively serial mediation model without any direct effect. X is measured at t = 1 and Y is a measured at t = T . The independent variable X has an effect on M t = 2 , which in turn has an effect on M t = 3 , and so on up to M t = T−1 having an effect on Y at t = T . In mediation terms, there are T -2 mediators, from M t = 2 to M T −1 , with an effect only on the next mediator and finally on Y . Although this kind of mediation is an extreme case compared with the typical simple mediation model, it is nonetheless mediation in the sense that all effects are transmitted by way of an intervening effect. As a result, regardless of the time scale, the TE always equals the IE . Although extreme, such a model is a reasonable one for some time series data, e.g., it seems quite realistic that one's general mood (as distinct from ephemeral emotional states) of today mediates between one's mood of yesterday and one's mood of tomorrow. For some variables, there may be also an effect from earlier values than the previous measurement, i.e., longer lags, but such a more complex process is still a mediation process.

To help make our points more concrete we conducted a small-scale simulation. We generated data for 3, 10, 50, or 100 time points with a constant correlation of 0.10, 0.50, or 0.90 between consecutive time points, and with N = 10, 50, or 100 for each, for a total of 36 conditions. Initial time points were drawn from a standard normal distribution. We generated 500 replications per condition. All tests were done using 5,000 bootstraps and α = 0.05. These results are shown in Table 1 . One can easily see that rejections of the null hypothesis for the total effect TE 1 scarcely exceed the α level in nearly all conditions, which is unsurprising because of the near zero magnitude of the total effect. The only exceptions to these low rejections rates were for N = 10—but this is due to bootstrapping underestimating the standard error here for such small sample sizes—and for cases where the TE was of appreciable magnitude, i.e., for T = 3 and r = 0.5 or 0.9 or T = 10 and r = 0.9 ( TE = IE = 0.25, 0.81, and 0.38742, respectively). For such large effects the TE 1 is easily rejected. In contrast, the indirect effect is almost always significant, and the rejection rates are always greater than those of the TE 1 , even when the true size of the indirect effect is extremely small (as small as the true total effect). For nearly all cases where r = 0.5 or 0.9 the test of the IE exhibited higher power than the test of the TE 1 , with the minor caveat that for r = 0.5 and N = 10 the difference was minimal. In total, for 20 conditions of the 36 we considered here, rejection rates were 89–100%, with the observed power advantage for the IE relative to the TE 1 as great as 94% higher (6 vs. 100%) when the TE 1 is small, e.g., when T = 50 or 100. We will use this illustration to elaborate on the different perspectives on mediation, and specific aspects of the results will be focused on as necessary for the perspectives we discuss.

Table 1 . Simulation results.

Five Pairs of Perspectives

Each of the five pairs of perspectives we discuss here offers a choice regarding how to view, use, and study mediation models. Each of the perspectives we discuss here has its own merits, and we do not mean to imply that any perspective or approach we discuss here is “better”—there are simply too many criteria to exhaust to evaluate such a claim, and researchers must work within the context of the problem at hand to decide what is most appropriate.

We dichotomize and treat each perspective both within and between pairs as largely independent for the purposes of explication, but there are many points of intersection and we do not wish to imply an absence of a middle ground or that each perspective from a given pair cannot be meaningfully integrated. The perspectives we discuss here are not meant to be exhaustive, and were selected because of their relevance to common topics in the mediation literature. No pair of perspectives is strictly limited to any one topic, as the various discussions regarding mediation are each better understood when looked at from multiple angles. A brief summary of each pair of perspectives we discuss is provided in Table 2 , as well as a few example areas of research where the perspectives are relevant.

Table 2 . Comparison of perspectives.

With vs. Without a Mediation Hypothesis

A common concern that has emerged in the mediation literature is whether or not TE 1 should be required before testing indirect effects. Given that the reason researchers use mediation analysis is to test for indirect effects, whether or not there is a total effect can seem an irrelevant preliminary condition. Our time-series example is one example of why the presence of TE 1 is not required for an indirect effect to be detected with a null hypothesis test, but even in more mundane cases involving three variables the IE test has greater power than the TE 1 test under some parameter configurations ( Rucker et al., 2011 ; Kenny and Judd, 2014 ; Loeys et al., 2015 ; O'Rourke and MacKinnon, 2015 ). Further, two competing effects can suppress each other ( MacKinnon et al., 2000 ) such that two roughly equal (and potentially large) direct and indirect effects of opposing direction can result in a near-zero total effect. As can be seen in Table 1 , a large proportion of the tests of the IE were significant even when the corresponding test of the TE 1 was not significant. These are not new findings, but they illustrate that even for extremely small effect sizes such as, at the bottom of Table 1 (e.g., 1.58e-30) the IE is significant. Given a mediation hypothesis there is then no need to consider the significance of the TE 1 because it is irrelevant to the presence of an IE , as the IE is estimated by different statistical models than TE 1 is and a mediation hypothesis refers solely to the IE (though a more general causal relationship may be hypothesized to include both).

However, such work should not be taken as a blanket justification for testing the IE in the absence of TE 1 if there is not an a priori hypothesized indirect effect. While there is great value and need for exploratory research (with later replication and validation in a separate study) and we do not wish to discourage such practices, if the XY relationship is not significant based on Model 1 then one is likely better served by staying with the null hypothesis of no relationship because of the increased risk of false positives associated with so-called “fishing expeditions” ( Wagenmakers et al., 2011 ). Although a non-significant relationship does not exclude the possibility that there is a true and perhaps mediated relationship between X and Y —the world is full of relationships that cannot be differentiated from noise without consideration of indirect effects—a preference for parsimony and a desire to avoid false positives would suggest that one does not generate additional explanations for relationships that are not significant when first tested. Although the results shown in Table 1 show that a large proportion of indirect are significant in the absence of a significant TE 1 it would not be a good idea to follow up all non-significant correlations, regression weights, F -tests, t -tests, etc. with a post-hoc mediation analysis and then attempting to explain it after the results are known ( Kerr, 1998 ). When working with real data there are simply too many alternative explanations to consider. Absent an a priori hypothesis, the Judd and Kenny (1981) and Baron and Kenny (1986) condition requiring that the relationship between X and Y be significant makes sense.

The two perspectives represent two different and contrasting lines of reasoning and motivations—either the study is based on a mediation hypothesis or it is not. If it is, there is no preliminary condition regarding the total effect because it is irrelevant to whether or not an indirect effect may be present. It is simply necessary to conduct the appropriate test for the indirect effect. If however there was no pre-specified hypothesis, the logic of null hypothesis significance testing (NHST) requires that one stays with the conclusion of no relationship if the null hypothesis is not rejected by the data rather than conducting additional unplanned tests (with the caveat that appropriate corrections for multiple comparisons may be employed).

Specific Effects vs. Global Model

To put it colloquially, this pair of perspectives refers to whether one is interested in the forest or in the tree when investigating mediation. An effect-focused approach implies that a global model for all relationships is less important, and that one focuses instead on the tests of the effects of interest. These effects can be tested within a global statistical model (i.e., one can be interested in specific effects while still estimating all relationships), or from separate regression models. In the latter case, the global model is then primarily a conceptual one because there is not one statistical model to be used for estimation of the effects. For example, when using separate regressions the indirect effect is the product of two parameters from different statistical models, and while TE 1 is an effect in one model, TE 2 is a composite of two effects that stem from two separate models.

In contrast, a globally focused approach implies formulating and testing a global model for all variables, evaluating it based on relevant criteria (e.g., model fit, theoretical defensibility). The various examples of network models are examples of global models ( Salter-Townshend et al., 2012 ), but most commonly in the social sciences global models are realized using a structural equation model approach (SEM) for the covariance of the three variables, with or without making use of any latent variables ( Iacobucci et al., 2007 ; MacKinnon, 2008 ). If latent variables are used then there is the advantage of correcting for measurement error, but it is not necessary to use latent variables in a global model. Within the model, the specific mediation effect can be derived as a product of single path effects (e.g., Rijnhart et al., 2017 ).

The choice between, and discussions regarding, these two approaches comes with a few relevant considerations. First, there is the matter of model saturation (i.e., the same number of estimated parameters as there are variables). For the simple situation of one mediator variable and thus three variables in total, and effects described by a, b , and c ′, the global model is a saturated model, and as a result the point estimate of the indirect effect is the same whether one uses different regression models or one global SEM. To some degree then the matter of specific effects vs. the global model distinction is irrelevant because simple mediation models are saturated. However, when the mediation relationships are more complex the global model is no longer necessarily a saturated model. For example, a two-mediator model is either a serial or parallel mediator model, with the former having a path between the two mediators and the latter not ( Hayes, 2013 ). As such, a parallel two-mediator model is not saturated whereas a serial two-mediator model is. In general, from a global model perspective one would first want to test the goodness of fit of the global model, before a particular mediation effect is considered at all because the effects are conditional on the model.

Second, the power anomaly discussed in recent work reflects an effect-focused perspective based on separate regressions and vanishes when one focuses on the effect within a global statistical model, where the covariance between X and Y is simply a descriptive statistic used for model estimation and not a parameter (i.e., not a total effect to estimate). The total effect is estimated through two within-model effects. TE 1 is one observed covariance among the other observed covariance measures to be explained with the model. Further, instead of two separate TE estimates (stemming from separate regressions), there is only one TE to be considered: TE 2 as estimated from the model TE model :

Where a *, b *, and c ′* are model parameters. Of course, when c ′* = 0, then T E S E M = a * × b * .

Although the point estimates of TE 1 and TE 2 are equal for a simple mediation model, neither their associated models nor their sampling distributions are. For example, it is well known that the sampling distribution of the indirect effect estimate is skewed unless the sample size is extremely large ( MacKinnon et al., 2004 ) and this also applies when estimated from a global model (the product of a * and b *). The skewness is inherent to the distribution of a product, and this transfers to the distribution of TE 2 whether estimated based on a global model or through separate regressions. In contrast, there is no reason to expect skewness in the sampling distribution of TE 1 because it is a simple parameter in Equation (2) and Figure 1 , and not a product of two parameters.

The study of mediation is almost entirely effect-focused because the substantive hypotheses are mostly about particular mediation effects and their presence or not (typically defined by statistical significance), and so a global model test makes less sense from that perspective. This is particularly true because perfect model fit for the covariance of the variables is guaranteed in a simple mediation model with just the three variables X, M , and Y , despite a simple mediation model being almost certainly incomplete ( Baron and Kenny, 1986 ; Sobel, 2008 ). If one is primarily interested in the effects, it further makes sense to be liberal on the model side because model constraints can lead to bias in the parameter estimates (e.g., forcing a genuine DE to be equal to 0 will bias the IE estimate) and the standard errors.

In contrast, one can expect a model testing approach to prevail in a global process theory that describes the set of variable relationships as a whole. In such a case an SEM makes more sense, and within the model one or more indirect effects are tested (e.g., van Harmelen et al., 2016 ). The time series example is another case where a global model approach makes sense. From an effects perspective the mediation effect for a series of 100 would be a product of 99 parameters and the direct effect would span 99 time intervals, but these would be of relatively little interest or importance. Instead it is the model that matters, and within the model the autoregressive parameter is of interest (and not the IE as a product of all these autoregressive parameters as we did for the simulation study). In a simple autoregressive model with lag 1, i.e., AR ( 1 ), a = b (and so on, depending on the number of time points), and c ′ = 0. The AR(1) autoregressive model characterizes the relevant system, e.g., mood, self-esteem, etc.

