Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: New procedures and recommendations.

Abstract

The authors propose new procedures for evaluating direct, indirect, and total effects in multilevel models when all relevant variables are measured at Level 1 and all effects are random. Formulas are provided for the mean and variance of the indirect and total effects and for the sampling variances of the average indirect and total effects. Simulations show that the estimates are unbiased under most conditions. Confidence intervals based on a normal approximation or a simulated sampling distribution perform well when the random effects are normally distributed but less so when they are nonnormally distributed. These methods are further developed to address hypotheses of moderated mediation in the multilevel context. An example demonstrates the feasibility and usefulness of the proposed methods. Keywords: multilevel model, hierarchical linear model, indirect effect, mediation, moderated mediationIn psychology and other social sciences, hypotheses often concern the causal pathways through which key predictors transmit their effects to specific outcomes. For example, Wei, Mallinckrodt, Russell, and Abraham (2004) examined the extent to which attachment anxiety and avoidance were related to maladaptive perfectionism and, in turn, depressive mood. Similarly, Catanzaro and Laurent (2004) hypothesized that alcohol expectancies play a role in drinking as a means of coping, which then predicts a number of drinking behaviors. In both of these cases, the causal effects of the original predictor are transmitted at least partially through an intervening variable, as diagrammed in Figure 1. In the diagram, the product of the paths labeled a and b represents the indirect effect of X on Y, the path labeled cЈ represents the direct effect of X on Y, and c ϭ ab ϩ cЈ is the total effect of X on Y (Alwin & Hauser, 1975;Bollen, 1987Bollen, , 1989. Depending on the pattern of these effects, the variable M may be called a mediator, a suppressor, or simply an intervening variable (MacKinnon, Krull, & Lockwood, 2000). We generally use the terms mediator and mediation to be consistent with the focus of much of the literature on indirect effects, although our exposition also pertains to other patterns of indirect effects.Within the context of linear regression and path analysis, a number of methods have been proposed for evaluating mediation, and this remains an active area of research (e.g., MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002;MacKinnon, Lockwood, & Williams, 2004;Shrout & Bolger, 2002). Such methods are, however, inappropriate if the analyzed data are actually hierarchical in nature (i.e., composed of two or more nested levels). Two forms of hierarchical data are common in psychological research. First, individuals may be assessed from a number of groups. Individuals are then said to be nested within groups. To the extent that individuals within a group share common experiences, we would expect their scores on the outcome variable to be correlated across members of the group, which violates the independence assumption of ...

A novel measure of effect size for mediation analysis.

“…The relationships among X, M, and Y can be described in a system of two linear regressions. The relationship between X and M is expressed as In this simple mediation model, the two methods yield equivalent indirect effects, but estimates will differ if the outcome is not continuous or data are nested (Bauer, Preacher, & Gil, 2006;Krull & MacKinnon, 1999;MacKinnon & Dwyer, 1993). Whereas the two approaches both yield unbiased and efficient estimates, the product of coefficients approach is preferred because when there is more than one indirect effect,…”

“…Lower values of bias indicate that the mean sample estimate is closer to the population parameter, and an unbiased estimator has a bias of 0. It was hypothesized that because the sample estimate of the indirect effect is an unbiased estimate of the indirect effect (Bauer, Preacher, & Gil, 2006), then  would be an unbiased estimate of  . Relative bias was defined as the ratio of the bias to the population parameter:…”

The pleasure of making a difference: Perceived social contribution explains the relation between extraverted behavior and positive affect.

“…Mediation hypotheses were examined using a multilevel structural equation modeling (MSEM) framework (Bauer, Preacher, & Gil, 2006;Muthén & Asparouhov, 2011).…”

The scare tactic: Do fear appeals predict motivation and exam scores?

“…As the perceived threat of fear appeals and autonomous motivation are internally represented sociocognitive constructs, these were represented as individual-level variables in subsequent analyses. Multilevel mediational models are structured in such a way that a group-level predictor can estimate a mediating variable at a group or individual level, whereas an individual-level predictor can estimate a mediating variable only at the individual level (Bauer, Preacher, & Gil, 2006;Krull & MacKinnon, 2001). As we propose that self-determined motivation is an individual-level predictor, the hierarchical structure of the data can be modeled in one of two ways.…”