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)

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:

• (569 / 14145) / (16761 / 546625)

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.

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). 

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:

1. Generate dissolved multi-ring buffers for a venue type (i.e., bars) 

2. Calculate the geographical area of each dissolved multi-ring buffer for each venue type (i.e., within 100m of a bar is 0.17 square miles, within 200m of a bar is 0.28 square miles)

3. Count the number of crimes of interest which occur within each dissolved multi-ring buffer

4. Calculate the LQ as (# of crimes within 100m of venue / number of crimes in the study area) / (geographic area within 100m of venue / geographic area of the study area) 

5. Repeat for each venue type and each distance buffer

 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. 

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

• Andresen, M.A. (2014) Measuring crime specializations and concentrations. CrimRxiv. https://doi.org/10.21428/cb6ab371.0fc32225 Accessed 29.10.2023.  

• Block, S., Clarke, R.V. & Maxfield, M.G. (2011) Estimating the number of U.S. Vehicles stolen for export using crime location quotients. In M. Andresen and Kinney, J.B. Patterns, Prevention, and Geometry of Crime. Taylor & Francis.

• Brantingham P.L. & Brantingham, P.J. (1998) Mapping crime for analytic purposes: location counts and rates. In D.Weisburd and T.McEwen (Eds.), Crime mapping and crime prevention (pp.263-288). Monsey, NY, CJ Press. https://www.crimrxiv.com/pub/u4s84pmi/release/1 Accessed 29.10.2023.

• Caplan, J.M. and Kennedy, L.W (2011) Risk Terrain Modeling Compendium for Crime Analysis. Rutgers Center on Public Security. https://www.rutgerscps.org/uploads/2/7/3/7/27370595/riskterrainmodelingcompendium_caplankennedy2011.pdf Accessed 29.10.2023.

• Petrossian, G. and Clarke, R.V. (2012) Export of Stolen Vehicles Across Land Borders. USDOJ, COPS. https://popcenter.asu.edu/sites/default/files/sites/default/files/problems/pdfs/export_stolen_vehicles.pdf Accessed 29.10.2023.

• Taniguchi, A., Rengert, G.F. and McCord, Eric. S. (2011) Where Size Matters: Agglomeration Economies of Illegal Drug Markets in Philadelphia. In Walker, J.T., Social, Ecological and Environmental Theories of Crime. Taylor & Francis. https://www.researchgate.net/figure/Location-quotients-by-facility-type_tbl1_248967267 Accessed 29.10.2023.

• Wuschke, K., Andresen, M.A. and Brantingham, P.L. (2021) Pathways of crime: Measuring crime concentration along urban roadways. Wiley. https://onlinelibrary.wiley.com/doi/10.1111/cag.12676 Accessed 29.10.2023.