A conservative way to decide how to refine the model would be to begin by examining the highest-order term in the current model and its interaction. The final model may still include unnecessary terms but there are likely to be fewer of these and, consequently, efficiency should be greater. Model specification procedures which involve dropping any term at any stage of the analysis are more dangerous and more likely to yield biased estimates because of the considerable multicolinearity which will exist between the terms in the model. It's easier to understand how data from a RD Design is analyzed by showing an example. The data for this example are shown in Figure 10.
Several things are apparent visually.
First, there is a whopping treatment effect. In fact, Figure 10 shows simulated data where the true treatment effect is 10 points. Thus, the initial model we'll specify is the full quadratic one shown above in Figure 9. The results of our initial specification are shown in Figure 11. But notice that there is evidence that several of the higher-order terms are not statistically significant and may not be needed in the model.