Regression discontinuity gallery: Simulations in R

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I recently presented a paper on spatial regression discontinuity at the annual conference of the American Evaluation Association in Orlando. I wanted to graphically illustrate regression discontinuity and its spatial analogue, so I simulated some examples in Rlogo.jpg. Plots such as these and William Trochim's can be a good way to convey some of the key concepts of regression discontinuity design and analysis, such as curvilinear relationships between the assignment and outcome variable, local treatment effects, and the questionable validity of extrapolating program inferences beyond the cutoff.

Local effect (left) and no effect (right) with continuous linear relationship between the assignment and outcome variable
Local_Effect_Continuous_Linear_Relationship.png No_Effect_Continuous_Linear_Relationship.png

Average effect (left) and no effect (right) with no relationship between the assignment and outcome variable
Average_Effect_No_Relationship.png No_Effect_No_Relationship.png

Local effects with curvilinear relationships between the assignment and outcome variable
Local_Effect_Continuous_Quadratic_Relationship.png Local_Effect_Continuous_Cubic_Relationship.png

Extrapolation: Local effect (left) and no local effect (right) with potentially larger effects beyond the cutoff due to discontinuous linear relationship between the assignment and outcome variable*
Local_Effect_Discontinuous_Linear_Relationship.png No_Effect_Discontinuous_Linear_Relationship.png
*Note: Extrapolations beyond the cutoff are rarely valid. Repetitious and abundant distal pretest observations may support extrapolating effect size estimates beyond the cutoff.

Spatial regression discontinuity: Local effect (left) and no effect (right) with continuous linear relationship between the assignment (distance from border) and outcome variable
Local_Effect_Continuous_Linear_SpatialRD.png No_Effect_Continuous_Linear_Relationship_SpatialRD.png

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