From lwaller@sph.emory.edu Fri Jun 4 05:50:49 1999 Received: from mxu2.u.washington.edu (mxu2.u.washington.edu [140.142.32.9]) by lists.u.washington.edu (8.9.3+UW99.02/8.9.3+UW99.01) with ESMTP id FAA38550 for ; Fri, 4 Jun 1999 05:50:48 -0700 Received: from viper.sph.emory.edu (lwaller@viper.sph.emory.edu [170.140.4.1]) by mxu2.u.washington.edu (8.9.3+UW99.02/8.9.3+UW99.01) with ESMTP id FAA13929 for ; Fri, 4 Jun 1999 05:50:47 -0700 Received: from localhost (lwaller@localhost) by viper.sph.emory.edu (8.9.3/8.9.3) with ESMTP id IAA24067 for ; Fri, 4 Jun 1999 08:50:42 -0400 (EDT) Date: Fri, 4 Jun 1999 08:50:42 -0400 (EDT) From: Lance Waller X-Sender: lwaller@viper To: waphgis@u.washington.edu Subject: Re: areal interpolation In-Reply-To: <017801beae12$91a979c0$7b790518@olmpi1.wa.home.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII The "beauty" of a Bayesian approach is that the analyst obtains an entire distribution for the interpolated values, not just a point estimate. So you can see a histogram of the whole thing (to check skewness, etc), make credible sets (Bayesian confidence intervals), or just the mean/median/mode as a point estimate. The "bad news" is that implementations generally require custom programming (in C or FORTRAN). The canned routines for areal interpolation usually follow an algorithm similar to what was called the "cookie cutter" approach by Tim Aldrich in North Carolina: Suppose you want the population in a circle that overlaps several census block groups (or other favorite set of regions). (1) add the circle as a layer in your GIS (2) find the proportion of area falling within the circle for any block group intersecting the circle. (3) Assign the same proportion of people as area from the block group to the circle. (4) Add up the number of people you've assigned to the circle. This assumes a homogeneous population density within block groups, which may be a fine assumption for some applications, and not so great for others. (This is the basic algorithm described on the YRAD webpage Richard mentioned...which contains a nice description of many issues involved, thanks for pointing out Richard!) The work described in Alice Rarig's message by demographers is more complex and (as you read in her message) often involves temporal as well as spatial interpolation. My guess is that the more sophisticated interpolations require specialized programming (but would be interested in comments to the contrary). My impression from Tom's original email is that he was looking to fit a model where the outcome and explanatory variables were measured on different zonal systems (also goal of YRAD). The Mugglin papers are based on Andy's dissertation, which in turn was based on some papers by Flowerdew and Green that address the areal interpolation issue fairly nicely. (They propose an EM-algorithm that provides point estimates but not interval estimates, if I remember correctly). A review appears in: Flowerdew, R. and Green, M. (1992) Developments in areal interpolation methods. Annals of Regional Science 26, 67-78. Areal interpolation is an interesting and important problem, especially since the layering capabilities of GIS link data that one can't quite analyze using traditional methods. Lance Waller On Thu, 3 Jun 1999, Richard E. Hoskins wrote: > DO any of those papers explain how to calculate a standard error for an > aerial interpolation? > > Richard Hoskins > > > ----- Original Message ----- > From: Tom Howze > To: > Sent: Thursday, June 03, 1999 2:23 PM > Subject: RE: areal interpolation > > > > Thanks Lance. This is exactly what I was hoping for. > > > > I've read some of the Flowerdew papers. I'll check these out. > > > > Cheers, > > > > Tom > > > > -----Original Message----- > > From: WAPHGIS-owner@u.washington.edu > [mailto:WAPHGIS-owner@u.washington.edu] > > On Behalf Of Lance Waller > > Sent: Thursday, June 03, 1999 1:19 PM > > To: waphgis@u.washington.edu > > Subject: Re: areal interpolation > > > > Tom: > > > > You might check some recent papers by Andy Mugglin and Brad Carlin > > at the University of Minnesota. > > > > Mugglin, A., and Carlin, B.P. (1998) Hierarchical modeling in GIS: > > population interpolation over incompatible zones. Journal of > > Agricultural, Biological, and Environmental Statistics, 3, 111-130. > > (this references other literature including some work by Flowerdew > > and Green that you may be interested in). > > > > Mugglin, A.S., Carlin, B.P., Zhu, L., and Conlon E. (1999) ``Bayesian > > areal interpolation, estimation, and smoothing: an inferential > > approach for GIS'' to appear in Environment and Planning A. > > > > Both are available (as compressed postscript files) at > > > > http://www.biostat.umn.edu/cgi-bin/rrs?print+1997 > > > > (under the research report, 1997 listing at http://www.biostat.umn.edu > > if the direct link doesn't work). > > > > Hope this helps. > > > > Lance Waller > > > > > > On Thu, 3 Jun 1999, Tom Howze wrote: > > > > > > > > Greetings. > > > > > > I just signed on to this list in the last month and apologize if this > > topic > > > has been covered recently. > > > > > > I am looking for any reference material (including people :)) that might > > aid > > > me in my quest for an accurate methodology to perform small area > > estimation, > > > or interpolation. > > > > > > I am working to collect archival data at various geographies that are > > > indicators of risk and protective factors for adolescent substance abuse > > and > > > delinquency. Much of the data I'm receiving is at a larger geography > > > (county, zip code, etc.) than the areas being studied. I am looking to > > find > > > a method to estimate or interpolate the data from the larger geographies > > to > > > smaller geographies (blocks, block groups, neighborhoods, etc.). > > > > > > Has anyone worked on this problem and what are some of the basic data > > > necessities needed to be able to estimate the smaller areas accurately? > I > > > have seen a couple different methods of doing this, but am looking for > > > any/all hands on experience you might have. > > > > > > Cheers, > > > > > > Tom Howze > > > Geographer > > > Social Development Research Group > > > University of Washington > > > > > > > > > > > > > > > .