6.3. Verifying the Common Support Condition
Another important step in investigating the validity or performance of the propensity scorematching estimation is to verify the common support or overlap condition. We assume that the probability of participation in an intervention, conditional on observed characteristics, lies between 0 and 1 (implying participation is not perfectly predicted, that is, 0 < P( D = 1 | X ) < 1). This assumption is critical to estimation, as it ensures that units with the same X values have a positive probability of being both participants and nonparticipants. Checking the overlap or region of common support between treatment and comparison groups can be done with relatively straightforward strategies. One obvious approach is through visual inspection of the propensity score distributions for both the treatment and comparison groups. Simple histograms or density-distribution plots of propensity scores for the two groups, along with a comparison of the minimum and maximum propensity score values in each distribution, can typically give the researcher a good, initial reading of the extent to which there is overlap in the propensity scores of the treatment and comparison units. See Box 11 for an example.
Box 11: Visual Inspection of the Propensity Scores
In addition to the mean equality tests presented in box 10, it is useful to plot the distributions of the propensity scores for treated and untreated groups to visually check the overlap condition and to see if the matching is able to make the distributions more similar. The distributions of the propensity scores, before and after the matching, for the case of PROMSA are plotted in figure B.2.
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