how to interpret mediation analysis

Does anyone have a template of how to report results in APA style of simple moderation analysis done with SPSS's PROCESS macro? Clin. I am currently analysing data for my Bachelor thesis. 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. 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. All tests were done using 5,000 bootstraps and α = 0.05. (SPS). 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). Mediation analysisallows you to explore whether a mediating variable can explain the relationship between two variables. Soc. J. R. Stat. It is desirable that for the normal distribution of data the values of skewness should be near to 0. Mediation analysis in social psychology: current practices and new recommendations. I have read that there is no assumption of distribution for this method but I was unsure if I have misinterpreted this? From the above discussion of the various perspectives we wish to conclude that there is not just one way to look at mediation. 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. This was a workshop I gave at the Crossroads 2015 conference at Dalhousie University, March 27, 2015. doi: 10.1016/S1057-7408(07)70020-7, Imai, K., Keele, L., and Yamamoto, T. (2010). 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. 98, 550–558. Yuan, Y., and MacKinnon, D. P. (2014). Kind regards, To some degree then the matter of specific effects vs. the global model distinction is irrelevant because simple mediation models are saturated. Psychol. 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. 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. 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. Could you clarify- when do we consider unstandarized coefficient and why? This chapter surveys many of the more common simple inferential tests for testing null hypotheses about correlations, counts, and means. 23, 246–258. If the presumed model is not correct, the results from the mediation analysis are of little value. That the data are in line with the hypothesis and even that several alternative explanations can be eliminated does not prove causality. 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. Standardized vs Unstandardized regression coefficients? Thank you all. Det er gratis at tilmelde sig og byde på jobs. I have included the SPSS output in a Word document below to make things more visual. (2) Mediation causes the relationship between X and Y. Anal. 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). 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. 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. 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 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). Methods 20, 193–203. 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. The examples will not demonstrate full mediation, i.e., the effect of the independent variable will not go from being … Behav. 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). Hi, Does age not have an effect after all? Having similar personalities could lead to more time spend together doing shared activities, which in turn could lead to more marital satisfaction. 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). This is an intriguing asymmetry between the two possible outcomes of a study—supportive results are accepted, unsupportive results are retested. Am interested in knowing the new Hayes Process macro v3.2 models. Our time-series example is one example of why the presence of TE1 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 TE1 test under some parameter configurations (Rucker et al., 2011; Kenny and Judd, 2014; Loeys et al., 2015; O'Rourke and MacKinnon, 2015). Psychol. The INUS view is consistent with indirectness and systemic causation, whereas Humean regularity theory is better in agreement with directness of causes. Methods, 47:424. doi: 10.3758/s13428-014-0481-z. Some perspectives may be more often correct than others (e.g., more tenable assumptions, better clarification of what constitutes a mediator, etc. When moderation is mediated and mediation is moderated. 5, 602–619. 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. 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). How do you interpret the moderation / Mediation test using Hayes' PROCESS tool in SPSS? Bayesian quantile structural equation models. Many of these tests help the researchers for evaluating a variety of hypotheses. Psychol. The three variables may be exhaustive, or a subset of much larger set of variables. The Pearson product‐moment correlation is a measure o... Join ResearchGate to find the people and research you need to help your work. We say two or three because the first, Model 1, is somewhat controversial and is not always necessary (Kenny and Judd, 2014). Friendships and family support reduce subsequent depressive symptoms in at-risk adolescents. This simple mediation model can also be portrayed as a path diagram shown below. (2013). Researchers may further focus on hypothesized or competing alternative explanations when testing for mediation. 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. 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. 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. 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). Model. doi: 10.3758/BRM.40.3.879, Preacher, K. J., and Kelley, K. (2011). Effect measures for mediation models. 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. However, such work should not be taken as a blanket justification for testing the IE in the absence of TE1 if there is not an a priori hypothesized indirect 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). I am a bit confused now a I really appreciate your answers to help me get rid of this confusion. 