As before, the two perspectives are both meaningful. One can either be interested in a global model for the relationships or one can give priority to the effects and minimize the importance of the overall model. The fewer modeling assumptions associated with an effects-perspective may lead to poorer precision and replication (e.g., larger standard errors and greater risk of overfitting), but model-based constraints are avoided. Conversely, making more assumptions leads to better precision and possibly to better replication (if the model constraints are valid). One can also make the statistical model more in line with the theoretical model in order to impose a stronger test of a theory. However, the assumptions are made at the risk of distorted parameter estimates, and the effect estimates are also conditional on the global model they belong to, which can complicate interpretation somewhat. Therefore, it can make sense to stay with separate regression analyses without a test of the global model.

Effect Size vs. Null Hypothesis Testing

Based on criticism of NHST (e.g., Kline, 2004 ), effect size and confidence intervals have been proposed as an alternative approach to statistical analyses (e.g., Cumming, 2012 ). These points have emerged in the mediation literature as well, with mediation-specific effect sizes discussed and proposed (e.g., Kraemer et al., 2008 ; Preacher and Kelley, 2011 ), and bootstrapped confidence intervals are now the standard for testing indirect effects (e.g., Shrout and Bolger, 2002 ; Hayes, 2013 ; Hayes and Scharkow, 2013 ).

Numerous effect size indices have been proposed for the IE , and these indices may take the form of either variance in the DV explained or in terms of the relative effects as in the case of the ratio ab/c ′ (an excellent review may be found in Preacher and Kelley, 2011 ; note however the specific effect size proposed by these authors was later shown to be based on incorrect calculations; Wen and Fan, 2015 ). As it is not our intention to promote one particular measure, but rather to make a general point regarding effect size vs. null hypothesis testing perspectives, we simply use the product of the standardized a and b coefficients.

In the largest time series model illustrated previously, the indirect effect is a product of 99 terms, and as a result the expected effect size with an autoregressive coefficient of 0.90 is still a negligible 0.00003. Even so, this extremely small effect can easily lead to a rejection of the null hypothesis when the IE is tested, as illustrated in Table 1 . The confidence intervals are very narrow for such a small effect, but they do not include zero. In practice, such an example would represent mediation from the NHST perspective (supported by the confidence intervals) and it could potentially be a very meaningful finding, but from the effect size perspective the effect may seem too small to be accepted or worth consideration for any practical decisions. Both points of view make sense. There is clearly mediation in the time series example, but the resulting effect is negligible in terms of the variance explained at time 100. The distance between X and Y is too large for a difference in X to make a difference for Y while in fact the underlying process is clearly a mediation process with possibly a very large magnitude from time point to time point (i.e., as small as 0.9).

As before, neither perspective is strictly superior because both perspectives have advantages and disadvantages. One possible problem when approaching mediation from the NHST perspective is that it is perhaps too attractive to look for possible mediators between X and Y after failing to reject the initial null hypothesis because of the work showing that a test of the IE has higher power, in particular given the high rates at which the TE is not rejected but the IE is as shown in Table 1 (to be clear, a strict NHST perspective would not permit such an approach, as discussed previously). Other problems are the dichotomous view on mediation (mediation vs. no mediation) while effects are in fact graded ( Cumming, 2012 ), and the fact that rejection of the null hypothesis does not speak to how well the variance of Y is explained.

The effect size logic has its own drawbacks as well, of course. Competing indirect effects, regardless of size, can cancel each other out (note this holds true for all effects in a mediation model, e.g., a may be small because of competing effects from X to M ). Another issue is that the effect size is commonly expressed in a relative way (e.g., in terms of the standard deviation of the DV or a percentage explained variance) and therefore it depends on the variance in the sample and on other factors in the study that raise questions about the appropriateness of many mediation effect sizes ( Preacher and Kelley, 2011 ). What constitutes a relevant effect size is also not always immediately clear, as it depends immensely on the problem at hand, e.g., what the dependent variable is, how easily manipulated the independent variable(s) are, etc. A further complicating factor is that most psychological variables have arbitrary units, such as, units on a point-scale or response option numerical anchors for a questionnaire. For variables with natural units, such as, the number of deadly accidents on the road or years of life after a medical intervention, one would not need a standard deviation or a percentage of variance to express the effect size in a meaningful way.

As with the previous perspectives, these two perspectives throw light on two relevant but different aspects of the same underlying reality. The null hypothesis test is a test of a hypothesized process and whether it can be differentiated from noise, whereas the effect size and confidence intervals tell us how large the result of the process is and what the width of the uncertainty is. Not all processes have results of a substantial size—and this is clear in the time-series example we showed previously—but even an extremely small effect can be meaningful as the indication of a process.

Directness vs. Indirectness

Another pair of perspectives depends upon the semantics of causality. In both linguistics (e.g., Shibatani, 2001 ) and in law (e.g., Hart and Honore, 1985 ), directness is an enhancer of causal interpretation, and a remote cause is considered less of a cause or even no cause at all. In contrast, in the psychological literature a causal interpretation is supported when there is evidence for an intermediate psychological or biological process and thus for some indirectness. Causality claims seem supported if one can specify through which path the causality flows.

From the directness perspective, a general concern is that temporal distance allows for additional, unconsidered (e.g., unmodeled) effects to occur, and so the TE is emphasized. Regardless of the complexity of a model, a model is always just a model and by definition it does not capture all aspects of the variable relationships ( Edwards, 2013 ). In reality there are always intervening events such that with increasing time between measurements the chances are higher that unknown events are the proper causes of the dependent variable, rather than the mediator(s). Though a full discussion is too complex to engage in here, a similar view has been taken by philosophers such as, Woodwarth (2003) . The inclusion of a mediator necessarily increases the minimum distance between X and Y , and the associated paths are necessarily correlational and require additional model assumptions, and if these assumptions do not hold then the estimates of the IE and DE are biased ( Sobel, 2008 ). Additionally, one can manipulate X but not M at the same time without likely interfering with the proposed mediation process and thus potentially destroying it, and so the link between M and Y remains a correlational one.

Network models are an interesting example of an indirectness perspective on causation, and one that is taken to a relative extreme. In such models, a large number of variables cause one another, and possibly mutually so, e.g., insomnia may result in concentration difficulties and then work problems, which may then aggravate the insomnia due to excess worry, before ultimately resulting in a depressed state ( Borsboom and Cramer, 2013 ). Another example of an indirectness perspective can be found in relation to climate change: Lakoff (2012) posted an interesting discussion and introduced the term “systemic causation” for causation in a network with chains of indirect causation. Many mediation models one can find in the psychological literature would qualify for the label of systemic causation, both in terms of the model (e.g., multiple connected mediators) and in terms of the underlying processes (e.g., changes in neurotransmitters underlying changes in behavior). Somewhat akin to the effect vs. model testing perspectives, if the additional statistical and theoretical assumptions hold then the benefit is a fuller and more precise picture of the variable relationships, but if they do not then statistical analyses will yield biased estimates and the inferences drawn made suspect.

The two perspectives make sense for the example application from the simulation study. From the directness perspective, as the number of time points increases it becomes increasingly difficult to claim that X has a causal effect on Y . It is easy to make such claims for T = 3, but for a large number of time points such as, T = 50 or 100, claims of causation are most relevant to the mediators most proximal to Y (alternatively, to those shortly following X ). In contrast, for the indirectness perspective, a systems interpretation of causality makes perfect sense for time series. The autoregressive process does have causal relevance, and the identification of such a long chain of effects would likely be considered compelling evidence of causation.

Thus, indirectness and distance make a causal interpretation stronger from one perspective, whereas they make a causal interpretation less convincing from another perspective. These two perspectives are not in direct contradiction—they simply focus on different aspects of the same reality and reflect different needs and concerns. In the case of directness, the criterion is a minimizing ambiguity about whether or not there is an effect of X on Y . In contrast, in the case of adopting an indirectness perspective, the primary criterion is maximizing information about the process and thus about intermediate steps because it makes the causal process more understandable.

Hypothesized vs. Alternative Explanations

Our final pair of perspectives refers to whether one is primarily interested in a confirmatory test of a mediation hypothesis about the relationship between two variables or whether one would rather test one or more other explanations that would undermine a mediation claim. Loosely, the difference between these two perspectives is that the former focuses on showing that a mediation explanation is appropriate, and the latter focuses on showing that alternative explanations are not.

In practice this distinction can be a subtle one, as it is always necessary to control for confounders, but there are considerable differences in the information acquired and required for these two perspectives, as well as the amount of effort invested and what is attended to Rouder et al. (2016) .

For mediation, researchers generally work with a theory-derived mediation hypothesis and collect data that allows them to test the null hypothesis of no mediation. It is a search for a well-defined form of information, and further the search is considered complete when that information is obtained. If the null hypothesis of no relationship is rejected, the mediation claim is considered to be supported and the case closed. If it is not rejected, explanations are generated as to why the study failed, and the hypothesis is tested again (ideally in a separate study, but this also manifests as including unplanned covariates in the statistical models). Alternative explanations are often not generated or tested if the null hypothesis of mediation is rejected. This is an intriguing asymmetry between the two possible outcomes of a study—supportive results are accepted, unsupportive results are retested.

A somewhat different approach is to formulate alternative explanations for a significant effect that are in conflict with a mediation claim. The simplest and most common means of doing this is to include additional covariates in Models 2 and 3 that are competing explanations for the relationships between the three variables, or to experimentally manipulate these explanations as well. In cases where temporal precedence is not clear such as, in observational data or when there are only two time points, it is also useful to consider alternative variable orders, e.g., treating X as M or M as Y . Another approach is to assume that there are unmeasured confounders that bias the estimates and necessitate examining parameter sensitivity ( VanderWeele, 2010 ). Still another is to test the proposed mediator as a moderator instead (a distinction which is itself often unclear; Kraemer et al., 2008 ) or as a hierarchical effect ( Preacher et al., 2010 ).

Referring to the time series example, it was simply a test of an autoregressive model with a single lag and the power to detect such small effects in a constrained serial mediation model, but in practice it would also make sense to consider a moving-average model, where the value of an observation depends on the mean of the variable and on a coefficient associated with the error term ( Brockwell and Davis, 2013 ). Loosely, the residuals might “cause” the values of subsequent time points, and are not simply measurement errors but new and unrelated inputs specific for the time point in question.

As with each previous pair of perspectives, both perspectives have advantages and disadvantages. Focusing on confirmation has the general advantages of simplicity and expediency by utilizing past research to direct future research, with a relatively clearly defined set of criteria for what counts as supporting evidence. There are also cases where it is not necessary to exhaust all alternatives, and instead simplicity and sufficiency of an explanation are valued more strongly. However, this perspective comes with the risk of increased false-positives and a narrow search for explanations for relationships between variables because what is considered is determined in part by what is easy to consider. Finding that one explanation works does not prove there are no other—and possibly better—explanations, and a model is always just a model ( Edwards, 2013 ).

