Through a sensitivity analysis, the analyst attempts to determine whether a conclusion of causal inference could be easily reversed by a plausible violation of an identification assumption. Analytic conclusions that are harder to alter by such a violation are expected to add a higher value to scientific knowledge about causality. This article presents a weighting-based approach to sensitivity analysis for causal mediation studies. Extending the ratio-of-mediatorprobability weighting (RMPW) method for identifying natural indirect effect and natural direct effect, the new strategy assesses potential bias in the presence of omitted pretreatment or posttreatment covariates. Such omissions may undermine the causal validity of analytic conclusions. The weighting approach to sensitivity analysis reduces the reliance on functional form assumptions and removes constraints on the measurement scales for the mediator, the outcome, and the omitted covariates. In its essence, the discrepancy between a new weight that adjusts for an omitted confounder and an initial weight that omits the confounder captures the role of the confounder that contributes to the bias. The effect size of the bias due to omitted confounding of the mediator-outcome relationship is a product of two sensitivity parameters, one associated with the degree to which the omitted confounders predict the mediator and the other associated with the degree to which they predict the outcome. The article provides an application example and concludes with a discussion of broad applications of this new approach to sensitivity analysis. Online Supplemental Material includes R code for implementing the proposed sensitivity analysis procedure.

Maintaining learning engagement throughout adolescence is critical for long‐term academic success. This research sought to understand the role of metacognition and motivation in predicting adolescents' engagement in math learning over time. In two longitudinal studies with 2,325 and 207 adolescents (ages 11–15), metacognitive skills, interest, and self‐control each uniquely predicted math engagement. Additionally, metacognitive skills worked with interest and self‐control interactively to shape engagement. In Study 1, metacognitive skills and interest were found to compensate for one another. This compensatory pattern further interacted with time in Study 2, indicating that the decline in engagement was forestalled among adolescents who had either high metacognitive skills or high interest. Both studies also uncovered an interaction between metacognitive skills and self‐control, though with slightly different interaction patterns.

When a multisite randomized trial reveals between-site variation in program impact, methods are needed for further investigating heterogeneous mediation mechanisms across the sites. We conceptualize and identify a joint distribution of site-specific direct and indirect effects under the potential outcomes framework. A method-of-moments procedure incorporating ratio-of-mediator-probability weighting (RMPW) consistently estimates the causal parameters. This strategy conveniently relaxes the assumption of no Treatment × Mediator interaction while greatly simplifying the outcome model specification without invoking strong distributional assumptions. We derive asymptotic standard errors that reflect the sampling variability of the estimated weight. We also offer an easy-to-use R package, , that implements the proposed method. It is freely available at the Comprehensive R Archive Network (http://cran.r-project.org/web/packages/MultisiteMediation).

Summary This study provides a template for multisite causal mediation analysis using a comprehensive weighting‐based analytic procedure that enhances external and internal validity. The template incorporates a sample weight to adjust for complex sample and survey designs, adopts an inverse probability of treatment weight to adjust for differential treatment assignment probabilities, employs an estimated non‐response weight to account for non‐random non‐response and utilizes a propensity‐score‐based weighting strategy to decompose flexibly not only the population average but also the between‐site heterogeneity of the total programme impact. Because the identification assumptions are not always warranted, a weighting‐based balance checking procedure assesses the remaining overt bias, whereas a weighting‐based sensitivity analysis further evaluates the potential bias related to omitted confounding or to propensity score model misspecification. We derive the asymptotic variance of the estimators for the causal effects that account for the sampling uncertainty in the estimated weights. The method is applied to a reanalysis of the data from the National Job Corps Study.

This article used self-regulated learning as a theoretical lens to examine the individual and interactive associations between a growth mindset and metacognition on math engagement for adolescent students from socioeconomically disadvantaged schools. Across three longitudinal studies with 207, 897, and 2,325 11-to 15-yearold adolescents, students' beliefs that intelligence is malleable and capable of growth over time only predicted higher math engagement among students possessing the metacognitive skills to reflect upon and be aware of their learning progress. The results suggest that metacognitive skills may be necessary for students to realize their growth mindset. Thus, growth mindsets and metacognitive skills should be promoted together to capitalize on the mutually reinforcing effects of each, especially among students in socioeconomically disadvantaged schools.Xu Qin and Juan Del Toro have equal intellectual contribution to this manuscript.This study was supported by funding from National Science Foundation #1561382 and #1315943 to the first author (Ming-Te Wang).Author contribution: Wang conceived of the study (e.g., study questions, study design, literature review, result interpretation, development of the writing outline), and drafted and revised the full manuscript; Zepeda conceived of the study and drafted and revised part of the introduction and discussion sections; Qin and Del Toro performed the data analysis, participated in the interpretation of the data, and drafted the method section; Binning participated in the result interpretation and provided feedback on the draft. All authors read and approved the final manuscript.