In the secondary analysis, the geographic location of the address of the school was used as the center of the school (the centroid), and the gun-free zone was imagined as a circle with a 1000-foot radius surrounding this point. This is equivalent to a circle with an area of 3,141,592.7 ft2. To create unexposed, gun-allowing units of the same area, the area of the circle was doubled (therefore 6,283,185.4 ft2), which is equivalent to a radius of 1414.2 ft. Therefore, when the inner circle is subtracted from the outer circle, the two areas—gun-free school zone and gun-allowing zone—are equal. For consistency, 414.2 feet (1414.2 minus 1000 feet) was used in the primary analysis as the distance extending from the gun-free school zone to the end of the gun-allowing zone.

$$_\sim QuasiPoisson\left(\exp \left(_\right)\right)$$

$$_=_0+_i+_i_+_i_+\log \left(_i\right)$$

$$_i\sim N\Big(0,_b^2\Big)$$

Where:

i indexes on pair IDs

j = indexes observations within IDs.

n = counts of interpersonal shootings for unit i

A = area for each unit i, acting as an offset

β 0 = overall intercept

b i= random intercepts

X = gun-free zone = 1; gun-allowing zone = 0

L = street length (km)