Location Quotients 

1. What is a location quotient (LQ)

Location Quotient (LQ) is a widely used geographic index to measure specialisation. LQ is applied for measuring and mapping relative distributions/concentrations of a subarea (i.e. a census output area, census block or neighbourhood) within a larger area as a whole (i.e. a city or police force jurisdiction). Originally used within economic geography, the LQ was introduced into criminological research in the 1990s by the Brantinghams (Brantingham, P.L. & Brantingham, P.J., 1998)

Source: Brantingham and Brantingham (1998)

The equation for using the LQ to determine crime specialisation is shown in the figure. Here the equation would be measuring the 'crime mix' (distributions of crime types) and speciality within a geographic area, controlling for differences in population. Using the LQ in this way would help identify geographical areas that may be centres for property crime or violent crime for example. A cited benefit of this approach is that we could uncover specialised crime problems in otherwise low-crime areas that could be overlooked.

The table below illustrates how LQ can help understand over and under-representation of crime problems in a geographical area. In the table example, when considering the rate of theft of motor vehicles, an analyst in the East Area of London's Metropolitan Police would assess the problem in Barking & Dagenham as being greater than its neighbour Havering.  When using the LQ we are taking into account overall crime in an area.

Using the LQ alongside the rate, we can see that Havering in the East Area of London actually has a larger vehicle theft problem relative to its overall crime. Using another example - when looking at two London Boroughs Havering and Kensington & Chelsea - each has the same rate of vehicle theft, but there is an over-representation of vehicle thefts in Havering (1.6) and an under-representation in K&C (0.8) relative to their total crime problem.

The LQ calculation, using Barking & Dagenham as an example is as follows:

Example of LQ applied for theft of motor vehicle offences in Apr-2023 to Sep-2023, data from https://data.london.gov.uk/dataset/mps-monthly-crime-dahboard-data 

1.1 Interpreting Location Quotients

The LQ provides a standardised value whereby a score of 1.0 means that there is an average representation. 

Values greater than 1 indicate over-representation and values under 1 indicate under-representation.

2. Different applications of LQ

There are multiple examples of how LQ can be used to assess over and under-representation of crime. We've already looked at an example concerning larger geographical units (London Boroughs). Below are some visual representations of LQ applied using different types of locations.

2.1 Large geographical units

The first example shows the LQ for unrecovered motor vehicle thefts for counties in the US border states (Block, S. et al 2011). This map was republished in a POP Center problem guide The Export of Stolen Vehicles Across Land Borders. 

The LQ here is used to illustrate that areas in close proximity to Mexico and large ports had substantially higher unrecovered vehicle thefts than would otherwise be expected. Thefts of vehicles that were unrecovered were used as a proxy for stolen to export. 

At this geographic aggregation, LQ might offer new insights when observing the distribution of regional, national and cross-border threats.

Source: POP Center Guide, export of stolen vehicles https://popcenter.asu.edu/content/export-stolen-vehicles-appendix-b 

2.2 Small geographical units

The second example uses small neighbourhood areas of Vancouver, Canada (Andresen, 2014). Here we can see at a more granular level how using the LQ can reveal substantially different geographical patterns in risk. 

The map on the left side displays robbery rates, and as we might expect, these are highest in the downtown area and decrease with distance away from the centre. 

Source: Measuring crime specialisations and concentrations, Andresen, M.A. (2014) https://www.crimrxiv.com/pub/u4s84pmi/release/1 

However, the map on the right displays LQ for robbery, and we can identify multiple suburban and peripheral neighbourhoods where robbery is over-represented. This is an indication of different 'opportunity surfaces'. Different places might offer different types of opportunities for different crime types to occur. 

Used in this way adding LQ information into local profiles can assist prioritisation of problems and problem-solving in smaller neighbourhood policing areas (and places which perhaps are seldom explored in short-term tactical assessments or overlooked by the more obvious city centre or downtown hotspot). 

2.3 Street segments

Similar to the previous examples, here the LQ has been used in an assessment of crime concentration along urban roadways in Vancouver, Canada (Wuschke et al, 2021). In this case the LQ equation has been adapted whereby:

LQ = (count of crimes along road type / total distance of road type) / (count of crime in geographic area / total distance of road type in geographic area).

This determines a LQ based on the rate of criminal events per distance of one road type, standardised by the rate of criminal events per distance for the entire geographical area.

