Mapping Spatial Entropy in Southwark

I’ve been doing a bit of work recently on segregation with Pablo Mateos, and having gone through the motions with aspatial indices of segregation (the classics): dissimilarity, exposure and so on, I decided to investigate the more explicitly spatial ones. Taking a lead from Reardon and O’Sullivan’s (2004) paper “Measures of Spatial Segregation” in sociological methodology, I got in touch with David O’Sullivan and he, and his student Seong-Yun Hong, helped me with the implementation of some spatial measures of segregation. This post specifically concerns spatially weighted entropy – a measure of population diversity. Reardon and O’Sullivan define spatially weighted entropy as:

This equation describes the ‘entropy’, derived from Shannon’s information theory, for each grid cell in the image (below) in which each cell value results from the entropy computed for a 1km ‘neighbourhood’ p around each cell (essentially a circular buffer). The ethnic group in question is given by ‘m’ (with the pi representing the proportion of a given group in a given neighbourhood) and relates to ethnic groups defined from the Southwark patient register using Onomap, the groups defined are: African, East Asian and Pacific, European, Muslim, South Asian, British, Eastern European, Hispanic, and Unclassified or Other. The Onomap software is able to apply this classification by looking at the forename and surname combination of patients registered to use Southwark GPs, or patients living in Southwark but using GPs outside of Southwark. The cells in the image relate directly to the residential locations of patients, who were geocoded to their household using the Ordnance Survey’s Address Layer 2 product, therefore empty cells are areas within which no recorded patients were found, such as parks, and transport infrastructure. As the data underlying this is from patient registrations with GPs, we have to accept that the data is likely to be partial, with potentially systematic biases in those people who have registered – young men and people from countries where GPs as a method of primary care do not exist- may have been omitted.

In the image, higher values of entropy indicate greater diversity of population by ethnic group, the resultant images is unsurprising in terms of Southwark, with the Dulwich Village area showing as the least diverse place, home as it is to more affluent, generally ‘British’ groups. Likewise historical factors regarding access to housing have shaped the lower entropy scores in the middle of the borough – home to African populations and the North East, home to the British working classes who were rehoused from the now more African areas in the middle of the borough. Finally, the greater Waterloo- Elephant and Castle region in the north-west shows up as the ethnic melting pot in the borough.

In the image above, the 1km neighbourhood defined in the spatially weighted entropy score has a smoothing effect, I experimented with smaller values for the neighburhood size, and found that the resultant output did not change dramatically from that obtained above. At the end of the day, the selection of neighbourhood size is largely arbitrary and will depend on sociocultural factors of the area and it’s people. Similarly, as there is no data for the regions outside of Southwark we are more uncertain of the values at the edges than in the middle of the borough as we are only sampling from within Southwark itself. Nonetheless, this representation of Southwark goes somewhat beyond what is possible using the commonly used output zones defined by the census.