Regression-Discontinuity Design. A powerful, alternative design for causal inference that is underutilized in the health and intervention sciences is the regression discontinuity (RD) design (Thistlewaite & Campbell, 1960). In its simplest form, the RD design involves the use of a screening measure of some form that is continuous and given to all persons. A cut point or criterion is set, which determines whether individuals are assigned to an intervention condition or a comparison condition. The cut point is determined on the basis of need or a cost-benefit analysis. If an analysis of an outcome measure shows a change in the mean-level or slope-angle that occurs for individuals at the cut point, then a causal conclusion of the effectiveness
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The horizontal axis is the screening measure and the vertical axis is the dependent variable, math test scores. The counterfactual regression line is what the regression line would look like if the treatment had no effect. In a typical RD design, the form of the counterfactual regression line is assumed. It can, however, be estimated by adding a pretest comparison group, as Wing and Cook (2013) suggested (as detailed later). Usually the counterfactual regression line will be smooth across the cutoff point, as it is in Figure 2. Assuming a smooth pretest line across the cutoff point, a discontinuity in the actual regression line indicates a treatment effect, with the magnitude of the treatment effect being measured by the size of the discontinuity (Braden and Bryant, 1990). The discontinuity in Figure 2 indicates that the treatment did have an …show more content…
Conversely, if 0 was in place of 1, it would be the outcome of the untreated group. Pre_it is a dummy variable identifying observations during a pretest period prior where the treatment has yet to be implemented. If Pre_it=1, this would reflect observations for the treatment group during the pretest period. The θ_P parameter is a fixed difference of conditional mean outcomes across pretest and posttest periods. A unknown smoothing function is represented by the g(A_i ), and it is assumed to be constant across the pre- and posttest time periods (for further discussion of a smoothing parameter see Peng, 1999). The relationship between the assignment variable and the outcome variable during the pretest period are the foundation of this design, it allows for extrapolation beyond the assignment cut-off criterion in the posttest period (Wing and Cook,
The horizontal axis is the screening measure and the vertical axis is the dependent variable, math test scores. The counterfactual regression line is what the regression line would look like if the treatment had no effect. In a typical RD design, the form of the counterfactual regression line is assumed. It can, however, be estimated by adding a pretest comparison group, as Wing and Cook (2013) suggested (as detailed later). Usually the counterfactual regression line will be smooth across the cutoff point, as it is in Figure 2. Assuming a smooth pretest line across the cutoff point, a discontinuity in the actual regression line indicates a treatment effect, with the magnitude of the treatment effect being measured by the size of the discontinuity (Braden and Bryant, 1990). The discontinuity in Figure 2 indicates that the treatment did have an …show more content…
Conversely, if 0 was in place of 1, it would be the outcome of the untreated group. Pre_it is a dummy variable identifying observations during a pretest period prior where the treatment has yet to be implemented. If Pre_it=1, this would reflect observations for the treatment group during the pretest period. The θ_P parameter is a fixed difference of conditional mean outcomes across pretest and posttest periods. A unknown smoothing function is represented by the g(A_i ), and it is assumed to be constant across the pre- and posttest time periods (for further discussion of a smoothing parameter see Peng, 1999). The relationship between the assignment variable and the outcome variable during the pretest period are the foundation of this design, it allows for extrapolation beyond the assignment cut-off criterion in the posttest period (Wing and Cook,