 

Source: Pathways of crime: Measuring crime concentration along urban roadways https://onlinelibrary.wiley.com/doi/full/10.1111/cag.12676 

2.4 Points of interest

The final example uses GIS methods to assess whether particular venue types have a negative impact on the space surrounding them (Taniguchi et al, 2009). Here the authors analysed data assuming that if a particular type of facility or venue (drug treatment centres) had a negative effect on the surrounding area, then concentric circles (measured in feet) closest to the centres would contain more drug-related arrests than those further away (a distance decay). 

Using LQ and adapting the measure to use the geographic area as a denominator, we can see that the first four venue types had a negative impact on the surrounding area, decaying with distance. The research implied that drug treatment centres did not negatively impact the surrounding areas.

Source: Where Size Matters: Agglomeration Economies of Illegal Drug Markets in Philadelphia https://www.researchgate.net/figure/Location-quotients-by-facility-type_tbl1_248967267

3. Calculating LQ for points of interest

Calculating an LQ for aggregated geographical areas and streets is a relatively straightforward task. However, calculating LQ for points of interest using GIS methods can be more challenging. With desktop GIS it can become burdensome and repetitive, depending on how many points of interest and how many crime points you are analysing. Typically a workflow in desktop GIS would involve:

 A guide for achieving this in QGIS can be found here in section 6.3.

If you want to test numerous points of interest, you will no doubt want to produce a reproducible workflow that you write once and then reuse as and when required with only minor changes. 

3.1 Reproducibility with SQL and Python 

In the example provided below, I have used open-source data from NYC Open Data which I have stored in a PostgreSQL database. 

You will need to have crimes/incidents data and points of interest data. Both datasets will require geometry (easting/northing) using a projected coordinate reference system.

STEP 1: Generate dissolved buffers around each point of interest and calculate the area. The resulting output is shown in the image below. You can see that for each category, we see how many locations there are, and the area (in square miles) within different distances from them. Using ATMs as an example, there are 8,147 in New York City. Drawing 400ft buffer rings around NYC ATMs produces an area of 71.5 square miles. When extending the distance around ATMs to 800ft the total area is 149.3 square miles and so on.

If you wanted to use a smaller geographical study area, such as a borough, then you would re-run the script with an additional geographical filter applied for crimes and points of interest.

I have made available a commented SQL script that will generate this table. Click here for the SQL script. 

Output table - geographical area around different categories of points of interest at varying distance intervals

STEP 2: Calculate the distance between every crime/incident point with every point of interest. Then calculate how many crimes occur within specified distances of each type of point of interest. The resulting output is shown in the image below. In this example, we can see that for shooting incidents in NYC 2022 there were 248 that occurred within 400ft of a parking lot, 161 within 400ft of a park-recreation area and so on.

You can either run this for every single point of interest in your dataset or select only those of interest related to the problem under study. For example, if the problem you are interested in is the theft of vehicle parts, then you may be interested in seeing whether auto parts, auto services, and auto repairs have a negative impact on patterns (here you would be testing an assumption that such businesses could be handling or accepting stolen parts, thereby encouraging nearby thefts). 

To assist in thinking about the points of interest that might be useful to explore in relation to your crime problem, a good place to start is the 'Risk Terrain Modeling Compendium' (Caplan & Kennedy, 2011). This brings together research on geographic and place-based risk factors for a variety of crime problems.

I have made available a commented SQL script that will generate the counts of crimes within the buffers for each point of interest. Click here for the SQL script. 

STEP 3: Create a new table which merges the buffer areas and crime counts on the point of interest categories. Click here for the SQL script. 

This data, as shown in the image below, will be used to calculate the Location Quotients. 

STEP 4: The final stage is to calculate the Location Quotients. This can be done in a range of software, including spreadsheet software (Excel). 

Here I have manually written the calculations in a Jupyter Notebook after having connected to the SQL table shown above.

We can import the table (or load it to Excel), and use the crime counts and geographical area (along with the overall crime count and geographical area for NYC), to create LQ measures for each distance threshold ('lq400', 'lq800', 'lq1200', 'lq1600').

After reviewing the data, for NYC robberies in 2022, there were three points of interest categories where the LQs were high and decaying over distance. These were Pawnshops, Check Cashing and Subway Stations. I have included a map of robbery for one of the boroughs (The Bronx) along with the Pawnshop and Check Cashing locations (read in from postgresql and mapped in QGIS).

Further reading