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…

Regression discontinuity (RD) designs are increasingly used for causal evaluations. However, the literature contains little guidance for conducting a moderation analysis within an RDD context. The current article focuses on moderation with a single binary variable. A simulation study compares: (1) different bandwidth selectors and (2) local…

Many students of statistics and econometrics express frustration with the way a problem known as "bad control" is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is…

Three quantitative methods are compared for their ability to understand different COVID-19 fatality ratios in 33 OECD countries. Linear regression provides a limited overview without sensitivity to the diversity of cases. Cluster Analysis and Dynamic Patterns Synthesis (DPS) gives scrutiny to the granularity of case similarities and differences,…

Causal asymmetry is a situation where the causal factors under study are more suitable for explaining the outcome than its absence (or vice versa); they do not explain both equally well. In such a situation, presence of a cause leads to presence of the effect, but absence of the cause may not lead to absence of the effect. A conceptual discussion…

Previous research explicates ordinal and disordinal interactions through the concept of the "crossover point." This point is determined via simple regression models of a focal predictor at specific moderator values and signifies the intersection of these models. An interaction effect is labeled as disordinal (or ordinal) when the…

Regression discontinuity (RD) designs have gained significant popularity as a quasi-experimental device for evaluating education programs and policies. In this paper, we present a comprehensive review of RD designs, focusing on the continuity-based framework, the most widely adopted RD framework. We first review the fundamental aspects of RD…

A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

The view that empirical strategies in economics should be transparent and credible now goes almost without saying. The local average treatment effects (LATE) framework for causal inference helped make this so. The LATE theorem tells us for whom particular instrumental variables (IV) and regression discontinuity estimates are valid. This lecture…

Causal mediation analysis is a popular approach for investigating whether the effect of an exposure on an outcome is through a mediator to better understand the underlying causal mechanism. In recent literature, mediation analysis with multiple mediators has been proposed for continuous and dichotomous outcomes. In contrast, methods for mediation…

We are sometimes forced to use the Interrupted Time Series (ITS) design as an identification strategy for potential policy change, such as when we only have a single treated unit and cannot obtain comparable controls. For example, with recent county- and state-wide criminal justice reform efforts, where judicial bodies have changed bail setting…

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for…

Estimation of causal effects requires making comparisons across groups of observations exposed and not exposed to a a treatment or cause (intervention, program, drug, etc). To interpret differences between groups causally we need to ensure that they have been constructed in such a way that the comparisons are "fair." This can be…

A wide range of machine-learning-based approaches have been developed in the past decade, increasing our ability to accurately model nonlinear and nonadditive response surfaces. This has improved performance for inferential tasks such as estimating average treatment effects in situations where standard parametric models may not fit the data well.…

The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show…