Focusing on competing hypotheses has the advantage of potentially providing stronger evidence for a mediation claim by way of providing evidence that competing hypotheses are not appropriate. Conversely, when a competing hypothesis cannot be ruled out easily, it may turn out to be a better explanation than a mediation model upon further research. However, there are a few very strong limitations regarding competing evidence. The first is that for every explanation, there are an infinite number of competing explanations that are all equally capable of describing a covariance matrix. Some are ignorable due to their sheer absurdity, but there are still an infinite number of reasonable alternative explanations (for example, it is easy to generate a very long list of explanations for why self-esteem and happiness correlate) and criteria for evaluating these explanations are often unclear or extremely difficult to satisfy. Further, it is often impossible to estimate alternative statistical models because of the limited information provided by only a small set of variables (e.g., factors are difficult to estimate with a small number of indicators). Similarly, estimating a very large number of complicated interacting variable relationships may require sample sizes that are not realistic.

A Note Regarding Philosophical Considerations

Before turning to our discussion, we wish to note that philosophical views on causality differ with respect to whether a total effect is implied or necessary, and that there is substantial overlap between the philosophical views and our discussion of directness vs. indirectness distinction. We rely on a chapter by Psillos (2009) in the Oxford Handbook of Causality for a brief discussion of philosophical views, but see White (1990) for an introduction for psychologists.

In Humean regularity theories, X is a cause if it is regularly followed by Y . This suggests a total effect as a condition for X being a cause of Y . In a deductive-nomological view attributed to Hempel and Oppenheim, for X to be a cause it needs to be connected to Y through one or more laws so that X is sufficient for Y . Sufficiency would again imply a total effect, albeit possibly a very small one, because there may be multiple sufficient conditions. Only when a condition is at the same time sufficient and necessary can one expect a clear relationship.

Another view is formulated in the complex regularity view of Mackie (1974) and his INUS conditions. According to this view a cause is an I nsufficient but N on-redundant part of a condition which is itself U nnecessary but S ufficient for the effect. In other words, a cause is a term (e.g., A ) in a conjunctive bundle (e.g., A and B and C ), and there can be many such conjunctive bundles that are each sufficient for the effect. This expression is called the disjunctive normal form (e.g., Y if and only if A and B and C or D and E or F and G or H or I ). This form does not imply a total effect of X on Y (e.g., A as X ), because the disjunctive normal form may be highly complex and may therefore not lead to X and Y being correlated, while X is still accepted as a cause because it is part of that form. In other words, the relationship between a cause and the event to be explained is such that a cause can occur either with or without the event and vice versa. The INUS view is consistent with indirectness and systemic causation, whereas Humean regularity theory is better in agreement with directness of causes.

From the above discussion of the various perspectives we wish to conclude that there is not just one way to look at mediation. Researchers may approach mediation with or without an a priori hypothesis, or may focus on either a global model or a specific effect that derives either from the global model or that is estimated from separate regression analyses. A researcher may value directness or indirectness as causal evidence, or may prefer effect-focused or significance-focused tests. Researchers may further focus on hypothesized or competing alternative explanations when testing for mediation. Each pair of perspectives has associated advantages and disadvantages, and which is to be preferred depends on the nature of a given study or topic of interest.

The perspectives we have discussed here do not exhaust all common perspectives. Another common pair is a practical vs. a theoretical goal for testing a mediation claim. The aim of a mediation study can either be to find ways to change the level of the dependent variable, or the aim can be to understand the process through which the independent variable affects the dependent variable, or the purpose of the research may be prediction. Mediation can help to understand a process and advance a theoretical goal even when the total effect is negligible, but from a practical point of view, mediation is not helpful for such a case unless there is an easily addressed suppression effect or Y represents an important outcome such as, death. For applied settings where affecting change by way of an intervention of some sort, a direct effect or an unsuppressed large indirect effect is in general much more useful.

Another example is that the concept of mediation remains somewhat ambiguous despite the clarification provided by Baron and Kenny (1986) . That mediation explains the relationship between X and Y can mean two things: (1) Mediation explains values of Y as indirectly caused by values of X . (2) Mediation causes the relationship between X and Y . Following the second interpretation, the relationship itself (or absence of relationship) is explained by values of M . Here, we have interpreted the concept of mediation in the first sense. Note that the second way of understanding mediation is also commonly considered to be moderation , where M is supposed to explain why there sometimes is a relationship between X and Y and sometimes there is not (or why the strength of the relationship varies). The MacArthur approach provides some clarification regarding the latter sense (the approach is named after a foundation; Kraemer et al., 2002 , 2008 ), and notably it adds an interaction term between X and M to Model 3. The approach specifies that if X precedes M , there is an association between X and M , and there is either an interaction between X and M or a main effect of M on Y then M is said to mediate Y . In contrast, if there is an interaction between X and M , but no main effect of M on Y , then X is said to moderate M . In short, the approach specifies that a statistical interaction can still reflect mediation (see also Muller et al., 2005 ; Preacher et al., 2007 ). The approach further focuses on effect sizes over NHST, and states that causal inferences should not be drawn from observational data for reasons similar to those we provide in the discussion of the hypothesized vs. alternative explanations section. The approach also explicitly treats the indirect effect as only potentially causal, arguing that the Baron and Kenny approach to mediation and moderation can potentially bias the search for explanations because of its assumption that the causal process is already known but must only be tested. The MacArthur approach then seems to favor (or is at least mindful of) some of the specific perspectives we have discussed here, and it remains to be seen what the impact is of the approach on mediation and moderation practice and theory.

We have discussed mediation at a rather abstract, general level, and some of the details of the different perspectives we have discussed here are not always relevant to specific statistical analyses. In keeping with common practices we have utilized parametric mean and covariance-based approaches for our discussion, but median-based approaches to mediation have been proposed (e.g., Yuan and MacKinnon, 2014 ), and for such approaches the notion of global model testing by way of comparing the fit of different SEMs is largely irrelevant in a frequentist framework (though it may be done within a Bayesian framework; Wang et al., 2016 ). For network analysis, the strong focus on indirectness of effects within a larger system with a very large number of variables that each may be treated as X, M , or Y , renders the issue of a specific mediation hypothesis or a total effect irrelevant.

On the other hand, while we have discussed each perspective as independent views, there are obvious intersections between them and ample reasons to adopt the opposing perspective in some cases, or even both for the same study. For example, when working with a global model, specific effects within the model vary in how trustworthy they may be considered. Those effects that are considered less trustworthy can be interpreted more from a directness perspective because of the ambiguity regarding their effects, and those that are uncontroversial can be interpreted from an indirectness perspective. Confidence intervals and NHST also make use of the same information and if interpreted dichotomously (reject vs. not reject) the results will not differ. There are also intersections across pairs as well, e.g., testing competing explanations is facilitated by adopting a global model-focused approach, and the issue competing explanations in general provides much of the rationale for preferring a directness perspective on causation.

We wish to include a cautionary note concerning causality before concluding. A mediation hypothesis is a causal hypothesis ( James and Brett, 1984 ), but we realize that a causal relationship is difficult if not impossible to prove in general, let alone in the complex world of the social sciences ( Brady, 2008 ). Further, the statistical models used to test mediation are not inherently causal—they are simply predictive or descriptive, and the b path is necessarily correlational ( Sobel, 2008 ). That the data are in line with the hypothesis and even that several alternative explanations can be eliminated does not prove causality. It does not follow from the combination of the two premises “If A then B” (if M mediates then the null hypothesis of no indirect effect is rejected) and “B is the case” (null hypothesis rejected) that “A is the case.” (M mediates; i.e., the fallacy known as affirming the consequent). Instead, modus tollens (i.e., “B is not the case”) is a valid argument for the absence of A, so that one may want to believe that A is ruled out in the absence of B. Although the reasoning is logically correct, the problem with mediation analysis is that “B is not the case” in practice is simply a probabilistic non-rejection of a null hypothesis and does not directly implicate the truth of any other claim.

Human behavior and psychology emerges from dynamic and complicated systemic effects that are impossible to capture completely, and researchers choose what must be understood for a given problem—what fraction of the network of interacting variables is most relevant—and so which perspective to adopt. Ultimately, mediation analysis is simply a tool used for describing, discovering, and testing possible causal relationships. How the tool is used (or not used) and what information is most relevant depends on the problem to be solved and the question to be answered.

Author Contributions

RA was responsible for most of the writing, in particular any revisions and the introduction and discussion. PD provided most of the core points involved in the discussion of each perspective.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Baron, R. M., and Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J. Pers. Soc. Psychol. 51, 1175–1182. doi: 10.1037/0022-3514.51.6.1173

PubMed Abstract | CrossRef Full Text | Google Scholar

Borsboom, D., and Cramer, A. O. (2013). Network analysis: an integrative approach to the structure of psychopathology. Annu. Rev. Clin. Psychol. 9, 91–121. doi: 10.1146/annurev-clinpsy-050212-185608

Brady, H. E. (2008). Causation and Explanation in Social Science . Oxford, UK: Oxford University Press.

Google Scholar

Brockwell, P. J., and Davis, R. A. (2013). Time Series: Theory and Methods . New York, NY: Springer-Verlag.

Bullock, J. G., Green, D. P., and Ha, S. E. (2010). Yes, but what's the mechanism? (don't expect an easy answer). J. Pers. Soc. Psychol. 98, 550–558. doi: 10.1037/a0018933

Cumming, G. (2012). Understanding the New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis . New York, NY: Routledge.

Edwards, M. C. (2013). Purple unicorns, true models, and other things i've never seen. Meas. Interdiscipl. Res. Perspect. 11, 107–111. doi: 10.1080/15366367.2013.835178

CrossRef Full Text | Google Scholar

Fritz, M. S., Kenny, D. A., and MacKinnon, D. P. (2016). The combined effects of measurement error and omitting confounders in the single mediator model. Multivariate Behav. Res. 51, 681–697. doi: 10.1080/00273171.2016.1224154

Fritz, M. S., and MacKinnon, D. P. (2007). Required sample size to detect the mediated effect. Psychol. Sci. 18, 233–239. doi: 10.1111/j.1467-9280.2007.01882.x

Gelman, A., and Hennig, C. (2017). Beyond subjective and objective in statistics. J. R. Stat. Soc . 180, 1–31. doi: 10.1111/rssa.12276

Hart, H. L. A., and Honore, A. M. (1985). Causation in the Law . Oxford, UK: Clarendon Press.

Hayes, A. F. (2013). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach . New York, NY: Guilford.