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. Specifically, the DE is presented as the path from X to Y, c′. 42, 185–227. 1, 173–181. 27, 101–108. 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. (2013). X M Y a b c’ Analysis Visual Depiction However, there are a few very strong limitations regarding competing evidence. Psychol., 15 November 2017 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. For example, you might want to know whether the relationship between ‘personality similarity’ and ‘marital satisfaction’ is mediated by ‘shared activities’. Psychol. 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. Report Mediation Analysis in Thesis Figure 9. (2015). That is, I want to know the strength of relationship that existed. 7, 130–135. 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. 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. An introduction to mediation analysis using SPSS software (specifically, Andrew Hayes' PROCESS macro). 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. J. Pers. 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). For example, the mediator is presumed to cause the outcome and not vice versa. 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). Equ. The time series example is another case where a global model approach makes sense. Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. First, there is the matter of model saturation (i.e., the same number of estimated parameters as there are variables). In the case of directness, the criterion is a minimizing ambiguity about whether or not there is an effect of X on Y. Mediation analysis is typically applied when a researcher wants to assess the extent to which the effect of an exposure is explained, or is not explained by a given set of hypothesized mediators (also called intermediate variables1). (2016). Equivalence of the mediation, confounding and suppression effect. We will refer to the TE associated with Figure 1 as TE1, and the TE associated with Figure 2 as TE2. 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 TE1 as great as 94% higher (6 vs. 100%) when the TE1 is small, e.g., when T = 50 or 100. Arch. doi: 10.3102/1076998607307239, van Harmelen, A. L., Gibson, J. L., St Clair, M. C., Owens, M., Brodbeck, J., Dunn, V., et al. Res. doi: 10.1016/j.conctc.2017.06.005, Rouder, J. N., Morey, R. D., Verhagen, J., Province, J. M., and Wagenmakers, E. J. Addressing moderated mediation hypotheses: theory, methods, and prescriptions. 5:1549. doi: 10.3389/fpsyg.2014.01549. Some philosophical and linguistic considerations are briefly discussed, as well as some other perspectives we do not develop here. (See Kraemer, Wilson, Fairburn, and Agras (2002) who attempt to define mediation without making causal assumptions.) Det är gratis att anmäla sig och lägga bud på jobb. Sci. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. New York, NY: Lawrence Erlbaum. But he doesn't offer a guide for interpreting this. 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. Mediators, moderators, and tests for mediation. The total effect describes the total effect the independent variable (iv) sepal length has on the dependent variable (dv) likelihood to be pollinated by a bee.Basically, we want to understand if there is a relationship between the two variables. Alternative explanations are often not generated or tested if the null hypothesis of mediation is rejected. Further, instead of two separate TE estimates (stemming from separate regressions), there is only one TE to be considered: TE2 as estimated from the model TEmodel: Where a*, b*, and c′* are model parameters. Conversely, making more assumptions leads to better precision and possibly to better replication (if the model constraints are valid). I want to find out if people's decision-making ability (X) has a direct and/or indirect effect through their tendency to overeat (M) on their BMI (Y). Asked 22nd Jun, 2018; Thomas L. doi: 10.1023/A:1026595011371, MacKinnon, D. P., Lockwood, C. M., and Williams, J. Top. 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. Oxford, UK: Clarendon Pres. Reporting results with PROCESS macro model 1 (simple moderation) in APA style. 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. 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. Sci. Given a mediation hypothesis there is then no need to consider the significance of the TE1 because it is irrelevant to the presence of an IE, as the IE is estimated by different statistical models than TE1 is and a mediation hypothesis refers solely to the IE (though a more general causal relationship may be hypothesized to include both). Process analysis: estimating mediation in treatment evaluation. Soc. As far as I have (hopefully rightfully) concluded the effects are not significant. The following shows the basic steps for mediation analysis suggested by Baron & Kenny (1986). When running a simple moderated regression, the statistical output of Process macro is very much the same with 'Step 1 & Step 2' hierarchical regression using SPSS's linear regression tool (regression coeff, p & t-values, mean squared error, R2 & R2 change). I attach the output and the model to show you what i'm trying to understand. 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. This post will show examples using R, but you can use any statistical software. 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). 