Model Interpretation Through Lower-Dimensional Posterior Summarization

Mindsets, contexts, and college enrollment: Taking the long view on growth mindset beliefs at the transition to high school

Socioeconomic disparities in academic progress have persisted throughout the history of the United States, and growth mindset interventions-which shift beliefs about the malleability of intelligence-have shown promise in reducing these disparities. Both the study of such disparities and how to remedy them can benefit from taking the "long view" on adolescent development, following the tradition of John Schulenberg. To do so, this study focuses on the role of growth mindsets in short-term academic progress during the transition to high school as a contributor to longer-term educational attainment. Guided by the Mindset × Context perspective, we analyzed new follow-up data to a one-year nationally representative study of ninth graders (National Study of Learning Mindsets, n = 10,013; 50% female; 53% white; 63% from lower-SES backgrounds). A conservative Bayesian analysis revealed that adolescents' growth mindset beliefs at the beginning of ninth grade predicted their enrollment in college 4 years later. These patterns were stronger for adolescents from lower-SES backgrounds, and there was some evidence that the ninth-grade math teacher's support for the growth mindset moderated student mindset effects. Thus, a time-specific combination of student and teacher might alter long-term trajectories by enabling adolescents to develop and use beliefs at a critical transition point that supports a cumulative pathway of course-taking and achievement into college. Notably, growth mindset became less predictive of college enrollment after the onset of the COVID-19 pandemic, which occurred in the second year of college and introduced structural barriers to college persistence.

A BAYESIAN MACHINE LEARNING APPROACH FOR ESTIMATING HETEROGENEOUS SURVIVOR CAUSAL EFFECTS: APPLICATIONS TO A CRITICAL CARE TRIAL

Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development in tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for many participants in which case principal stratification is an appealing framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate mean models for the potential outcomes and latent stratum membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by biologic sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and degree of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field.

Mindset × Context: Schools, Classrooms, and the Unequal Translation of Expectations into Math Achievement

When do adolescents' dreams of promising journeys through high school translate into academic success? This monograph reports the results of a collaborative effort among sociologists and psychologists to systematically examine the role of schools and classrooms in disrupting or facilitating the link between adolescents' expectations for success in math and their subsequent progress in the early high school math curriculum. Our primary focus was on gendered patterns of socioeconomic inequality in math and how they are tethered to the school's peer culture and to students' perceptions of gender stereotyping in the classroom. To do this, this monograph advances Mindset × Context Theory. This orients research on educational equity to the reciprocal influence between students' psychological motivations and their school-based opportunities to enact those motivations. Mindset × Context Theory predicts that a student's mindset will be more strongly linked to developmental outcomes among groups of students who are at risk for poor outcomes, but only in a school or classroom context where there is sufficient need and support for the mindset. Our application of this theory centers on expectations for success in high school math as a foundational belief for students' math progress early in high school. We examine how this mindset varies across interpersonal and cultural dynamics in schools and classrooms. Following this perspective, we ask: 1. Which gender and socioeconomic identity groups showed the weakest or strongest links between expectations for success in math and progress through the math curriculum? 2. How did the school's peer culture shape the links between student expectations for success in math and math progress across gender and socioeconomic identity groups? 3. How did perceptions of classroom gender stereotyping shape the links between student expectations for success in math and math progress across gender and socioeconomic identity groups? We used nationally representative data from about 10,000 U.S. public school 9th graders in the National Study of Learning Mindsets (NSLM) collected in 2015-2016-the most recent, national, longitudinal study of adolescents' mindsets in U.S. public schools. The sample was representative with respect to a large number of observable characteristics, such as gender, race, ethnicity, English Language Learners (ELLs), free or reduced price lunch, poverty, food stamps, neighborhood income and labor market participation, and school curricular opportunities. This allowed for generalization to the U.S. public school population and for the systematic investigation of school- and classroom-level contextual factors. The NSLM's complete sampling of students within schools also allowed for a comparison of students from different gender and socioeconomic groups with the same expectations in the same educational contexts. To analyze these data, we used the Bayesian Causal Forest (BCF) algorithm, a best-in-class machine-learning method for discovering complex, replicable interaction effects. Chapter IV examined the interplay of expectations, gender, and socioeconomic status (SES; operationalized with maternal educational attainment). Adolescents' expectations for success in math were meaningful predictors of their early math progress, even when controlling for other psychological factors, prior achievement in math, and racial and ethnic identities. Boys from low-SES families were the most vulnerable identity group. They were over three times more likely to not make adequate progress in math from 9th to 10th grade relative to girls from high-SES families. Boys from low-SES families also benefited the most from their expectations for success in math. Overall, these results were consistent with Mindset × Context Theory's predictions. Chapters V and VI examined the moderating role of school-level and classroom-level factors in the patterns reported in Chapter IV. Expectations were least predictive of math progress in the highest-achieving schools and schools with the most academically oriented peer norms, that is, schools with the most formal and informal resources. School resources appeared to compensate for lower levels of expectations. Conversely, expectations most strongly predicted math progress in the low/medium-achieving schools with less academically oriented peers, especially for boys from low-SES families. This chapter aligns with aspects of Mindset × Context Theory. A context that was not already optimally supporting student success was where outcomes for vulnerable students depended the most on student expectations. Finally, perceptions of classroom stereotyping mattered. Perceptions of gender stereotyping predicted less progress in math, but expectations for success in math more strongly predicted progress in classrooms with high perceived stereotyping. Gender stereotyping interactions emerged for all sociodemographic groups except for boys from high-SES families. The findings across these three analytical chapters demonstrate the value of integrating psychological and sociological perspectives to capture multiple levels of schooling. It also drew on the contextual variability afforded by representative sampling and explored the interplay of lab-tested psychological processes (expectations) with field-developed levers of policy intervention (school contexts). This monograph also leverages developmental and ecological insights to identify which groups of students might profit from different efforts to improve educational equity, such as interventions to increase expectations for success in math, or school programs that improve the school or classroom cultures.

