The behavioral science literature is replete with studies demonstrating that a particular independent variable explains variability in a dependent variable. Establishing relationships between variables is important, because correlation is a necessary (but not sufficient) condition for claiming that two variables are causally related. Of even greater scientific interest is explaining how or by what means a causal effect occurs. Questions about causeeffect relations invoke the idea of mediation, the process by which some variables exert influences on others through intervening or mediator variables. For example, evidence suggests that job autonomy, cognitive ability, and job-related skills all predict job performance. But it is even more informative to be able to claim that they exert their effects on job performance through role breadth-the variety of tasks a person performs on the job (Morgeson, Delaney-Klinger, & Hemingway, 2005). Assad, Donnellan, and Conger (2007) found that the effect of optimism on romantic relationship quality is mediated by cooperative problem solving. Kalyanaraman and Sundar (2006) showed that perceived interactivity of a Web portal functions as a mediator of the effect of customization on attitudes toward the portal. Such hypotheses go beyond mere description and help to explain process and causality.There exists a large and growing literature on methods of testing simple mediation hypotheses-those in which the effect of some causal variable X on some proposed outcome Y is mediated by a single variable M. Our focus in this article is to discuss and illustrate the application of some of these methods to the estimation and testing of mediated effects in multiple mediator models-those with more than a single proposed mediator variable. We then discuss how statistical contrasts of two or more indirect effects in a multiple mediator model may be conducted, and present SAS, SPSS, Mplus, and LISREL syntax to facilitate the testing of multiple mediation hypotheses. MEDIATION IN BEHAVIORAL RESEARCHMediation hypotheses posit how, or by what means, an independent variable (X ) affects a dependent variable (Y ) through one or more potential intervening variables, or mediators (M ). We address only the situation in which the causal order of X, M, and Y can be established on theoretical or procedural grounds. If a logical ordering of X, M, and Y cannot be established, other methods should be used to investigate mediation (e.g., Azen, 2003).Mediation processes involving only one mediating variable we term simple mediation. Figure 1B depicts a simple mediation model and shows how variable X's causal effect can be apportioned into its indirect effect on Y through M and its direct effect on Y (path c ). Path a represents the effect of X on the proposed mediator, whereas path b is the effect of M on Y partialling out the effect of X. All of these paths would typically be quantified with unstandardized regression coefficients. The indirect effect of X on Y through Hypotheses involving mediation are common ...

Psychologists often conduct research to establish whether and to what extent one variable affects another. However, the discovery that two variables are related to each other is only one small part of the aim of psychology. Deeper understanding is gained when we comprehend the process that produces the effect. For example, it might be useful to know whether a management training program leads to an increase in employee satisfaction by affecting employee attitudes toward management or by changing behavioral habits. In this example, attitudes and habits are potential mediators of the relationship between the management training program and employee satisfaction.A variable may be called a mediator "to the extent that it accounts for the relation between the predictor and the criterion" (Baron & Kenny, 1986, p. 1176. 1 Panel A of Figure 1 represents the effect of some proposed cause (X ) on some outcome (Y ). Panel B of Figure 1 represents the simplest form of mediation-the type that occurs when one variable (M) mediates the effect of X on Y. We term this model simple mediation. More complex mediation models are possible, but we limit our discussion here to simple mediation because it is by far the most commonly employed type of mediation model.The simple relationship between X and Y is often referred to as the total effect of X on Y (see Figure 1, panel A); we denote the total effect c to distinguish it from c¢, the direct effect of X on Y after controlling for M (see Figure 1, panel B). The formal heuristic analysis often used to detect simple mediation effects is straightforward and follows directly from the definition of a mediator provided by Baron and Kenny (1986). Variable M is considered a mediator if (1) X significantly predicts Y (i.e., c 0 in Figure 1), (2) X significantly predicts M (i.e., a 0 in Figure 1), and (3) M significantly predicts Y controlling for X (i.e., b 0 in Figure 1). Baron and Kenny discuss several analyses that should be performed and the results assessed with respect to the criteria just described. These criteria are assessed by estimating the following equations:where i is an intercept coefficient. When the effect of X on Y decreases to zero with the inclusion of M, perfect mediation is said to have occurred (James & Brett, 1984, call this situation complete mediation). When the effect of X on Y decreases by a nontrivial amount, but not to zero, partial mediation is said to have occurred. 2 In addition to satisfying these requirements, two further assumptions must be met in order to claim that mediation has occurred, according to Baron and Kenny; namely, there should be no measurement error in M, and Y should not cause M. Thê Researchers often conduct mediation analysis in order to indirectly assess the effect of a proposed cause on some outcome through a proposed mediator. The utility of mediation analysis stems from its ability to go beyond the merely descriptive to a more functional understanding of the relationships among variables. A necessary component of mediation is a statist...

This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

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I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator-a parameter that I call the index of moderated mediation. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert ( 2007 ) and Preacher, Rucker, and Hayes ( 2007 ) as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.

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

924Behavioral science researchers long ago moved beyond the business of theorizing about and testing simple bivariate cause and effect relationships, since few believe that any effects are independent of situational, contextual, or individual-difference factors. Furthermore, we understand some variable's effect on another better when we understand what limits or enhances this relationship, or the boundary conditions of the effect-for whom or under what circumstances the effect exists and where and for whom it does not. Theoretical accounts of an effect can be tested and often are strengthened by the discovery of moderators of that effect. So testing for moderation of effects, also called interaction, is of fundamental importance to the behavioral sciences.A moderated effect of some focal variable F on outcome variable Y is one in which its size or direction depends on the value of a third, moderator variable M. Analytically, moderated effects reveal themselves statistically as an interaction between F and M in a mathematical model of Y. In statistical models such as ordinary least squares (OLS) regression or logistic regression, moderation effects frequently are tested by including the product of the focal independent variable and the moderator as an additional predictor in the model. When an interaction is found, it should be probed in order to better understand the conditions (i.e., the values of the moderator) under which the relationship between the focal predictor and the outcome is strong versus weak, positive versus negative, and so forth.One approach for probing interactions that we have seen used in the literature is the subgroup analysis or separate regressions approach, where the data file is split into various subsets defined by values of the moderator and the analysis is repeated on these subgroups. But this method does not properly represent how the focal predictor variable's effect varies as a function of the moderator, especially when additional variables in the model are used as statistical controls. For details about the problems with this method-a method we do not recommend-see Newsom, Prigerson, Schulz, and Reynolds (2003) and Stone-Romero and Anderson (1994).Fortunately, there are more rigorous and appropriate methods for probing interactions in linear models, two of which we will describe in this article. The first method we discuss, the pick-a-point approach, is one of the more commonly used. This approach involves selecting representative values (e.g., high, moderate, and low) of the moderator variable and then estimating the effect of the focal predictor at those values (see, e.g., Aiken & West, 1991;Cohen, Cohen, West, & Aiken, 2003;Jaccard & Turrisi, 2003). A difficulty with this approach is that, frequently, there are no nonarbitrary guidelines for picking the points at which to probe the interaction. An alternative is the Johnson-Neyman (J-N ) technique (Johnson & Fay, 1950;Johnson & Neyman, 1936;Potthoff, 1964) Researchers often hypothesize moderated effects, in which the effect of ...