I'm planning to do regression analysis (GWR) on several datasets, where all but one is based on census areas (UK OS lower level super output areas, lsoa) for which I have a shapefile that describes the polygons. Regression with the census-based variables is easy to set up and execute because both the dependent and explanatory variables are held within the same Input feature.

But I'm finding difficulty with my final explanatory variable - concentrations at x,y coordinates (UK OS co-ordinates). I believe I need to 'join' or 'relate' with my lsoa shapefile (which is what I've done with the other variables); I've tried all sorts of things such as kriging and extracting to vector, 'relates', 'joins', adding new fields, calculating new fields, but to no avail.

I'm sure there is someone out there who has done this before - I'd really appreciate your advice.


Coming in 10.1 you could give Areal Interpolation a shot.

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What does your XY coordinates represent? You can always try to aggregate them within boundaries of LSOAs using sum, count, mean/median, etc. use Spatial Join for that purpose specifying correct join operation(s).

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    Thanks for the speedy reply Radek, I will give that a go and post back. – Jane Cloke Jun 13 '12 at 13:51
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    +1 If the concentration data are sparse compared to the Census units, a good approach is to interpolate them to a grid and then aggregate them via zonal means. (If they were dependent variables instead of explanatory variables, the solution would be very different.) It is somewhat troubling, though, to realize that most regression technology (like GWR) assumes the explanatory variables are measured without a lot of error or variation, whereas concentration measurements often have huge amounts of variation. Provided GWR is used as intended in a purely exploratory mode, this should be ok. – whuber Jun 13 '12 at 16:27
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    Thanks Whuber, the concentrations are modelled data and I have several per census unit. You're absolutely right about the variability with measurements and with modelled data it is very easy to forget about the uncertainties involved. We are exploring relationships at the moment. – Jane Cloke Jun 14 '12 at 9:29
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    FYI I give a few references in the comments to this question on the stats site that utilize error measurements from such interpolation in errors in variables type regression models. Note those aren't for GWR models though. It would perhaps be interesting to assess the effects of such measurement error on GWR, I suspect it would result in grotesque amounts of variability in the estimates. Especially given in conjunction with that GWR models tend to be susceptible to collinearity and influential data points in general. – Andy W Jun 15 '12 at 19:22

The question asks about connecting point data (measurements of concentrations of a substance in samples of an environmental medium) to areal (aka "lattice") data, which represent aggregate values collected within administrative units.

The objective is to look at relationships among multiple variables. One of them is intended to be some sort of representative summary of the concentrations within each Census unit; all the rest already are attributes of the Census units. Therefore, we need to aggregate the point values to the Census unit level, not the other way around!

To do this, some thought about what the concentrations mean will be useful. Their meaning depends on how they were collected and what is important to know about the environment.

To clarify this point, consider two different situations with the same formal data. In the first one, scientists sample (say) two locations randomly within each Census area. The purpose is to obtain concentrations useful for estimating average concentrations within each area. One would want to use some average, or perhaps weighted average, of the concentrations within and near any Census area to estimate the true average concentration within that area. In the second situation, suppose scientists sample locations thought to be contaminated (such as air near smokestacks or water just downstream of industrial outfalls in creeks and rivers) without regard to the Census areas. (This is a typical application.) Their purpose is to assess extreme (not average) conditions. Due to this focused sampling, some Census areas may include many samples and some may have none. Here, averages could be meaningless (or deceptive), whereas the maximum concentration observed within each Census area might be useful (perhaps leaving Null values within Census areas without data). In other applications, distance-weighted averages of the concentrations might be more appropriate.

Other scenarios are possible, but these make the point that there is no universal, general-purpose answer to "how do I combine these data?".

Nevertheless, in many cases it can be reasonable to do the following:

  1. For each point location, identify its containing Census area (if any). This is done in GIS with a spatial join. This adds a new field to the point attribute table. The field contains a Census unit identifier.

  2. Compute a statistical summary of the concentrations, such as a mean (in the first scenario) or maximum (in the second) for each Census unit. This is done in GIS (or in any database application) with a summarize operation applied to the point attribute table, using the Census unit identifier as the grouping attribute. (At the same time one can pick up auxiliary information, such as counts and variances per Census unit, almost for free: these can be useful in many circumstances for weighting the data in statistical analyses.)

  3. If necessary, join the statistical summaries (of which there will be at most one per Census unit) to the Census unit attribute table.

The resulting attribute table now has a new column representing the points (here, the concentration summaries). It contains all the data needed for statistical analysis, whether it be GWR (which presumably would use coordinates of central locations of the Census units), ordinary least squares regression, or anything else.

  • Thanks Whuber, that has been really helpful, I have now spatially joined my data (although I do have some problems now with census units that appear to have no data, which they quite clearly should have, grr) and looking forward to getting stuck-in with the statistical analyses. Jane – user8229 Jun 15 '12 at 14:40
  • @Jane: Might be worth checking projections of the data in such cases. – radek Jun 15 '12 at 20:39

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