Hayes, A. F., and Scharkow, M. (2013). The relative trustworthiness of inferential tests of the indirect effect in statistical mediation analysis: does method really matter? Psychol. Sci. 24, 1918–1927. doi: 10.1177/0956797613480187

Iacobucci, D., Saldanha, N., and Deng, X. (2007). A meditation on mediation: evidence that structural equation models perform better than regressions. J. Consum. Psychol. 17, 140–154. doi: 10.1016/S1057-7408(07)70020-7

Imai, K., Keele, L., and Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Stat. Sci. 25, 51–71. doi: 10.1214/10-STS321

James, L. R., and Brett, J. M. (1984). Mediators, moderators, and tests for mediation. J. Appl. Psychol. 69, 307–321. doi: 10.1037/0021-9010.69.2.307

Jo, B. (2008). Causal inference in randomized experiments with mediational processes. Psychol. Methods 13, 314–336. doi: 10.1037/a0014207

Judd, C. M., and Kenny, D. A. (1981). Process analysis: estimating mediation in treatment evaluation. Eval. Rev. 5, 602–619. doi: 10.1177/0193841X8100500502

Kenny, D. A., and Judd, C. M. (2014). Power anomalies in testing mediation. Psychol. Sci. 25, 334–339. doi: 10.1177/0956797613502676

Kerr, N. L. (1998). HARKing: hypothesizing after the results are known. Pers. Soc. Psychol. Rev. 2, 196–217. doi: 10.1207/s15327957pspr0203_4

Kline, R. B. (2004). Beyond Significance Testing. Reforming Data Analysis Methods in Behavioral Research. Washington DC: APA Books.

Kraemer, H. C., Kiernan, M., Essex, M., and Kupfer, D. J. (2008). How and why criteria defining moderators and mediators differ between the Baron & Kenny and MacArthur approaches. Health Psychol. 27, 101–108. doi: 10.1037/0278-6133.27.2(Suppl.).S101

Kraemer, H. C., Wilson, G. T., Fairburn, C. G., and Agras, W. S. (2002). Mediators and moderators of treatment effects in randomized clinical trials. Arch. Gen. Psychiatry 59, 877–883. doi: 10.1001/archpsyc.59.10.877

Lakoff, G. (2012). Global Warming Systemically Caused Hurricane Sandy . Available online at: http://blogs.berkeley.edu/2012/11/05/global-warming-systemically-caused-hurricane-sandy/

Loeys, T., Moerkerke, B., and Vansteelandt, S. (2015). A cautionary note on the power of the test for the indirect effect in mediation analysis. Front. Psychol. 5:1549. doi: 10.3389/fpsyg.2014.01549

Mackie, J. L. (1974). The Cement of the Universe . Oxford, UK: Clarendon Pres.

MacKinnon, D. (2008). Introduction to Statistical Mediation Analysis . New York, NY: Lawrence Erlbaum.

MacKinnon, D. P., Krull, J. L., and Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect. Prev. Sci. 1, 173–181. doi: 10.1023/A:1026595011371

MacKinnon, D. P., Lockwood, C. M., and Williams, J. (2004). Confidence limits for the indirect effect. Distribution of the product and resampling methods. Multivariate Behav. Res. 39, 99–128. doi: 10.1207/s15327906mbr3901_4

Muller, D., Judd, C. M., and Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. J. Pers. Soc. Psychol. 89:852. doi: 10.1037/0022-3514.89.6.852

O'Rourke, H. P., and MacKinnon, D. P. (2015). When the test of mediation is more powerful than the test of the total effect. Behav. Res. Methods , 47:424. doi: 10.3758/s13428-014-0481-z

Pearl, J. (2009). Causality . Cambridge University Press.

PubMed Abstract | Google Scholar

Preacher, K. J., and Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behav. Res. Methods 40, 879–891. doi: 10.3758/BRM.40.3.879

Preacher, K. J., and Kelley, K. (2011). Effect measures for mediation models. Quantitative strategies for communication indirect effects. Psychol. Methods 16, 93–115. doi: 10.1037/a0022658

Preacher, K. J., Rucker, D. D., and Hayes, A. F. (2007). Addressing moderated mediation hypotheses: theory, methods, and prescriptions. Multivariate Behav. Res. 42, 185–227. doi: 10.1080/00273170701341316

Preacher, K. J., Zyphur, M. J., and Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychol. Methods 15, 209–233. doi: 10.1037/a0020141

Psillos, S. (2009). “Regularity theories,” in Oxford Handbook of Causation , eds H. Bebee, P. Menzies, and C. Hitchcock (New York, NY: Oxford University Press), 131–157.

Rijnhart, J. J., Twisk, J. W., Chinapaw, M. J., de Boer, M. R., and Heymans, M. W. (2017). Comparison of methods for the analysis of relatively simple mediation models. Contemp. Clin. Trials Commun . 7, 130–135. doi: 10.1016/j.conctc.2017.06.005

Rouder, J. N., Morey, R. D., Verhagen, J., Province, J. M., and Wagenmakers, E. J. (2016). Is there a free lunch in inference?. Top. Cogn. Sci. 8, 520–547. doi: 10.1111/tops.12214

Rucker, D. D., Preacher, K. J., Tormala, Z. L., and Petty, R. E. (2011). Mediation analysis in social psychology: current practices and new recommendations. Soc. Pers. Psychol. Compass 5, 359–371. doi: 10.1111/j.1751-9004.2011.00355.x

Salter-Townshend, M., White, A., Gollini, I., and Murphy, T. B. (2012). Review of statistical network analysis: models, algorithms, and software. Statist. Anal. Data Mining 5, 243–264. doi: 10.1002/sam.11146

Shibatani, M. (2001). “Some basic issues in the grammar of causation,” in Grammar of Causation and Interpersonal Manipulation , ed M. Shibatani (Philadelphia, PA: John Benjamins Publishing Company), 1–22.

Shrout, P. E., and Bolger, N. (2002). Mediation in experimental and nonexperimental studies: new procedures and recommendations. Psychol. Methods 7, 422–455. doi: 10.1037/1082-989X.7.4.422

Sobel, M. E. (2008). Identification of causal parameters in randomized studies with mediating variables. J. Educ. Behav. Stat. 33, 230–251. doi: 10.3102/1076998607307239

van Harmelen, A. L., Gibson, J. L., St Clair, M. C., Owens, M., Brodbeck, J., Dunn, V., et al. (2016). Friendships and family support reduce subsequent depressive symptoms in at-risk adolescents. PLoS ONE 11:e0153715. doi: 10.1371/journal.pone.0153715

VanderWeele, T. J. (2010). Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology 21, 540–551. doi: 10.1097/EDE.0b013e3181df191c

Wagenmakers, E. J., Wetzels, R., Borsboom, D., and Van Der Maas, H. L. (2011). Why psychologists must change the way they analyze their data: the case of psi: comment on Bem (2011). J. Pers. Soc. Psychol. 100, 426–432. doi: 10.1037/a0022790

Wang, Y., Feng, X. N., and Song, X. Y. (2016). Bayesian quantile structural equation models. Struct. Equ. Model. Multidiscipl. J. 23, 246–258. doi: 10.1080/10705511.2015.1033057

Wen, Z., and Fan, X. (2015). Monotonicity of effect sizes: questioning kappa-squared as mediation effect size measure. Psychol. Methods 20, 193–203. doi: 10.1037/met0000029

White, P. (1990). Ideas about causation in philosophy and psychology. Psychol. Bull. 108, 3–18. doi: 10.1037/0033-2909.108.1.3

Woodwarth, J. (2003). Making Things Happen. A Theory of Causal Explanation . Oxford: Oxford University Press.

Yuan, Y., and MacKinnon, D. P. (2014). Robust mediation analysis based on median regression. Psychol. Methods 19, 1–20. doi: 10.1037/a0033820

Keywords: mediation, causation, total effect, direct effect, indirect effect

Citation: Agler R and De Boeck P (2017) On the Interpretation and Use of Mediation: Multiple Perspectives on Mediation Analysis. Front. Psychol . 8:1984. doi: 10.3389/fpsyg.2017.01984

Received: 06 July 2017; Accepted: 30 October 2017; Published: 15 November 2017.

Reviewed by:

Copyright © 2017 Agler and De Boeck. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Robert Agler, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here .

Loading metrics

Open Access

Peer-reviewed

Research Article

Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression

Affiliations Department of Psychology, University of Gothenburg, Gothenburg, Sweden, Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden

Affiliation Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden

Affiliations Department of Psychology, University of Gothenburg, Gothenburg, Sweden, Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden, Department of Psychology, Education and Sport Science, Linneaus University, Kalmar, Sweden

* E-mail: [email protected]

Affiliations Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden, Center for Ethics, Law, and Mental Health (CELAM), University of Gothenburg, Gothenburg, Sweden, Institute of Neuroscience and Physiology, The Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden

• Ali Al Nima, 
• Patricia Rosenberg, 
• Trevor Archer, 
• Danilo Garcia

• Published: September 9, 2013
• https://doi.org/10.1371/journal.pone.0073265
• Reader Comments

23 Sep 2013: Nima AA, Rosenberg P, Archer T, Garcia D (2013) Correction: Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression. PLOS ONE 8(9): 10.1371/annotation/49e2c5c8-e8a8-4011-80fc-02c6724b2acc. https://doi.org/10.1371/annotation/49e2c5c8-e8a8-4011-80fc-02c6724b2acc View correction

Mediation analysis investigates whether a variable (i.e., mediator) changes in regard to an independent variable, in turn, affecting a dependent variable. Moderation analysis, on the other hand, investigates whether the statistical interaction between independent variables predict a dependent variable. Although this difference between these two types of analysis is explicit in current literature, there is still confusion with regard to the mediating and moderating effects of different variables on depression. The purpose of this study was to assess the mediating and moderating effects of anxiety, stress, positive affect, and negative affect on depression.

Two hundred and two university students (males  = 93, females  = 113) completed questionnaires assessing anxiety, stress, self-esteem, positive and negative affect, and depression. Mediation and moderation analyses were conducted using techniques based on standard multiple regression and hierarchical regression analyses.

Main Findings

The results indicated that (i) anxiety partially mediated the effects of both stress and self-esteem upon depression, (ii) that stress partially mediated the effects of anxiety and positive affect upon depression, (iii) that stress completely mediated the effects of self-esteem on depression, and (iv) that there was a significant interaction between stress and negative affect, and between positive affect and negative affect upon depression.

The study highlights different research questions that can be investigated depending on whether researchers decide to use the same variables as mediators and/or moderators.

Citation: Nima AA, Rosenberg P, Archer T, Garcia D (2013) Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression. PLoS ONE 8(9): e73265. https://doi.org/10.1371/journal.pone.0073265

Editor: Ben J. Harrison, The University of Melbourne, Australia

Received: February 21, 2013; Accepted: July 22, 2013; Published: September 9, 2013

Copyright: © 2013 Nima et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The authors have no support or funding to report.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Mediation refers to the covariance relationships among three variables: an independent variable (1), an assumed mediating variable (2), and a dependent variable (3). Mediation analysis investigates whether the mediating variable accounts for a significant amount of the shared variance between the independent and the dependent variables–the mediator changes in regard to the independent variable, in turn, affecting the dependent one [1] , [2] . On the other hand, moderation refers to the examination of the statistical interaction between independent variables in predicting a dependent variable [1] , [3] . In contrast to the mediator, the moderator is not expected to be correlated with both the independent and the dependent variable–Baron and Kenny [1] actually recommend that it is best if the moderator is not correlated with the independent variable and if the moderator is relatively stable, like a demographic variable (e.g., gender, socio-economic status) or a personality trait (e.g., affectivity).

