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.

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the conditional relations is often a tedious and error-prone task. This article provides an overview of methods used to probe interaction effects and describes a unified collection of freely available online resources that researchers can use to obtain significance tests for simple slopes, compute regions of significance, and obtain confidence bands for simple slopes across the range of the moderator in the MLR, HLM, and LCA contexts. Plotting capabilities are also provided.

Several methods for testing mediation hypotheses with 2-level nested data have been proposed by researchers using a multilevel modeling (MLM) paradigm. However, these MLM approaches do not accommodate mediation pathways with Level-2 outcomes and may produce conflated estimates of between-and within-level components of indirect effects. Moreover, these methods have each appeared in isolation, so a unified framework that integrates the existing methods, as well as new multilevel mediation models, is lacking. Here we show that a multilevel structural equation modeling (MSEM) paradigm can overcome these 2 limitations of mediation analysis with MLM. We present an integrative 2-level MSEM mathematical framework that subsumes new and existing multilevel mediation approaches as special cases. We use several applied examples and accompanying software code to illustrate the flexibility of this framework and to show that different substantive conclusions can be drawn using MSEM versus MLM. Researchers in behavioral, educational, and organizational research settings often are interested in testing mediation hypotheses with hierarchically clustered data. For example, Bacharach, Bamberger, and Doveh (2008) investigated the mediating role of distress in the relationship between the intensity of involvement in work-related incidents and problematic drinking behavior among firefighting personnel. They used data in which firefighters were nested within ladder companies and all three variables were assessed at the subject level. Using data from customer service engineers working in teams, Maynard, Mathieu, Marsh, and Ruddy (2007) found that team-level interpersonal processes mediate the relationship between team-level resistance to empowerment and individual job satisfaction. Both of these examples-and many others-involve data that vary both within and between higher level units. Traditional methods for assessing mediation (e.g., Baron & Kenny, 1986;MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002;MacKinnon, Warsi, & Dwyer, 1995) are inappropriate in these multilevel settings, primarily because the assumption of independence of observations is violated when clustered data are used, leading to downwardly biased standard errors if ordinary regression is used. For this reason, several methods have been proposed for addressing mediation hypotheses when the data are hierarchically organized.These recommended procedures for testing multilevel mediation have been developed and framed almost exclusively within the standard multilevel modeling (MLM) paradigm (for thorough treatments of MLM, see Bryk, 2002, andSnijders &Bosker, 1999) and implemented with commercially available MLM software, such as SAS PROC MIXED, HLM, or MLwiN. For example, some authors have discussed models in which the independent variable X, mediator M, and dependent variable Y all are measured at Level 1 of a two-level hierarchy (a 1-1-1 design, adopting notation proposed by Krull & MacKinnon, 2001), 1 and slopes either are fixed (Pituch, Whittaker, & Stapleton, 2005...

The authors examine the practice of dichotomization of quantitative measures, wherein relationships among variables are examined after 1 or more variables have been converted to dichotomous variables by splitting the sample at some point on the scale(s) of measurement. A common form of dichotomization is the median split, where the independent variable is split at the median to form high and low groups, which are then compared with respect to their means on the dependent variable. The consequences of dichotomization for measurement and statistical analyses are illustrated and discussed. The use of dichotomization in practice is described, and justifications that are offered for such usage are examined. The authors present the case that dichotomization is rarely defensible and often will yield misleading results.We consider here some simple statistical procedures for studying relationships of one or more independent variables to one dependent variable, where all variables are quantitative in nature and are measured on meaningful numerical scales. Such measures are often referred to as individual-differences measures, meaning that observed values of such measures are interpretable as reflecting individual differences on the attribute of interest. It is of course straightforward to analyze such data using correlational methods. In the case of a single independent variable, one can use simple linear regression and/or obtain a simple correlation coefficient. In the case of multiple independent variables, one can use multiple regression, possibly including interaction terms. Such methods are routinely used in practice.However, another approach to analysis of such data is also rather widely used. Considering the case of one independent variable, many investigators begin by converting that variable into a dichotomous variable by splitting the scale at some point and designating individuals above and below that point as defining two separate groups. One common approach is to split the scale at the sample median, thereby defining high and low groups on the variable in question; this approach is referred to as a median split. Alternatively, the scale may be split at some other point based on the data (e.g., 1 standard deviation above the mean) or at a fixed point on the scale designated a priori. Researchers may dichotomize independent variables for many reasons-for example, because they believe there exist distinct groups of individuals or because they believe analyses or presentation of results will be simplified. After such dichotomization, the independent variable is treated as a categorical variable and statistical tests then are carried out to determine whether there is a significant difference in the mean of the dependent variable for the two groups represented by the dichotomized independent variable. When there are two independent variables, researchers often dichotomize both and then analyze effects on the dependent variable using analysis of variance (ANOVA).There is a considerable methodological literature exam...

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.

The statistical analysis of mediation effects has become an indispensable tool for helping scientists investigate processes thought to be causal. Yet, in spite of many recent advances in the estimation and testing of mediation effects, little attention has been given to methods for communicating effect size and the practical importance of those effect sizes. Our goals in this article are to (a) outline some general desiderata for effect size measures, (b) describe current methods of expressing effect size and practical importance for mediation, (c) use the desiderata to evaluate these methods, and (d) develop new methods to communicate effect size in the context of mediation analysis. The first new effect size index we describe is a residual-based index that quantifies the amount of variance explained in both the mediator and the outcome. The second new effect size index quantifies the indirect effect as the proportion of the maximum possible indirect effect that could have been obtained, given the scales of the variables involved. We supplement our discussion by offering easy-to-use R tools for the numerical and visual communication of effect size for mediation effects.