The intent of this post is not simply to uncover where the highest density of people belonging to a particular ethnic group are, but rather to use the ‘location quotient’ (LQ) technique to compare the ethnic density in any one area to the overall ethnic density in Southwark, thus providing a relative insight into where the density of particular groups is more, less or as dense as expected.
Location Quotients tend to work with areal units, characterising different areas subject to a larger region and providing a basic insight into where functions are clustered. Because the Southwark patient register data is address geocoded, we would be losing some spatial information if we choose to aggregate the data, not to mention the question of which areal aggregation is best. More info on how to create location quotients here.
A Location Quotient has 3 possible interpretations; if it is around 1 then the ethnic population in that area is at the level we would expect given what we observe nationally. If the LQ is less than 1 then that area has a lesser population of a particular ethnic group that what we would expect based upon national figures. Finally, in the LQ value is over 1 this suggests a concentration of the ethnic group in the area which is greater than we would expect given nationally observed levels. A LQ is quite simply a rate-ratio.
Instead of the standrad areal approach, the maps here use a density estimation approach in which disaggregate point data is transformed into a representation of the continuous density function of the point distribution. The LQ can then be computed for each cell based on the density of that cell with respect to the total density of the surface. This creates a smoothed LQ surface which is readily interpretable in the same manner as above. The Kernel Density Estimation used to create the ethnic and total population density surfaces should be parameterised in the same way; these examples use a 250m bandwidth and a 25m cells size, which is largely empirically redundant, based on the input dataset’s spatial resolution, but creates a more aesthetically appealing mapped representation. Naturally, the procedure works well for clustered data, in Southwarks case for the African and Muslim groups.
June 18th, 2011
by Jon
Not that you’re using the LQ for this yet, but it may become relevant if you’re experimenting with them here…
There’s a good article in Regional Studies by O’Donoghue and Gleave (2004) on testing for significance in the LQs because, of course, it can be hard to say whether an LQ of 1.5 or 15 is meaningful in the context of the overall distribution.
So the authors suggest testing for normality (or log normality) in your LQs and, if your data is plausibly normal, then selecting those areas where the LQ value is more than ‘x’ standard deviations above or below the mean.
I didn’t use their suggested 1-Sample Kolmogorov-Smirnov test though, but used the Lilliefors test in MATLAB with slightly loser values instead.
Hope this is vaguely helpful.
June 26th, 2011
by Daniel Lewis
The Author
Yes, I think there is something in this, as the LQ is basically a rate ratio (I think) it should be possible to infer whether a value is significantly different from expectations. I’ll have a look at the article, thanks a lot Jon.
September 14th, 2011
by Spencer
Also worth checking out: http://ideas.repec.org/p/por/fepwps/273.html
Describes a fairly simple significance test for the location quotient, I used it for the maps in:
http://www.tfl.gov.uk/microsites/freight/documents/GLAEconomicswp37.pdf