Although both types of analysis lead to different conclusions [3] and the distinction between statistical procedures is part of the current literature [2] , there is still confusion about the use of moderation and mediation analyses using data pertaining to the prediction of depression. There are, for example, contradictions among studies that investigate mediating and moderating effects of anxiety, stress, self-esteem, and affect on depression. Depression, anxiety and stress are suggested to influence individuals' social relations and activities, work, and studies, as well as compromising decision-making and coping strategies [4] , [5] , [6] . Successfully coping with anxiety, depressiveness, and stressful situations may contribute to high levels of self-esteem and self-confidence, in addition increasing well-being, and psychological and physical health [6] . Thus, it is important to disentangle how these variables are related to each other. However, while some researchers perform mediation analysis with some of the variables mentioned here, other researchers conduct moderation analysis with the same variables. Seldom are both moderation and mediation performed on the same dataset. Before disentangling mediation and moderation effects on depression in the current literature, we briefly present the methodology behind the analysis performed in this study.

Mediation and moderation

Baron and Kenny [1] postulated several criteria for the analysis of a mediating effect: a significant correlation between the independent and the dependent variable, the independent variable must be significantly associated with the mediator, the mediator predicts the dependent variable even when the independent variable is controlled for, and the correlation between the independent and the dependent variable must be eliminated or reduced when the mediator is controlled for. All the criteria is then tested using the Sobel test which shows whether indirect effects are significant or not [1] , [7] . A complete mediating effect occurs when the correlation between the independent and the dependent variable are eliminated when the mediator is controlled for [8] . Analyses of mediation can, for example, help researchers to move beyond answering if high levels of stress lead to high levels of depression. With mediation analysis researchers might instead answer how stress is related to depression.

In contrast to mediation, moderation investigates the unique conditions under which two variables are related [3] . The third variable here, the moderator, is not an intermediate variable in the causal sequence from the independent to the dependent variable. For the analysis of moderation effects, the relation between the independent and dependent variable must be different at different levels of the moderator [3] . Moderators are included in the statistical analysis as an interaction term [1] . When analyzing moderating effects the variables should first be centered (i.e., calculating the mean to become 0 and the standard deviation to become 1) in order to avoid problems with multi-colinearity [8] . Moderating effects can be calculated using multiple hierarchical linear regressions whereby main effects are presented in the first step and interactions in the second step [1] . Analysis of moderation, for example, helps researchers to answer when or under which conditions stress is related to depression.

Mediation and moderation effects on depression

Cognitive vulnerability models suggest that maladaptive self-schema mirroring helplessness and low self-esteem explain the development and maintenance of depression (for a review see [9] ). These cognitive vulnerability factors become activated by negative life events or negative moods [10] and are suggested to interact with environmental stressors to increase risk for depression and other emotional disorders [11] , [10] . In this line of thinking, the experience of stress, low self-esteem, and negative emotions can cause depression, but also be used to explain how (i.e., mediation) and under which conditions (i.e., moderation) specific variables influence depression.

Using mediational analyses to investigate how cognitive therapy intervations reduced depression, researchers have showed that the intervention reduced anxiety, which in turn was responsible for 91% of the reduction in depression [12] . In the same study, reductions in depression, by the intervention, accounted only for 6% of the reduction in anxiety. Thus, anxiety seems to affect depression more than depression affects anxiety and, together with stress, is both a cause of and a powerful mediator influencing depression (See also [13] ). Indeed, there are positive relationships between depression, anxiety and stress in different cultures [14] . Moreover, while some studies show that stress (independent variable) increases anxiety (mediator), which in turn increased depression (dependent variable) [14] , other studies show that stress (moderator) interacts with maladaptive self-schemata (dependent variable) to increase depression (independent variable) [15] , [16] .

The present study

In order to illustrate how mediation and moderation can be used to address different research questions we first focus our attention to anxiety and stress as mediators of different variables that earlier have been shown to be related to depression. Secondly, we use all variables to find which of these variables moderate the effects on depression.

The specific aims of the present study were:

• To investigate if anxiety mediated the effect of stress, self-esteem, and affect on depression.
• To investigate if stress mediated the effects of anxiety, self-esteem, and affect on depression.
• To examine moderation effects between anxiety, stress, self-esteem, and affect on depression.

Ethics statement

This research protocol was approved by the Ethics Committee of the University of Gothenburg and written informed consent was obtained from all the study participants.

Participants

The present study was based upon a sample of 206 participants (males  = 93, females  = 113). All the participants were first year students in different disciplines at two universities in South Sweden. The mean age for the male students was 25.93 years ( SD  = 6.66), and 25.30 years ( SD  = 5.83) for the female students.

In total, 206 questionnaires were distributed to the students. Together 202 questionnaires were responded to leaving a total dropout of 1.94%. This dropout concerned three sections that the participants chose not to respond to at all, and one section that was completed incorrectly. None of these four questionnaires was included in the analyses.

Instruments

Hospital anxiety and depression scale [17] ..

The Swedish translation of this instrument [18] was used to measure anxiety and depression. The instrument consists of 14 statements (7 of which measure depression and 7 measure anxiety) to which participants are asked to respond grade of agreement on a Likert scale (0 to 3). The utility, reliability and validity of the instrument has been shown in multiple studies (e.g., [19] ).

Perceived Stress Scale [20] .

The Swedish version [21] of this instrument was used to measures individuals' experience of stress. The instrument consist of 14 statements to which participants rate on a Likert scale (0 =  never , 4 =  very often ). High values indicate that the individual expresses a high degree of stress.

Rosenberg's Self-Esteem Scale [22] .

The Rosenberg's Self-Esteem Scale (Swedish version by Lindwall [23] ) consists of 10 statements focusing on general feelings toward the self. Participants are asked to report grade of agreement in a four-point Likert scale (1 =  agree not at all, 4 =  agree completely ). This is the most widely used instrument for estimation of self-esteem with high levels of reliability and validity (e.g., [24] , [25] ).

Positive Affect and Negative Affect Schedule [26] .

This is a widely applied instrument for measuring individuals' self-reported mood and feelings. The Swedish version has been used among participants of different ages and occupations (e.g., [27] , [28] , [29] ). The instrument consists of 20 adjectives, 10 positive affect (e.g., proud, strong) and 10 negative affect (e.g., afraid, irritable). The adjectives are rated on a five-point Likert scale (1 =  not at all , 5 =  very much ). The instrument is a reliable, valid, and effective self-report instrument for estimating these two important and independent aspects of mood [26] .

Questionnaires were distributed to the participants on several different locations within the university, including the library and lecture halls. Participants were asked to complete the questionnaire after being informed about the purpose and duration (10–15 minutes) of the study. Participants were also ensured complete anonymity and informed that they could end their participation whenever they liked.

Correlational analysis

Depression showed positive, significant relationships with anxiety, stress and negative affect. Table 1 presents the correlation coefficients, mean values and standard deviations ( sd ), as well as Cronbach ' s α for all the variables in the study.

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

https://doi.org/10.1371/journal.pone.0073265.t001

Mediation analysis

Regression analyses were performed in order to investigate if anxiety mediated the effect of stress, self-esteem, and affect on depression (aim 1). The first regression showed that stress ( B  = .03, 95% CI [.02,.05], β = .36, t  = 4.32, p <.001), self-esteem ( B  = −.03, 95% CI [−.05, −.01], β = −.24, t  = −3.20, p <.001), and positive affect ( B  = −.02, 95% CI [−.05, −.01], β = −.19, t  = −2.93, p  = .004) had each an unique effect on depression. Surprisingly, negative affect did not predict depression ( p  = 0.77) and was therefore removed from the mediation model, thus not included in further analysis.

The second regression tested whether stress, self-esteem and positive affect uniquely predicted the mediator (i.e., anxiety). Stress was found to be positively associated ( B  = .21, 95% CI [.15,.27], β = .47, t  = 7.35, p <.001), whereas self-esteem was negatively associated ( B  = −.29, 95% CI [−.38, −.21], β = −.42, t  = −6.48, p <.001) to anxiety. Positive affect, however, was not associated to anxiety ( p  = .50) and was therefore removed from further analysis.

A hierarchical regression analysis using depression as the outcome variable was performed using stress and self-esteem as predictors in the first step, and anxiety as predictor in the second step. This analysis allows the examination of whether stress and self-esteem predict depression and if this relation is weaken in the presence of anxiety as the mediator. The result indicated that, in the first step, both stress ( B  = .04, 95% CI [.03,.05], β = .45, t  = 6.43, p <.001) and self-esteem ( B  = .04, 95% CI [.03,.05], β = .45, t  = 6.43, p <.001) predicted depression. When anxiety (i.e., the mediator) was controlled for predictability was reduced somewhat but was still significant for stress ( B  = .03, 95% CI [.02,.04], β = .33, t  = 4.29, p <.001) and for self-esteem ( B  = −.03, 95% CI [−.05, −.01], β = −.20, t  = −2.62, p  = .009). Anxiety, as a mediator, predicted depression even when both stress and self-esteem were controlled for ( B  = .05, 95% CI [.02,.08], β = .26, t  = 3.17, p  = .002). Anxiety improved the prediction of depression over-and-above the independent variables (i.e., stress and self-esteem) (Δ R 2  = .03, F (1, 198) = 10.06, p  = .002). See Table 2 for the details.

https://doi.org/10.1371/journal.pone.0073265.t002

A Sobel test was conducted to test the mediating criteria and to assess whether indirect effects were significant or not. The result showed that the complete pathway from stress (independent variable) to anxiety (mediator) to depression (dependent variable) was significant ( z  = 2.89, p  = .003). The complete pathway from self-esteem (independent variable) to anxiety (mediator) to depression (dependent variable) was also significant ( z  = 2.82, p  = .004). Thus, indicating that anxiety partially mediates the effects of both stress and self-esteem on depression. This result may indicate also that both stress and self-esteem contribute directly to explain the variation in depression and indirectly via experienced level of anxiety (see Figure 1 ).

Changes in Beta weights when the mediator is present are highlighted in red.

https://doi.org/10.1371/journal.pone.0073265.g001

For the second aim, regression analyses were performed in order to test if stress mediated the effect of anxiety, self-esteem, and affect on depression. The first regression showed that anxiety ( B  = .07, 95% CI [.04,.10], β = .37, t  = 4.57, p <.001), self-esteem ( B  = −.02, 95% CI [−.05, −.01], β = −.18, t  = −2.23, p  = .03), and positive affect ( B  = −.03, 95% CI [−.04, −.02], β = −.27, t  = −4.35, p <.001) predicted depression independently of each other. Negative affect did not predict depression ( p  = 0.74) and was therefore removed from further analysis.

The second regression investigated if anxiety, self-esteem and positive affect uniquely predicted the mediator (i.e., stress). Stress was positively associated to anxiety ( B  = 1.01, 95% CI [.75, 1.30], β = .46, t  = 7.35, p <.001), negatively associated to self-esteem ( B  = −.30, 95% CI [−.50, −.01], β = −.19, t  = −2.90, p  = .004), and a negatively associated to positive affect ( B  = −.33, 95% CI [−.46, −.20], β = −.27, t  = −5.02, p <.001).

