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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 statistically and practically significant indirect effect. Although mediation hypotheses are frequently explored in psychological research, formal significance tests of indirect effects are rarely conducted. After a brief overview of mediation, we argue the importance of directly testing the significance of indirect effects and provide SPSS and SAS macros that facilitate estimation of the indirect effect with a normal theory approach and a bootstrap approach to obtaining confidence intervals, as well as the traditional approach advocated by Baron and Kenny (1986). We hope that this discussion and the macros will enhance the frequency of formal mediation tests in the psychology literature. Electronic copies of these macros may be downloaded from the Psychonomic Society's Web archive at www.psychonomic.org/archive/.

Testing multilevel mediation using hierarchical linear modeling (HLM) has gained tremendous popularity in recent years. However, potential confounding in multilevel mediation effect estimates can arise in these models when within-group effects differ from between-group effects. This study summarizes three types of HLM-based multilevel mediation models, and then explains that in two types of these models confounding can be produced and erroneous conclusions may be derived when using popularly recommended procedures. A Monte Carlo simulation study illustrates that these procedures can underestimate or overestimate true mediation effects. Recommendations are provided for appropriately testing multilevel mediation and for differentiating within-group versus between-group effects in multilevel settings.

Mediation analysis has become one of the most widely used tools for investigating the mechanisms through which variables influence each other. When conducting mediation analysis with fully nested data (e.g., individuals working in teams) or partially nested data (e.g., individuals working alone in one study arm but working in teams in another arm) special considerations arise. In this article we (a) review traditional approaches for analyzing mediation in nested data, (b) describe multilevel structural equation modeling (MSEM) as a versatile technique for assessing mediation in fully nested data, and (c) explain how MSEM can be adapted for assessing mediation in partially nested data (MSEM-PN) and introduce two new MSEM-PN specifications. MSEM-PN affords options for testing equality of level-specific mediation effects in the nested arm with mediation effects in the nonnested arm. We demonstrate the application of MSEM and MSEM-PN in simulated examples from the group processes literature involving fully and partially nested data. Finally, we conclude by providing software syntax and guidelines for implementation.

Researchers often combine longitudinal panel data analysis with tests of interactions (i.e., moderation). A popular example is the cross-lagged panel model (CLPM). However, interaction tests in CLPMs and related models require caution because stable (i.e., between-level, B) and dynamic (i.e., within-level, W) sources of variation are present in longitudinal data, which can conflate estimates of interaction effects. We address this by integrating literature on CLPMs, multilevel moderation, and latent interactions. Distinguishing stable B and dynamic W parts, we describe three types of interactions that are of interest to researchers: 1) purely dynamic or WxW; 2) cross-level or BxW; and 3) purely stable or BxB. We demonstrate estimating latent interaction effects in a CLPM using a Bayesian SEM in Mplus to apply relationships among work-family conflict and job satisfaction, using gender as a stable B variable. We support our approach via simulations, demonstrating that our proposed CLPM approach is superior to a traditional CLPMs that conflate B and W sources of variation. We describe higher-order nonlinearities as a possible extension, and we discuss limitations and future research directions.

This article compares a general cross-lagged model (GCLM) to other panel data methods based on their coherence with a causal logic and pragmatic concerns regarding modeled dynamics and hypothesis testing. We examine three "static" models that do not incorporate temporal dynamics: random- and fixed-effects models that estimate contemporaneous relationships; and latent curve models. We then describe "dynamic" models that incorporate temporal dynamics in the form of lagged effects: cross-lagged models estimated in a structural equation model (SEM) or multilevel model (MLM) framework; Arellano-Bond dynamic panel data methods; and autoregressive latent trajectory models. We describe the implications of overlooking temporal dynamics in static models and show how even popular cross-lagged models fail to control for stable factors over time. We also show that Arellano-Bond and autoregressive latent trajectory models have various shortcomings. By contrasting these approaches, we clarify the benefits and drawbacks of common methods for modeling panel data, including the GCLM approach we propose. We conclude with a discussion of issues regarding causal inference, including difficulties in separating different types of time-invariant and time-varying effects over time.