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I have some data gathered from a survey conducted within my city. All responses include an approximate geo location of where they were gathered (accurate to probably a couple of hundred yards which is relatively small), and things like the respondents age, sex, income range, number of dependents, etc. There are approx. 4000 responses.

What I would like to is to be able to generate what I guess you would call a model, so that given a geo point (or box) I could characterize the typical respondent from there (it doesn't really have to be really rigorous, although some kind of formal confidence measurement would be nice).

So, is the right thing to do to simply treat all the gathered attributes separately and say "Well the age of your typical respondent in that area is m with stdev s, and their income range is ..., etc."

Or is there some better way to analyse the data together to get a better profile of the respondents.

Some key phrases to google would even help at this stage, because I'm a bit lost. I thought this might be "data fusion" but I don't think it is.

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  • $\begingroup$ I've added the spatial and survey tags. Feel free to remove them if you feel they are inappropriate. $\endgroup$ – Andy W Mar 11 '13 at 5:51
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    $\begingroup$ Obligatory RA Fisher quote required here: "To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of" $\endgroup$ – Spacedman Mar 11 '13 at 7:32
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The short answer is the "usual" way in the social sciences is to have pre-defined discrete areas and provide summary statistics for samples within those areas aggregated up. Examples of pre-defined areas may be census geographies, zip-codes, or any other neighborhood unit you can dream up.

This is the usual because it is fairly rare to have surveys geocoded to the exact location or be able to utilize that information due to privacy reasons, so typically surveys can't be geolocated besides within a general area anyway. Even if you don't have pre-defined areas you could always create a uniform grid (i.e. quadrats) and provide summary statistics. If your sampling over the city diverges from uniform though this approach will not work as well, as you could have some quadrats with few (or zero) samples and some with many samples (in fact some people justify aggregation to larger units because of such concerns).

More novel is to utilize what van Ham & Manley (2012) refer to as bespoke neighborhoods. One essentially picks a point, and then some arbitrary buffer around that point, and then estimates whatever summary statistic one is interested in based on samples around that point. Related examples can be found in Lee et al. (2008), Li & Radke (2012) and Ratcliffe & Taniguchi (2008).

If you want more continuous measurements over the entire study space, you can utilize geo-statistical kriging to estimate a continuous surface (although this is also pretty novel for social science). Similar examples can be found in the social science literature under area-to-point kriging (which is a slightly different context). See this other answer of mine for a list of scholarly examples.


Citations

  • Lee, B. A., Reardon, S. F., Firebaugh, G., Farrell, C. R., Matthews, S. A., and O'Sullivan, D. (2008). Beyond the census tract: Patterns and determinants of racial segregation at multiple geographic scales. American Sociological Review, 73(5):766-791. PDF Here.
  • Li, W. and Radke, J. D. (2012). Geospatial data integration and modeling for the investigation of urban neighborhood crime. Annals of GIS, 18(3):185-205.
  • Ratcliffe, J. H. and Taniguchi, T. A. (2008). Is crime high around drug-gang street corners?: Two spatial approaches to the relationship between gang set spaces and local crime levels. Crime Patterns and Analysis, 1(1):23-46. PDF at link
  • van Ham, M. and Manley, D. (2012). Neighbourhood effects research at a crossroads: Ten challenges for future research. Environment and Planning A, 44(12):2787-2793.
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What about an estimator which is an average over its closest k neighbors with the weights given to the neighbors decreasing with distance from the target point.

The right taper for the weights could be fit beforehand using some sort of error minimization training scheme?

Alternatively, I was thinking of a Voronoi tessalation. For a point of interest find its Voronoi cell and add in the effect of next-neighbor cells with a reduced weight and so on?

Too simplistic?

PS. Would there be a chance that the Income (say) at a location is better predicted by $fn(income, age, sex)$ of its neighbors than by merely $fn(income)$ of its neighbors?

In essence, can mixing predictors get a better predictive model than keeping them separate?

In the extreme could one ever have a situation where neighbor age alone was a better predictor of a points income than neighbor income? Just wondering.

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    $\begingroup$ What about an estimator which is an average over its closest k neighbors with the weights given to the neighbors decreasing with distance from the target point. This is essentially inverse distance weighting, which could be viewed as the simplest type of kriging model. A very similar context for estimating correlations between variables is geographically weighted regression. $\endgroup$ – Andy W Mar 11 '13 at 20:21

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