A hierarchical regression analysis using depression as the outcome and anxiety, self-esteem, and positive affect as the predictors in the first step, and stress as the predictor in the second step, allowed the examination of whether anxiety, self-esteem and positive affect predicted depression and if this association would weaken when stress (i.e., the mediator) was present. In the first step of the regression anxiety ( B  = .07, 95% CI [.05,.10], β = .38, t  = 5.31, p  = .02), self-esteem ( B  = −.03, 95% CI [−.05, −.01], β = −.18, t  = −2.41, p  = .02), and positive affect ( B  = −.03, 95% CI [−.04, −.02], β = −.27, t  = −4.36, p <.001) significantly explained depression. When stress (i.e., the mediator) was controlled for, predictability was reduced somewhat but was still significant for anxiety ( B  = .05, 95% CI [.02,.08], β = .05, t  = 4.29, p <.001) and for positive affect ( B  = −.02, 95% CI [−.04, −.01], β = −.20, t  = −3.16, p  = .002), whereas self-esteem did not reach significance ( p < = .08). In the second step, the mediator (i.e., stress) predicted depression even when anxiety, self-esteem, and positive affect were controlled for ( B  = .02, 95% CI [.08,.04], β = .25, t  = 3.07, p  = .002). Stress improved the prediction of depression over-and-above the independent variables (i.e., anxiety, self-esteem and positive affect) (Δ R 2  = .02, F (1, 197)  = 9.40, p  = .002). See Table 3 for the details.

https://doi.org/10.1371/journal.pone.0073265.t003

Furthermore, the Sobel test indicated that the complete pathways from the independent variables (anxiety: z  = 2.81, p  = .004; self-esteem: z  =  2.05, p  = .04; positive affect: z  = 2.58, p <.01) to the mediator (i.e., stress), to the outcome (i.e., depression) were significant. These specific results might be explained on the basis that stress partially mediated the effects of both anxiety and positive affect on depression while stress completely mediated the effects of self-esteem on depression. In other words, anxiety and positive affect contributed directly to explain the variation in depression and indirectly via the experienced level of stress. Self-esteem contributed only indirectly via the experienced level of stress to explain the variation in depression. In other words, stress effects on depression originate from “its own power” and explained more of the variation in depression than self-esteem (see Figure 2 ).

https://doi.org/10.1371/journal.pone.0073265.g002

Moderation analysis

Multiple linear regression analyses were used in order to examine moderation effects between anxiety, stress, self-esteem and affect on depression. The analysis indicated that about 52% of the variation in the dependent variable (i.e., depression) could be explained by the main effects and the interaction effects ( R 2  = .55, adjusted R 2  = .51, F (55, 186)  = 14.87, p <.001). When the variables (dependent and independent) were standardized, both the standardized regression coefficients beta (β) and the unstandardized regression coefficients beta (B) became the same value with regard to the main effects. Three of the main effects were significant and contributed uniquely to high levels of depression: anxiety ( B  = .26, t  = 3.12, p  = .002), stress ( B  = .25, t  = 2.86, p  = .005), and self-esteem ( B  = −.17, t  = −2.17, p  = .03). The main effect of positive affect was also significant and contributed to low levels of depression ( B  = −.16, t  = −2.027, p  = .02) (see Figure 3 ). Furthermore, the results indicated that two moderator effects were significant. These were the interaction between stress and negative affect ( B  = −.28, β = −.39, t  = −2.36, p  = .02) (see Figure 4 ) and the interaction between positive affect and negative affect ( B  = −.21, β = −.29, t  = −2.30, p  = .02) ( Figure 5 ).

https://doi.org/10.1371/journal.pone.0073265.g003

Low stress and low negative affect leads to lower levels of depression compared to high stress and high negative affect.

https://doi.org/10.1371/journal.pone.0073265.g004

High positive affect and low negative affect lead to lower levels of depression compared to low positive affect and high negative affect.

https://doi.org/10.1371/journal.pone.0073265.g005

The results in the present study show that (i) anxiety partially mediated the effects of both stress and self-esteem on depression, (ii) that stress partially mediated the effects of anxiety and positive affect on depression, (iii) that stress completely mediated the effects of self-esteem on depression, and (iv) that there was a significant interaction between stress and negative affect, and positive affect and negative affect on depression.

Mediating effects

The study suggests that anxiety contributes directly to explaining the variance in depression while stress and self-esteem might contribute directly to explaining the variance in depression and indirectly by increasing feelings of anxiety. Indeed, individuals who experience stress over a long period of time are susceptible to increased anxiety and depression [30] , [31] and previous research shows that high self-esteem seems to buffer against anxiety and depression [32] , [33] . The study also showed that stress partially mediated the effects of both anxiety and positive affect on depression and that stress completely mediated the effects of self-esteem on depression. Anxiety and positive affect contributed directly to explain the variation in depression and indirectly to the experienced level of stress. Self-esteem contributed only indirectly via the experienced level of stress to explain the variation in depression, i.e. stress affects depression on the basis of ‘its own power’ and explains much more of the variation in depressive experiences than self-esteem. In general, individuals who experience low anxiety and frequently experience positive affect seem to experience low stress, which might reduce their levels of depression. Academic stress, for instance, may increase the risk for experiencing depression among students [34] . Although self-esteem did not emerged as an important variable here, under circumstances in which difficulties in life become chronic, some researchers suggest that low self-esteem facilitates the experience of stress [35] .

Moderator effects/interaction effects

The present study showed that the interaction between stress and negative affect and between positive and negative affect influenced self-reported depression symptoms. Moderation effects between stress and negative affect imply that the students experiencing low levels of stress and low negative affect reported lower levels of depression than those who experience high levels of stress and high negative affect. This result confirms earlier findings that underline the strong positive association between negative affect and both stress and depression [36] , [37] . Nevertheless, negative affect by itself did not predicted depression. In this regard, it is important to point out that the absence of positive emotions is a better predictor of morbidity than the presence of negative emotions [38] , [39] . A modification to this statement, as illustrated by the results discussed next, could be that the presence of negative emotions in conjunction with the absence of positive emotions increases morbidity.

The moderating effects between positive and negative affect on the experience of depression imply that the students experiencing high levels of positive affect and low levels of negative affect reported lower levels of depression than those who experience low levels of positive affect and high levels of negative affect. This result fits previous observations indicating that different combinations of these affect dimensions are related to different measures of physical and mental health and well-being, such as, blood pressure, depression, quality of sleep, anxiety, life satisfaction, psychological well-being, and self-regulation [40] – [51] .

Limitations

The result indicated a relatively low mean value for depression ( M  = 3.69), perhaps because the studied population was university students. These might limit the generalization power of the results and might also explain why negative affect, commonly associated to depression, was not related to depression in the present study. Moreover, there is a potential influence of single source/single method variance on the findings, especially given the high correlation between all the variables under examination.

Conclusions

The present study highlights different results that could be arrived depending on whether researchers decide to use variables as mediators or moderators. For example, when using meditational analyses, anxiety and stress seem to be important factors that explain how the different variables used here influence depression–increases in anxiety and stress by any other factor seem to lead to increases in depression. In contrast, when moderation analyses were used, the interaction of stress and affect predicted depression and the interaction of both affectivity dimensions (i.e., positive and negative affect) also predicted depression–stress might increase depression under the condition that the individual is high in negative affectivity, in turn, negative affectivity might increase depression under the condition that the individual experiences low positive affectivity.

Acknowledgments

The authors would like to thank the reviewers for their openness and suggestions, which significantly improved the article.

Author Contributions

Conceived and designed the experiments: AAN TA. Performed the experiments: AAN. Analyzed the data: AAN DG. Contributed reagents/materials/analysis tools: AAN TA DG. Wrote the paper: AAN PR TA DG.

• View Article
• Google Scholar
• 3. MacKinnon DP, Luecken LJ (2008) How and for Whom? Mediation and Moderation in Health Psychology. Health Psychol 27 (2 Suppl.): s99–s102.
• 4. Aaroe R (2006) Vinn över din depression [Defeat depression]. Stockholm: Liber.
• 5. Agerberg M (1998) Ut ur mörkret [Out from the Darkness]. Stockholm: Nordstedt.
• 6. Gilbert P (2005) Hantera din depression [Cope with your Depression]. Stockholm: Bokförlaget Prisma.
• 8. Tabachnick BG, Fidell LS (2007) Using Multivariate Statistics, Fifth Edition. Boston: Pearson Education, Inc.
• 10. Beck AT (1967) Depression: Causes and treatment. Philadelphia: University of Pennsylvania Press.
• 21. Eskin M, Parr D (1996) Introducing a Swedish version of an instrument measuring mental stress. Stockholm: Psykologiska institutionen Stockholms Universitet.
• 22. Rosenberg M (1965) Society and the Adolescent Self-Image. Princeton, NJ: Princeton University Press.
• 23. Lindwall M (2011) Självkänsla – Bortom populärpsykologi & enkla sanningar [Self-Esteem – Beyond Popular Psychology and Simple Truths]. Lund:Studentlitteratur.
• 25. Blascovich J, Tomaka J (1991) Measures of self-esteem. In: Robinson JP, Shaver PR, Wrightsman LS (Red.) Measures of personality and social psychological attitudes San Diego: Academic Press. 161–194.
• 30. Eysenck M (Ed.) (2000) Psychology: an integrated approach. New York: Oxford University Press.
• 31. Lazarus RS, Folkman S (1984) Stress, Appraisal, and Coping. New York: Springer.
• 32. Johnson M (2003) Självkänsla och anpassning [Self-esteem and Adaptation]. Lund: Studentlitteratur.
• 33. Cullberg Weston M (2005) Ditt inre centrum – Om självkänsla, självbild och konturen av ditt själv [Your Inner Centre – About Self-esteem, Self-image and the Contours of Yourself]. Stockholm: Natur och Kultur.
• 34. Lindén M (1997) Studentens livssituation. Frihet, sårbarhet, kris och utveckling [Students' Life Situation. Freedom, Vulnerability, Crisis and Development]. Uppsala: Studenthälsan.
• 35. Williams S (1995) Press utan stress ger maximal prestation [Pressure without Stress gives Maximal Performance]. Malmö: Richters förlag.
• 37. Garcia D, Kerekes N, Andersson-Arntén A–C, Archer T (2012) Temperament, Character, and Adolescents' Depressive Symptoms: Focusing on Affect. Depress Res Treat. DOI:10.1155/2012/925372.
• 40. Garcia D, Ghiabi B, Moradi S, Siddiqui A, Archer T (2013) The Happy Personality: A Tale of Two Philosophies. In Morris EF, Jackson M-A editors. Psychology of Personality. New York: Nova Science Publishers. 41–59.
• 41. Schütz E, Nima AA, Sailer U, Andersson-Arntén A–C, Archer T, Garcia D (2013) The affective profiles in the USA: Happiness, depression, life satisfaction, and happiness-increasing strategies. In press.
• 43. Garcia D, Nima AA, Archer T (2013) Temperament and Character's Relationship to Subjective Well- Being in Salvadorian Adolescents and Young Adults. In press.
• 44. Garcia D (2013) La vie en Rose: High Levels of Well-Being and Events Inside and Outside Autobiographical Memory. J Happiness Stud. DOI: 10.1007/s10902-013-9443-x.
• 48. Adrianson L, Djumaludin A, Neila R, Archer T (2013) Cultural influences upon health, affect, self-esteem and impulsiveness: An Indonesian-Swedish comparison. Int J Res Stud Psychol. DOI: 10.5861/ijrsp.2013.228.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Prev Med Public Health
• v.54(3); 2021 May

Introduction to Mediation Analysis and Examples of Its Application to Real-world Data

Sun jae jung.

