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From |
"Dimitriy V. Masterov" <dvmaster@gmail.com> |

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.

**Follow-Ups**:**Re: st: Computing minimum driving distance to an area (rather than a specific point)***From:*"Dimitriy V. Masterov" <dvmaster@gmail.com>

**References**:**st: Computing minimum driving distance to an area (rather than a specific point)***From:*Jen Zhen <jenzhen99@gmail.com>

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