A general multilevel SEM framework for assessing multilevel mediation.

Abstract

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...

Enhancing daily well-being at work through lunchtime park walks and relaxation exercises: Recovery experiences as mediators.

“…Preacher and Hayes, we focused on the specific indirect effect of the predictor on the outcome through the mediator (Preacher & Hayes, 2008;Preacher, Zyphur, & Zhang, 2010). The indirect effect is quantified as ab, which is equal to the difference between total and direct effect, and is used to assess the presence, strength, and significance of the indirect effect (Preacher & Hayes, 2008;Preacher, Rucker, & Hayes, 2007).…”

A Primer on Multilevel Mediation Models for Egocentric Social Network Data

“…Since the single indirect effect estimate contains two sources of variations in multilevel mediation models, we cannot make a definite claim regarding the nature of such indirect effects if within-and between-components are conflated within a single indirect effect estimate. This may be seen as a rather trivial issue, yet it poses some concerns regarding the precision of the statistical inferences and the validity of the corresponding interpretation of the model parameters when such models are used, therefore literature strongly advocates the use of deconflated models over conflated models (Lüdtke, Mars, Robitzsch, & Ulrich, 2008;Preacher et al, 2010). 3.…”

“…However, one should bear in mind that such aggregation into a higher unit (e.g., deriving a single summary measure) is a considerable loss of information (Raudenbush & Bryk, 2002;Snijders & Bosker, 2012). Recent application of structural equation modeling (SEM) to multilevel analysis can overcome aforementioned limitations, and is readily available in many instances (e.g., Du Toit & Du Toit, 2008;Preacher, 2011;Preacher et al, 2010). Yet, SEM frameworks generally rely on large sample procedures (Hayes, Montoya, & Rockwood, 2017).…”

“…First, MLM assumes all of the observed variables are perfectly reliable (i.e., without measurement error), which in many of the cases may be unrealistic. Second, and perhaps the greatest limitation of traditional MLM framework, is it is impossible to accommodate an upper-level dependent variable, where the conceptual independent variable lies at the lower level and the dependent variable is in the upper level (Preacher, Zyphur, & Zhang, 2010). Such a "bottom-up inference" may be of considerable interest to communication scholars, yet because the MLM framework cannot accommodate the upper level dependent variable, some researchers instead rely on the aggregation of the lower-level information to create a summary measure defined at the upper-level.…”

“…Next, we create the upper-level variables ("between-" components) that correspond to a lower-level X and M by aggregating the respective lower-level variables, and use the group-mean centering procedure to capture a strict "within-" component of variations. As such, we treat the within-and between-component of variations as two distinctive constructs, in order to statistically distinguish those components in indirect effect estimates (Preacher, 2011;Preacher et al, 2010;Zhang et al, 2009). We could then express a deconflated multilevel mediation model, conceptually described as in Panel A of Figure 2 below, which consists of the MLM equations predicting M from X, and the MLM equations predicting Y from the joint function of X and M, as follows.…”