1 Department of Preventive Medicine, Yonsei University College of Medicine, Seoul, Korea

2 Department of Public Health, Yonsei University Graduate School, Seoul, Korea

Traditional epidemiological assessments, which mainly focused on evaluating the statistical association between two major components-the exposure and outcome-have recently evolved to ascertain the in-between process, which can explain the underlying causal pathway. Mediation analysis has emerged as a compelling method to disentangle the complex nature of these pathways. The statistical method of mediation analysis has evolved from simple regression analysis to causal mediation analysis, and each amendment refined the underlying mathematical theory and required assumptions. This short guide will introduce the basic statistical framework and assumptions of both traditional and modern mediation analyses, providing examples conducted with real-world data.

INTRODUCTION

In the early days, traditional analytic epidemiological methods mainly focused on the statistical association between two major variables: the exposure (E) and the outcome (Y). However, methods have evolved to explore the “black box” between the E and the Y by investigating the mechanism underlying the association and various pathways. In the same context, the mechanism has also been visualized as being near the center of “Chinese boxes,” or a set of nested boxes. The “black box” is presumed to contain factors, both above and below the level of the individual—the factors above the individual may contain items such as interpersonal dynamics and socioeconomic status, including items related to ethnicity and politics, whereas the factors below the individual level comprise genes, proteins, cells, and organ systems [ 1 ].

Mediation analysis was developed to assess this “black box,” and psychologists and social scientists have utilized this framework particularly frequently. Mediation analysis can explore and evaluate biological or social mechanisms, thereby elucidating unknown biological pathways and/or aiding in policy-making [ 2 ]. However, because of advances in methodologies, including biostatistics, epidemiological research designs, and causal inference, traditional mediation analysis has evolved and been applied in various fields. In particular, the concept of mediation analysis has been especially appealing in social sciences and psychology. There are several overviews of these topics [ 3 - 6 ], and this study is a guide to the full literature.

TRADITIONAL REGRESSION-BASED MEDIATION ANALYSIS

Mediation was initially hypothesized as a variable in the middle of a causal chain. Previously, most of the epidemiological reports focused on evaluating the simple association between E and Y as in Figure 1A . However, as in Figure 1B , it is shown that an E affects a mediator (M), which in turn affects an Y. The M fully mediates the effect from the E to the Y. However, situations were identified where the M does not fully mediate the effect of E on the Y, which led to the concept of partial mediation, as depicted in Figure 1C . As shown in Figure 1C , the effect of an E can be exerted directly on an Y (direct effect, path c’) or take a detour via a M (indirect effect, paths a and b). Initially, the criteria to be regarded as a M were that E should have a statistically significant association with M, and that M should also have a statistically significant association with Y. The initial criteria also included the condition that the mediation analysis could be performed only if there was a statistically significant association between E and Y; this significant relationship between E and Y should be no longer significant after controlling for the previous paths from E to M and M to Y. However, the latter two conditions were further criticized due to the existence of inconsistent and partial mediation, and were therefore omitted from the essential conditions needed for mediation analysis.

A conceptual diagram of mediation analysis (A) traditional epidemiological assessment, (B) full mediation, and (C) partial mediation.

In contrast to a moderator or confounder, a M is interpreted as involving a causal pathway between E and Y. A detailed definition of a M is provided in the work of Robins and Greenland [ 7 ]. The seminal work on this concept of a M or intervening variable was based on Judd and Kenny [ 8 , 9 ] and Baron and Kenny [ 10 ]’s article utilizing the regression method.

In Judd and Kenny[ 8 , 9 ]’s difference of coefficients approach, mediation analysis can be conceptualized as utilizing two regressions, as follows. First, we run a simple regression analysis with E on Y without M to estimate path c’.

Second, we carry out a multivariable regression with E and M to predict Y.

In this case, as the coefficient B reflects the total effect (TE), the direct effect from the E to Y c’ shown in Figure 1C , corresponds to B 1 in equation 2 . The difference method calculates the indirect effect by subtracting the direct effect (c’) from the TE, as follows:

This is a simple and widely used approach to screen for the possible presence of a M. However, the logistic regression method has been criticized for lacking a causal interpretation. The difference method has been used to check for mediation, but non-significant findings using this method do not exclude the chance of possible mediation [ 11 ].

The other approach is the product method, which was introduced by Sobel and used by Baron and Kenny [ 10 ]. In this method, again, a multivariable regression is conducted with E and M to predict Y.

However, the next step is to regress M on X and can be written as

In equation 3 , B reflects path a in Figure 1C , and B 2 in equation 2 reflects b in Figure 1C . The coefficient of the indirect effect, B indirect , is calculated by multiplying the 2 coefficients, B 2 and B.

Generally, when there is no interaction between an E and a M, these two methods coincide, except for logistic regression. In particular, for rare Ys (approximately under 10%) with no confounding factors, these 2 estimates will, from a practical standpoint, reflect the natural indirect effect (NIE), which will be discussed in the causal mediation section. The difference method is beneficial because there is no restriction of the M distribution; it can be continuous or categorical (including binary). In contrast, the product method requires a linear model to be applied for the M [ 11 ]. In situations with common Ys, especially when they are binary, a log-linear regression model instead of logistic regression is recommended [ 12 ].

To calculate the confidence interval (CI) of the indirect effect, 2 approaches have been suggested. The first approach utilizes the Sobel test, which is based on the product of 2 normally distributed values of coefficients. In this case, an assumption should be made about the shape of the sampling distribution of the indirect effect. The second approach uses resampling methods, such as bootstrap testing, which does not require a prior assumption of the sampling distribution. Usually, the bootstrap method involves resampling at least 750 times, for which reason the default resampling setting is 1000 times in many macros (e.g., R and the PROCESS macro in SAS [ 13 , 14 ]).

EXAMPLE OF REGRESSION-BASED MEDIATION ANALYSIS

Kim et al. [ 15 ] conducted a study to estimate the mediating effect of lifestyle factors on the association between social networks and metabolic syndrome, utilizing the baseline data of the community-based Cardiovascular and Metabolic Diseases Etiology Research Center cohort. In total, 10 103 participants were recruited from 2013 to 2018, and their egocentric social network properties were measured using a social network card that was previously applied and standardized [ 16 ]. From the raw data of the social network cards, the authors extracted and calculated the size of the social network and the closeness of the social network, which were used as quantitative E variables. Measurements of blood pressure, the lipid profile, fasting glucose, and waist circumference were made in the initial cohort, and metabolic syndrome was defined based on the National Cholesterol Education Program Adult Treatment Panel III criteria as the presence of 3 or more criteria.

As potential Ms, the authors tested 4 domains: physical inactiveness (3 categories: vigorous activities, moderate activities, and walking), alcohol consumption (binary variable: current drinker vs. non-drinker), cigarette smoking (binary variable: current smoker vs. non-smoker), and depressive symptoms (continuous variable: range 0-63 by Beck Depressive Inventory-II score).

After conducting the multivariable logistic regression for the E (social network properties, continuous variables) and Y (metabolic syndrome, yes/no), mediation analysis was performed with the ‘mediation’ package developed by Imai et al. [ 17 ] in the R software [ 18 ]. The analysis was conducted in 3 steps: (1) producing a M model, (2) producing an Y model, and (3) conducting a mediation analysis and sensitivity analysis. In the M model, social network properties and other covariates were regressed to explain lifestyle factors. The metabolic syndrome variable was then regressed on social network properties, lifestyle factors, and other covariates. These two models were grouped with the “mediate” function, which was run to estimate the direct effect, indirect effect, and their 95% CI by a quasi-Bayesian Monte Carlo method, including 5000 simulations per estimate set.

As there were 4 potential Ms, the authors applied each M and tested the indirect effect. They found that only physical activity significantly mediated the relationship between social network size and metabolic syndrome in both genders (men: effect size [ES]=5.2×10 -3 , p=0.024; women: ES=3.1×10 -3 , p <0.001) ( Figure 2A )

Brief conceptual diagrams of examples in this review. (A) Brief conceptual diagram by Kim et al. 2020 [ 15 ]. (B) Brief conceptual diagram by Lee et al. 2021 [ 23 ]. NDE, natural direct effect; OR, odds ratio; CI, confidence interval; NIE, natural indirect effect; TE, total effect. * p<0.05.

INTRODUCING CAUSAL MEDIATION ANALYSIS

After the rise of the counterfactual framework for modern causal inference, the traditional approach in mediation analyses was expanded and re-developed to solve the previous limitations regarding non-linearities and interactions, focusing on the decomposition of direct and indirect effects [ 19 , 20 ]. Among the major issues raised, assumptions related to confounding factors and the interaction between the E and the M were reflected and re-developed in causal mediation analysis [ 7 , 21 ]. In the counterfactual concept, an individual is hypothetically compared under an E and in the absence of the E in identical situations, including time and surrounding conditions. If the potential Ys are different based on this comparison, the E is regarded as causal for the Y [ 22 ].

In causal mediation analysis, 3 terms regarding the previous indirect and direct effects are suggested. The natural direct effect (NDE) and NIE can be interpreted in traditional mediation analysis. There would be a difference between the counterfactual Ys if an individual was exposed to 2 different counterfactual situations, where the M value would be random at the reference value of the E. In contrast, the controlled direct effect (CDE) is different regarding the mediation value used in the calculation since the M is set to a certain fixed level. If there is no interaction between E and M, then the CDE usually coincides with the NDE [ 4 ].

For example, an analysis using the NDE would ask “how much would the Y (e.g., suicide rate) change if the E was set at e=1 versus e=0 (e.g., exercise program), but for each participant, the M (e.g., the Patient Health Questionnaire [PHQ]-9) was kept at the level it would have been in the absence of the E (i.e., the mean depressive symptom score of the group that did not participate in the exercise program)?” An analysis using the CDE would ask, “how much would the Y (e.g., suicide rate) would change on average if the M was controlled at a certain level (e.g., PHQ-9=5) uniformly in the population?” Likewise, an analysis using the NIE would answer the question, “how much would the Y (e.g., suicide rate) would change on average if the E was controlled at the level it would be with the E present (e.g., with everyone participating in the exercise program), but with the M (e.g., PHQ-9 change) changed from the level it would be with the E at the reference level (e.g., the usual rate of people in the exercise program) to the level it would be if the E is present?” In sum, the TE would correspond to the question, “how much would the Y (e.g., suicide rate) change overall with a change in the E from the reference value to the present?” This implies that the sum of the NDE and NIE equals the TE. Generally, the CDE has received more interest for policy evaluations, whereas the NIE and NDE have been used to elucidate the actions of various biological mechanisms.

