Originally used in economics and regional planning to measure the concentration of a particular industry, or industrial specialization, in a region relative to a larger geographical unit (e.g. block to city or city to state or state to country), location quotients* can be used to quantify the concentration of certain crimes in a specific area relative to a larger reference area. This way, a city could be identified as a center for car theft, another for household theft, another for homicide, and so on. More than an alternative, the Location Quotient (LQ) should be considered a complement to counts and rates for analyzing crime patterns and trends.
Since LQ is a relative measure, no single location can have high LQs for all crimes; a specialized crime structure indicates that a particular location has certain characteristics that make it prone to certain crime patterns. As a ratio, the LQ differs from a normal proportion (% of total) in that it offers a comparative view vis-à-vis a larger reference area. Sub-units of a spatial unit (e.g. municipalities in a state) can thus be compared to each other in reference to the larger unit, providing an additional perspective to the crime problem in an area.
An LQ that is greater than 1 means that the study area has a disproportionately larger share of a particular crime than in the larger area; if the LQ is less than 1 the area has a disproportionately smaller share of a particular crime; an LQ equal to 1 is the baseline, meaning the area has a proportional share of that crime. One advantage of the LQ is that it provides additional consideration to low-crime areas that would normally be ignored if measured using counts or rates. Low crime counts, however, can pose problems given how high variability across time can significantly affect LQs. To minimize this, it’s best to use moving averages or other longitudinal approaches (across several years if using annual data, for example).
In Mexico, as in other countries, there are regions or cities that usually have the highest counts and/or rates of crime. Yet even in lower crime states or cities, there can be certain types of offenses that are disproportionally present compared to their surrounding areas and to higher-crime-rate cities or states. Table 1 shows the states with high vehicle theft rates (i.e. equal or above the national rate of 7 thefts per 1,000 vehicles) in Mexico in the year 2011.
In the state of Nuevo León (NL), for instance, vehicle theft accounts for 30% of its total crime count. Its vehicle theft rate of 10 is above the national rate, but well below that of Baja California and Chihuahua. Nonetheless, the LQ in NL is the second highest nationwide (2.21), only behind Chihuahua (2.45) and relatively higher than Baja California (1.45).
So how does one interpret the LQ in relation to the larger reference area? Since it’s a ratio, the LQ can be interpreted as a percentage: an LQ of 2.21 means that NL has 121% more vehicle theft relative to the country as a whole. The LQ indicates a high concentration of vehicle theft, meaning NL has a regional “specialization” of crime for vehicle theft. State authorities should therefore zoom in on that particular type of theft.
Now consider vehicle theft in the state of NL (see Table 2). Of the 51 municipalities statewide, nine registered high vehicle theft rates – equal to or above the state rate of 10. Three of these states – General Bravo, Los Ramones, and General Escobedo – all had vehicle theft rates of 11. However, two of those (G. Bravo and Los Ramones) had relative low total crime and vehicle theft counts. Focusing on rates would tell us that the risk of vehicle theft is the same in the three municipalities, but the LQ adds some context. It shows a larger concentration of vehicle theft in G. Bravo and Los Ramones. Despite having significantly lower crime counts, these two municipalities seem to have a particular problem with vehicle theft. Moreover, with an LQ of 2.02, G. Bravo has a higher concentration of vehicle theft than Los Ramones, which has the same rate and very similar count.
One more example: an LQ of 1.14 in the municipality of Juarez implies that vehicle theft is 14% greater than in NL as a whole. Juarez has a relatively high concentration of vehicle theft, meaning it has a local “specialization” of crime for vehicle theft and should probably consider directing more law enforcement resources to addressing that type of theft. On the other hand, the municipality of Garcia has an LQ of 0.60. Having both a vehicle theft count and rate similar to that of Juarez, its LQ corresponds with a much lower concentration of vehicle theft – 40% less than at the state level. Garcia could thus focus more of its limited law enforcement resources on tackling other crimes that have a larger concentration in that locality.
Measures of crime should be carefully selected, used and interpreted. Crime counts are useful for identifying priority targeting for policing (i.e. ‘hot spots’, or locations with high volumes of crime) but do not consider the underlying factors that make those locations ‘hot spots’ in the first place. Crime rates help identify at-risk targets, but choosing the proper denominator can have significant changes in the rate and thus in the crime patterns identified. By themselves, these two measures are flawed measures for crime analysis.
Just like crime counts and rates, the location quotient should not be used by itself. The LQ is a useful tool for measuring crime patterns across geographic areas, and when used across time it provides an additional layer of context that can help identify crime trends. Nonetheless LQs must also be applied judiciously, for example, when using low crime counts or when looking for specific patterns that are sometimes hidden in certain levels of aggregation. For instance, Monterrey might have an LQ of 0.90 for vehicle theft, but disaggregating vehicle theft into car theft and motorcycle theft might show that the former has an LQ of 1.57 while the latter has an LQ of 0.19. In that case, the concentration of car theft in Monterrey points to a specialization of car theft in that city.
Future posts will explore more in detail the use of counts, rates and LQs in crime analysis, particularly for visualizing spatial patterns and for analyzing the underlying factors that help explain why a specific area has certain crime structure.
* Other useful resources on the Location Quotient:
- (2006) ‘Location Quotients: A Tool for Comparing Regional Industry Compositions’, InContext, Vol. 7, No. 3, March. Available here
- Andersen, M.A. et al (2009) ‘Cartograms, crime and location quotients’, Crime Patterns and Analysis, Vol. 2, No. 1, January. Available here
- Andersen, M.A. (2014) ‘Measuring crime specialization using the location quotient’ in The Science of Crime Measurement: Issues for Spatially-Referenced Crime Data, pp. 72-74, Routledge, New York. Available here
- Bureau of Economic Analysis, 11 January 2008, What are location quotients (LQs)? Available here
- Sypion-Dutkowska, N. and Michael Leitner, M. (2017) ‘Land Use Influencing the Spatial Distribution of Urban Crime: A Case Study of Szczecin, Poland’, International Journal of Geo-Information, Vol. 6, No. 3. Available here