Causal-formative indicators are often used in social science research. To achieve identification in causal-formative indicator modeling, constraints need to be applied. A conventional method is to constrain the weight of a formative indicator to be 1. The selection of which indicator to have the fixed weight, however, may influence statistical…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In…

The consequence of a change in school leadership (e.g., principal turnover) on student achievement has important implications for education policy. The impact of such an event can be estimated via the popular Difference in Difference (DiD) estimator, where those schools with a turnover event are compared to a selected set of schools that did not…

Regression discontinuity (RD) designs are increasingly used for causal evaluations. For example, if a student's need for a literacy intervention is determined by a low score on a past performance indicator and that intervention is provided to all students who fall below a cutoff on that indicator, an RD study can determine the intervention's main…

Most methods for structural equation modeling (SEM) focused on the analysis of covariance matrices. However, "Historically, interesting psychological theories have been phrased in terms of correlation coefficients." This might be because data in social and behavioral sciences typically do not have predefined metrics. While proper methods…

In the complex world of educational policy, causal inferences will be debated. As we review non-experimental designs in educational policy, we focus on how to clarify and focus the terms of debate. We begin by presenting the potential outcomes/counterfactual framework and then describe approximations to the counterfactual generated from the…

Recurrent event analyses have found a wide range of applications in biomedicine, public health, and engineering, among others, where study subjects may experience a sequence of event of interest during follow-up. The R package reReg offers a comprehensive collection of practical and easy-to-use tools for regression analysis of recurrent events,…

Sensitivity analysis, a statistical method crucial for validating inferences across disciplines, quantifies the conditions that could alter conclusions (Razavi et al., 2021). One line of work is rooted in linear models and foregrounds the sensitivity of inferences to the strength of omitted variables (Cinelli & Hazlett, 2019; Frank, 2000). A…

Mediation analysis plays an important role in understanding causal processes in social and behavioral sciences. While path analysis with composite scores was criticized to yield biased parameter estimates when variables contain measurement errors, recent literature has pointed out that the population values of parameters of latent-variable models…

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and…

Parallel process latent growth curve mediation models (PP-LGCMMs) are frequently used to longitudinally investigate the mediation effects of treatment on the level and change of outcome through the level and change of mediator. An important but often violated assumption in empirical PP-LGCMM analysis is the absence of omitted confounders of the…

We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning (AutoDML). These popular "doubly robust" or "de-biased machine learning estimators" combine outcome modeling with balancing weights -- weights that achieve covariate balance directly in lieu of estimating and…

Given the increased focus of educational research on what works for whom and under what circumstances over the last decade, educational researchers are increasingly turning toward mixture models to identify heterogeneous subgroups among students. Such data are inherently nested, as students are nested within classrooms and schools. Yet there has…

Mediation analysis is widely used to study whether the effect of an independent variable on an outcome is transmitted through a mediator. Bayesian methods have become increasingly popular for mediation analysis. However, limited research has been done on formal Bayesian hypothesis testing of mediation. Although hypothesis testing using Bayes…