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. Thanks in advance. Keywords: Mediation formula, Identi cation, confounding, graphical models 1 Introduction Mediation analysis aims to uncover causal pathways along which changes are transmitted from causes to e ects. The combined effects of measurement error and omitting confounders in the single mediator model. What is the acceptable range of skewness and kurtosis for normal distribution of data? 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). 180, 1–31. Effect size, power, and sample size determination for For such large effects the TE1 is easily rejected. In contrast, there is no reason to expect skewness in the sampling distribution of TE1 because it is a simple parameter in Equation (2) and Figure 1, and not a product of two parameters. Eval. 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. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). Though a full discussion is too complex to engage in here, a similar view has been taken by philosophers such as, Woodwarth (2003). 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. 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). Confidence limits for the indirect effect. Impact Factor 2.067 | CiteScore 3.2More on impact ›, National University of Singapore, Singapore, Australian National University, Australia. Another view is formulated in the complex regularity view of Mackie (1974) and his INUS conditions. 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. Hart, H. L. A., and Honore, A. M. (1985). 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 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. A mediation analysis is comprised of three sets of regression: X → Y, X → M, and X + M → Y. MacKinnon, D. (2008). Mackie, J. L. (1974). © 2008-2021 ResearchGate GmbH. 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. Soc. Thus, indirectness and distance make a causal interpretation stronger from one perspective, whereas they make a causal interpretation less convincing from another perspective. Is it a case of interpreting the coefficient as you might a usual correlation coefficient (e.g. Psychometrika. Another approach is to assume that there are unmeasured confounders that bias the estimates and necessitate examining parameter sensitivity (VanderWeele, 2010). 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). 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. 11, 107–111. 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. doi: 10.1207/s15327957pspr0203_4. Therefore, it can make sense to stay with separate regression analyses without a test of the global model. The sem command introduced in Stata 12 makes the analysis of mediation models much easier as long as both the dependent variable and the mediator variable are continuous variables.. We will illustrate using the sem command with the hsbdemo dataset. 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. As before, the two perspectives are both meaningful. doi: 10.1037/a0020141. PLoS ONE 11:e0153715. (2008). Trials Commun. doi: 10.1177/0956797613480187, Iacobucci, D., Saldanha, N., and Deng, X. Interdiscipl. Oxford: Oxford University Press. 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. Helena. Introduction to Statistical Mediation Analysis. 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. The statistical significance of the indirect effect should be tested using bootstrapping (see Hayes [2013], Introduction to mediation, moderation, and conditional process analysis). 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. 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). Pers. However, since the age range of the tested participants is very broad, I decided to include the age as a covariate. The content introducing mediation analysis is in need of updating, and in particular the assumptions and proper specification of mediation analysis models so as to have a better understanding of the … with a post-hoc mediation analysis and then attempting to explain it after the results are known (Kerr, 1998). As a result, regardless of the time scale, the TE always equals the IE. 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. If the null hypothesis of no relationship is rejected, the mediation claim is considered to be supported and the case closed. Kraemer, H. C., Kiernan, M., Essex, M., and Kupfer, D. J. Psychol. 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. mediation using a widely available estimating method. Rev. 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. 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. Available online at: http://blogs.berkeley.edu/2012/11/05/global-warming-systemically-caused-hurricane-sandy/, Loeys, T., Moerkerke, B., and Vansteelandt, S. (2015). The Cement of the Universe. Shibatani, M. (2001). It is a search for a well-defined form of information, and further the search is considered complete when that information is obtained. 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. 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. 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. 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. In Humean regularity theories, X is a cause if it is regularly followed by Y. As such, a parallel two-mediator model is not saturated whereas a serial two-mediator model is. 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. Data Mining 5, 243–264. doi: 10.1111/j.1751-9004.2011.00355.x, Salter-Townshend, M., White, A., Gollini, I., and Murphy, T. B. Bias formulas for sensitivity analysis for direct and indirect effects. 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.

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