In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of post-treatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

Recent critiques of physics education research (PER) studies have revoiced the critical issues when drawing causal inferences from observational data where no intervention is present. In response to a call for a "causal reasoning primer" in PER, this paper discusses some of the fundamental issues in statistical causal inference. In…

Growing scholarship on the pedagogical applications of statistical modeling is currently taking place to create adaptations of this practice to introduce novices to statistics. These are intended to promote novices' reasoning, and are typically void of formal mathematical procedures and calculations. In this article, we define the potential…

Although there is recognition that there may be differential outcomes for groups of students within schools, examination of outcomes for subgroups presents challenges to researchers and policymakers. It complicates analytic procedures, particularly when the number of students per school in the subgroup is small. We explored five alternatives for…

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

Analyzing heterogeneous treatment effects (HTEs) plays a crucial role in understanding the impacts of educational interventions. A standard practice for HTE analysis is to examine interactions between treatment status and preintervention participant characteristics, such as pretest scores, to identify how different groups respond to treatment.…

Human one-on-one coaching involves complex multimodal interactions. Successful coaching requires teachers to closely monitor students' cognitive-affective states and provide support of optimal type, timing, and amount. However, most of the existing human tutoring studies focus primarily on verbal interactions and have yet to incorporate the rich…

Analyzing heterogeneous treatment effects (HTE) plays a crucial role in understanding the impacts of educational interventions. A standard practice for HTE analysis is to examine interactions between treatment status and pre-intervention participant characteristics, such as pretest scores, to identify how different groups respond to treatment.…

This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central…

Methods to assess the significance of mediated effects in education and the social sciences are well studied and fall into two categories: single sample methods and computer-intensive methods. A popular single sample method to detect the significance of the mediated effect is the test of joint significance, and a popular computer-intensive method…

The concept of direction dependence has attracted growing attention due to its potential to help decide which of two competing linear regression models (X ? Y or Y ? X) is more likely to reflect the correct causal flow. Several tests have been proposed to evaluate hypotheses compatible with direction dependence. In this issue, Thoemmes (2015)…

The development in information science has enabled an explosive growth of data, which attracts more and more researchers to engage in the field of big data analytics. Noticeably, in many real-world applications, large amounts of data are imbalanced data since the events of interests occur infrequently. Classification of imbalanced data is an…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…