Spatial Econometrics & Geography

Timothy F Leslie, PhD

The Co-Location Quotient (CLQ)

The Co-Location Quotient is a measurement of spatial description designed to quantify (potentially asymmetrical) correlation between categories of a population which may itself exhibit spatial auto-correlation. This metric answers research questions such as "Are points of type A located close to points of type B more often than expected given their overall presence in the population? Is the reverse true?" The odds-ratio based number is symantically comfortable for explanation.
The metric was developed as a point-based contingency-tables algorithm. We use Monte Carlo simulations to test for significance. The method is robust at a wide level of inputs. A wide number of applications have been published, including in the spatial analysis of health, criminology, ecology, and economic phenomena.

Core Publications

The initial paper in this line of research was published in Geographical Analysis.
• Full citation: Leslie, T.F and B.J. Kronenfeld. 2011. "The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points." Geographical Analysis , 43(3): 306-216.

A local CLQ was developed and published in The Professional Geographer.
• Full citation: Cromley, R.G., Hanink, D.M., and G.C. Bentley. 2014. "Geographically Weighted Colocation Quotients: Specification and Application." The Professional Geographer, 66(1): 138-148.

A separate paper detailed the significance test for the Local CLQ was subsequently published The Professional Geographer.
• Full Citation: Wang, F., Hu, U. Wang, S. and L. Xiaojuan. 2017. "Local Indicator of Colocation Quotient with a Statistical Significance Test: Examining Spatial Association of Crime and Facilities." The Professional Geogapher, 69(1): 22-31.

We have considered how the CLQ would change if we control for specific trends in the data, particularly those driven by same-sector association. That paper was published in Journal of Geographical Systems.
• Full citation: Kronenfeld, B.J. and T.F. Leslie. 2015. "Restricted random labeling: testing for between-group interaction after controlling for joint population and within-group spatial structure." Journal of Geographical Systems 17:1-28.

Software

The latest release from the CLQ authors is available at the Eastern Illinois University Archives here.

An Open Source implementation for R has been developed by Josiah Perry in the sfdep package. It is available here.

ESRI has also developed a set of CLQ toolbox for ArcPro. Documentation on these tools have been published here.