Similar to traditional mediation analysis, causal mediation analysis presumes the following temporal ordering: the E must precede the M measurement, and the Y measurement is performed after the M measurement. In addition, to interpret the mediation causally, 4 other assumptions related to confounding should be satisfied. First, all the known confounders should be controlled, and there should be no unmeasured confounding of the E-Y relationship (C 1 ) ( Figure 3 ). If the E is randomized (e.g., in randomized clinical trials), this assumption will be met. Second, all the known confounders should be controlled, and there should be no unmeasured confounding of the M-Y relationship (C 2 ). In this case, it would not be enough to randomize only the E. Third, there should be no unmeasured confounding of the E-M relationship, or all the known confounders should be controlled, which would be covered by E randomization. Lastly, there should be no confounding related to the M-Y relationship affected by the E, which means there is no arrow from E to C 2 in Figure 3 . As mentioned previously, randomizing the E (or treatment) is not enough to completely solve the confounding issue; randomizing E (which gives a probable even distribution of C 1 ) would not be sufficient to control the confounding, which can also occur between the M and Y, represented as C 2 . In this case, conducting several sensitivity analyses would help, including situations with unmeasured confounding. Most importantly, it is strongly recommended to construct a directed acyclic graph depicting the central hypothesis before conducting a causal mediation analysis.

Confounding assumptions in causal mediation analysis.

In 2013, SAS (SAS Institute Inc., Cary, NC, USA) macros were used to perform a causal mediation analysis by Valeri and VanderWeele [ 2 ]. This initial macro dealt with binary forms of E, binary forms of Ms, and continuous Y variables. Additionally, in this macro, count variables could be applied as the Ys. A full description of this macro has been published elsewhere [ 4 ].

EXAMPLE OF CAUSAL MEDIATION ANALYSIS

Lee et al. [ 23 ] performed a longitudinal analysis using data from 3347 participants aged 40-64 years in the Korean Genome and Epidemiology Study, who were followed up for 16 years. As the E, socioeconomic status, including educational attainment and monthly household income, were queried at the index year and categorized into 2 groups. As the Y, sleep quality was queried with the Pittsburgh Sleep Quality Index at 5 time points (years 2, 6, 8, 10, and 12). As a M, depressive symptoms were measured using the Beck Depression Inventory at year 4. Sleep quality patterns were the Y variable. Using latent class growth modeling with SAS Proc traj syntax, a group-based modeling approach was performed, and 5 subgroups were identified according to the pattern of sleep quality (“normal-stable,” “moderate-stable,” “poor-stable,” “developing to poor,” and “severely poor-stable”).

Using SAS Proc causalmed syntax, the potential mediation of depressive symptoms on the association between socioeconomic factors and longitudinal sleep quality patterns was tested. Based on the maximum likelihood method, this SAS procedure estimates the effect of causal mediation and CIs from 1000 bootstrap replications [ 24 ]. Since this procedure permits a binary Y only, the original 5 sleep quality patterns were grouped into 2 categories, including a reference category (e.g., normal-stable vs. moderate-stable, or normal-stable vs. severely poor-stable). Percentages were calculated to explain the mediation and interaction effects, and the percentage of the TE after controlling the level of the M was also calculated [ 24 ].

Overall, the associations between socioeconomic status variables and sleep patterns were not significant after full adjustment. However, depressive symptoms tended to fully mediate the associations between education/income variables and sleep quality patterns (e.g., for E=lower education vs. higher education, Y=developing to poor vs. normal-stable, TE: odds ratio [OR], 1.55; 95% CI, 0.64 to 6.03; NDE: OR, 1.38; 95% CI, 0.58 to 5.09); NIE: OR, 1.12; 95% CI, 1.04 to 1.24) ( Figure 2B ).

This paper reviewed the basic concepts of traditional mediation and causal mediation analysis with counterfactual approaches and provided examples in real-world settings.

One issue to be aware of is that a statistically significant association regarding M in the mediation analysis (e.g., a statistically significant indirect effect) does not always confirm that M is an actual M. Using different causal models does not make it possible for researchers to prove a unique M unless it is theoretically plausible. Furthermore, mediation analysis itself cannot provide that an intervening variable is a true M by probabilistic inference, since we cannot verify the likelihood distribution of all other potential Ms and alternative causal models [ 25 ]. Therefore, it is essential to understand that researchers should interpret mediation analysis within the logic of theoretical inferences.

Another issue lies in the measurement error for the M. According to a study conducted by le Cessie et al. [ 26 ], under the classical condition of a normally distributed M with non-differential misclassification, the estimated mediated association tended toward the null. If the direct and indirect effects were the same, the estimates tended away from the null. However, when the M was multinomial, this pattern did not always exist. Correction methods, such as using a weighting coefficient and attenuating the regression coefficient B2 in equation 2 , were also suggested by le Cessie et al. [ 26 ].

Theoretical concepts and statistical application methods regarding mediation analysis are rapidly developing. As a result, further discussions on filling the gap between theoretical assumptions and practical analytical issues are required. It has been suggested that conceptualization and formalism may be obstacles for epidemiologists to apply these methods to actual analysis [ 27 ] and future directions should involve the development of more unified and simple methods that could be utilized by a broader base of users. However, because of its usefulness in elucidating complex mechanisms in population data, the rapid adoption of mediation analysis in future epidemiological studies is expected.

Ethics Statement

As this review does not involve newly collected human data, institutional review board approval is not needed.

Acknowledgments

CONFLICT OF INTEREST

The author has no conflicts of interest associated with the material presented in this paper.

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2020R1C1C1003502) and a faculty research grant of Yonsei University College of Medicine for 2019 (6-2019-0114).

AUTHOR CONTRIBUTIONS

All work was done by SJJ.

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Mandatory Mediation in Family Disputes; The Solution to Northern Ireland's exponentially increasing Civil Legal-aid Crisis.

This dissertation will seek to address the civil legal aid crisis in Northern Ireland (Hereafter referred to as NI). It will contend that the current budget is unsustainable and that the proposed reforms are insufficient. It advocates for the use of mandatory mediation in family disputes as a means of bringing civil legal aid spending within budget whilst providing access to justice. It will examine how current family disputes are dealt with and the role of mediation in doing so. It will contend that an escalating rate of disputing is causing more delays on an already overburdened system. This dissertation will include research gathered from Mary Lynch, Director of Mediation NI and Joan Davis Director of Family Mediation NI to demonstrate the high success rates of mediation and will suggest reasons as to why it is being underutilised. The dissertation will argue that mandatory mediation whilst not a panacea has a proven track record and is not, as purist mediators would argue, an affront to the very principles of mediation. It will address the main arguments against its usage and demonstrate that it is a viable option by drawing upon various jurisdictions and their experiences and examine how these could effectively be used in NI.

Related Papers

Conflict resolution quarterly

Marian Roberts

Leonardo Valladares Pacheco de Oliveira

Treasa Kenny

As a process, mediation has evolved in the Republic of Ireland as an increasingly significant part of the work of alternative dispute resolution agencies and services funded by the State. This evolution has occurred without any overarching policy framework being in place. Yet the lack of an policy framework means that there is no integrated understanding of what is being done, by whom and to what return on the State’s investment. This 2020 project , funded by the Irish Research Council New Foundations programme, sets out to bring together all those ADR agencies and services currently involved in mediation provision in the Republic of Ireland, who are funded by the Irish State. There is limited research to date on mediation provision and impact in Ireland and a growing interest in developing a systematic evidence base in relation to mediation. The project will enable shared understanding of current mediation provision, the development of a draft public policy framework and a basis fo...

SCLS Law Review, Vol 3 No 3

M Jashim Ali Chowdhury

This paper argues that Mediation has been extremely emphasized recently in the administration of civil justice in the U.K. Explaining the series of English cases, particularly the most recent Lomax v Lomax decision, the paper sets out the English legal system's historic journey towards a full-fledged adoption of Mandatory Mediation. Experiences from Italy (E.U.), Canada and the U.S.A. are almost touched upon where relevant. The central argument of the paper remains that the legal world-common law or civil law alike-is moving towards Mandatory Mediation as a sensible alternative to the adversarial, time and money consuming traditional civil process. The prelude on Bangladesh at the beginning is added for setting a stage for the Bangladeshi readers from which they may feel the relevance of the topic we are talking about.

mieke brandon

Australian Journal of Family Law

Rachael Field

ACTA PROSPERITATIS

Jolanta Sondaite

The goal of this research is to examine the advantages and limitations of compulsory family mediation (CFM) as well as to understand subjective experience and attitude towards CFM from the perspective of family dispute resolution practitioners in Australia. The qualitative research method was chosen for this research. Information was collected using the semi‐structured interview method. The data analysis method was based on inductive thematic analysis. In completion of the data analysis, 4 main themes were identified: CFM is better option for conflict resolution, limitations caused by factors outside of the process, mediators create safe space to process disputes & emotions, the benefits of CMF on mediators. Findings of this study suggest that the practice of CFM is worth being embraced and that there are benefits to be had from an increased use of compulsory family mediation, both for families and legal system in Australia. The practitioners are optimistic of compulsory family medi...

Conflict Resolution Quarterly

Judy Corlyon

Review of European and Comparative Law

Agne Tvaronaviciene

The Mediation Directive (2008) obliged the Member States of the European Union to promote the use of mediation through their own means. A decade later, the results of several studies revealed that national efforts to foster mediation were not as effective as planned in most cases. Despite some scholars’ concerns about restricting mediation voluntariness as means for increasing its application, Italy introduced a mandatory mediation scheme which proved that forcing parties to mediate results in high numbers of mediation procedures with favorable success rates. This led other Member States to reconsider the role of the State in fostering mediation. This article tackles the prevalence of mandatory mediation in family disputes, as an area widely recognized as most suitable for it. The co-authors raised the research question of whether the introduction of mandatory mediation in family disputes is an emerging trend in the European Union. A short overview of the mandatory mediation concept...

RELATED PAPERS

Mesolithic Burials – Rites, Symbols and Social Organisation of Early Postglacial Communities

Rick Schulting

Humaera Sultana

RICARDO DANIEL TINAJERO CORIA

Revista Peruana de Investigación Materno Perinatal

claudia saldaña

International Journal of Cancer

Karin Mayer

Revista Española de Enfermedades Digestivas

Carlos Esparza

Aquatic Toxicology

Joanne Parrott

Production Planning &amp; Control

Babis Theodoulidis

Proceedings the European Design and Test Conference. ED&TC 1995

Carlos Valderrama

DIRK LAUWERS

Journal of Dental Education

carlos alberto bernal barrero

bibitdurian supertembaga

Nello Scarabottolo

Eliany Nazaré

Rachid Benbrik

Hiago Nagel Americo

European Journal of Pharmaceutics and Biopharmaceutics

sushama talegaonkar

International Journal of Molecular Sciences

Balaji Panchapakesan

CURRENT RESEARCH JOURNAL OF PHILOLOGICAL SCIENCES

Mahbuba Allamova

Neal Mundahl

Seibutsu Butsuri

Yeni Medya Çalışmaları V. Ulusal Kongre Kitabı

Tahsin Mert Saygin

Anna Rubartelli

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

• Bibliography
• More Referencing guides Blog Automated transliteration Relevant bibliographies by topics
• Automated transliteration
• Relevant bibliographies by topics
• Referencing guides