Where and with whom does a brief social-belonging intervention promote progress in college?

A promising way to mitigate inequality is by addressing students' worries about belonging. But where and with whom is this social-belonging intervention effective? Here we report a team-science randomized controlled experiment with 26,911 students at 22 diverse institutions. Results showed that the social-belonging intervention, administered online before college (in under 30 minutes), increased the rate at which students completed the first year as full-time students, especially among students in groups that had historically progressed at lower rates. The college context also mattered: The intervention was effective only when students' groups were afforded opportunities to belong. This study develops methods for understanding how student identities and contexts interact with interventions. It also shows that a low-cost, scalable intervention generalizes its effects to 749 4-year institutions in the United States.

Causal Bayesian machine learning to assess treatment effect heterogeneity by dexamethasone dose for patients with COVID-19 and severe hypoxemia

The currently recommended dose of dexamethasone for patients with severe or critical COVID-19 is 6 mg per day (mg/d) regardless of patient features and variation. However, patients with severe or critical COVID-19 are heterogenous in many ways (e.g., age, weight, comorbidities, disease severity, and immune features). Thus, it is conceivable that a standardized dosing protocol may not be optimal. We assessed treatment effect heterogeneity in the COVID STEROID 2 trial, which compared 6 mg/d to 12 mg/d, using a causal inference framework with Bayesian Additive Regression Trees, a flexible modeling method that detects interactive effects and nonlinear relationships among multiple patient characteristics simultaneously. We found that 12 mg/d of dexamethasone, relative to 6 mg/d, was probably associated with better long-term outcomes (days alive without life support and mortality after 90 days) among the entire trial population (i.e., no signals of harm), and probably more beneficial among those without diabetes mellitus, that were older, were not using IL-6 inhibitors at baseline, weighed less, or had higher level respiratory support at baseline. This adds more evidence supporting the use of 12 mg/d in practice for most patients not receiving other immunosuppressants and that additional study of dosing could potentially optimize clinical outcomes.

Teacher Mindsets Help Explain Where a Growth-Mindset Intervention Does and Doesn't Work

A growth-mindset intervention teaches the belief that intellectual abilities can be developed. Where does the intervention work best? Prior research examined school-level moderators using data from the National Study of Learning Mindsets (NSLM), which delivered a short growth-mindset intervention during the first year of high school. In the present research, we used data from the NSLM to examine moderation by teachers' mindsets and answer a new question: Can students independently implement their growth mindsets in virtually any classroom culture, or must students' growth mindsets be supported by their teacher's own growth mindsets (i.e., the mindset-plus-supportive-context hypothesis)? The present analysis (9,167 student records matched with 223 math teachers) supported the latter hypothesis. This result stood up to potentially confounding teacher factors and to a conservative Bayesian analysis. Thus, sustaining growth-mindset effects may require contextual supports that allow the proffered beliefs to take root and flourish.

Fast, Optimal, and Targeted Predictions using Parametrized Decision Analysis

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions-including linear actions with sparsity constraints for targeted variable selection-we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.

Combining shrinkage and sparsity in conjugate vector autoregressive models

Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models. But at the same time, they introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of postprocessing posterior estimates of a conjugate Bayesian VAR to effectively perform equation-specific covariate selection. Compared with existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variance-covariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability. We illustrate our approach by means of two applications. The first application uses synthetic data to investigate the properties of the model across different data-generating processes, and the second application analyzes the predictive gains from sparsification in a forecasting exercise for U.S. data.