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# Re: st: Computing minimum driving distance to an area (rather than a specific point)

 From "Dimitriy V. Masterov" To statalist@hsphsun2.harvard.edu Subject Re: st: Computing minimum driving distance to an area (rather than a specific point) Date Mon, 16 Apr 2012 09:46:38 -0400

```Jen,

In a geometric sense, you can think of your municipalities as
polygons. Every polygon has at least 4 distinct barycenters (i.e.,
centers of mass), so there's no straightforward answer to your
question.

1) The barycenter of its vertices.
2) The barycenter of its edges.
3) Its barycenter as a polygon, which can be obtained decomposing it
into triangles. The area-weighted average of these barycenters is the
polygon's barycenter.
4) X-weighted centroid, where X might be a people or blocks or block groups.

These may coincide in special cases, but are generally distinct
points. It may also happen that many of these centers are not
necessarily located within the interior of a polygon. Hopefully your
municipalities will be mostly convex, so this should be less of a
problem. You do have to worry that your barrycenter is in the middle
of lake, for example.

The three types differ on where the mass is presumed located: it
either is entirely on the vertices, spread uniformly on the edges, or
spread throughout the polygon itself, either uniformly or not.

You might be able to hack such calculations in Stata using the
coordinates file that you create when you convert the shapefile for
the municipal boundaries, but I think there's an easier way. I would
get the shapefile for the municipalities. Such files will usually have
columns for the lat and lon of the centroid. It's what ArcGIS uses
when you choose to label an area. Use that as your center.
Alternatively, you might want to see if you can track down a
population-weighted centroid as that seems relevant to your problem.
```