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…

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.…

Doubly robust (DR) estimators that combine regression adjustments and inverse probability weighting (IPW) are widely used in causal inference with observational data because they are claimed to be consistent when either the outcome or the treatment selection model is correctly specified (Scharfstein et al., 1999). This property of "double…

Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level…

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…

This article reviews important statistical methods for estimating the impact of interventions on outcomes in education settings, particularly programs that are implemented in field, rather than laboratory, settings. We begin by describing the causal inference challenge for evaluating program effects. Then four research designs are discussed that…

Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand…

The central purpose of this article is to provide an overview of the many ways in which special educators can generate and think about causal inference to inform policy and practice. Consideration of causality across different lenses can be carried out by engaging in multiple method and mixed methods ways of thinking about inference. This article…

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)…

When randomized experiments are infeasible, quasi-experimental designs can be exploited to evaluate causal treatment effects. The strongest quasi-experimental designs for causal inference are regression discontinuity designs, instrumental variable designs, matching and propensity score designs, and comparative interrupted time series designs. This…

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

A valuable extension of the single-rating regression discontinuity design (RDD) is a multiple-rating RDD (MRRDD). To date, four main methods have been used to estimate average treatment effects at the multiple treatment frontiers of an MRRDD: the "surface" method, the "frontier" method, the "binding-score" method, and…

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, "M", and the outcome, "Y". This assumption holds if individuals are randomly…

Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…