Here’s an interesting little plot I thought I’d share.  It shows Mean Angular Distance (MAD 320km scale) on the x axis and GDP per capita on the y.  High MAD means less accessible, so the plot shows a trend where less accessibility is associated with less productivity.

The blue outlier is Aberdeen, by the way – rich in oil income but situated in the back of beyond.  And London is a long way off the chart to the top left.

Interestingly, MAD measures only accessibility of spatial networks rather than raw quantity.  You might think raw network quantity (highly correlated with population and jobs, r2>0.9) would be a better predictor of GDP than accessibility.  Maybe it is, if you get the scale of measurement right (accessibility on a large scale could be a proxy for quantity on a small scale).  But for the range of scales I tested (10,20,40,80,160,320,640km) it wasn’t.

Anyway this is just interested tinkering, rather than a serious piece of research.  More importantly it was a test of a truly large scale network analysis with the upcoming sDNA version 2.  We saved computation time by only computing accessibility for a sample of points in each region (sDNA will have the capacity to do this); in fact the whole computation took less time than it took to load and save the data, which for a million-link feature class is quite substantial.  The whole job was done in an hour or two.

UPDATE 30/10/2014

I followed this up with the new sDNA+, making a model with population assigned to the network.  It was tested for many more radii: 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 100, 120, 140, 160, 180, 200, 240, 280, 320, 360 and 400 km; in each NUTS region I sampled 20 points on the network to compute accessibility on these scales.

It turns out by far the best predictor was plain ol’ population (Weight, within sDNA – when you have assigned population data to network weight).  Population within a 10km network buffer has r=0.7 with GDP per capita.  This beat network gravity models formed with the MAD, MED, NQPDA and NQPDE accessibility stats.

Computing accessibility on all those scales, for 20 points in each of 113 regions, ran overnight on my Core i3 (not too fast) processor.  I skipped the more expensive sDNA computations by putting nobetweenness;nojunctions;nohull into the advanced config.  In fact, I might as well paste the whole advanced config for this analysis here:

nobetweenness;nojunctions;nohull;skipzeroweightorigins;origweight=compute;destweight=link_population

Compute was a field I set to 1 for links I wanted to compute accessibility for; 0 otherwise.  I chose these at random with a probability inversely proportional to the number of links in each region.

Here are some images from some work we did for the Department of Public Health.  The first is a buffer analysis of access to footpaths, bridleways etc for each output area in Wales.  The buffers shown on the map are centered on OA centroids; designed to indicate the area accessible by driving 13km (on a road obviously) then walking 2km (as the crow flies – sadly nobody seems to have a definitive source of network data for rural paths).  The colouring shows access to public rights of way.

Network+Euclidean buffers around Output Area centroids in Wales, coloured to show access to footpaths and bridleways (green is more)

Somehow the shapes produced remind me of sheep, which is nice, but before anyone gets too parochial about that I should point out that most other countries would look the same.  As you can see, it’s the border with England that seems to have the best access to countryside; but that’s because the above map misses off the open space across which we are lucky enough to be able to wander freely.  So here’s the open space (this time ditching the sheep shapes and plotting access in the centre of LSOAs for legibility):

Access to open space within 13km buffers (green is more)

Now we see the truth of it – the backbone of Wales has an enormous amount of publicly accessible green space.  The people who miss out, on these measures, are the residents of Carmarthenshire which doesn’t seem to do well on either open space or rights of way.  (There is also the edge effect induced by the coastline – obviously people living by the sea have less land accessible to them – but then the coastline is nice feature in itself).  Anyway, all this is now being studied for its impacts on mental health.

What did sDNA do here and how can you do it?  It uses features of the upcoming sDNA version 2; namely (in advanced config) outputnetbuffers to produce the network buffers which are then processed to make the sheep shapes.  Also skiporiginifzero to restrict our production of buffers to the OA centroids we are measuring.  Of course, ArcGIS network analyst can do this – in theory!  In practice, it crashed when presented with such a large analysis, but sDNA didn’t.