Postcards from the Road I

EPID 684
Spatial Epidemiology
University of Michigan School of Public Health

Jon Zelner
[email protected]

Local vs. Global clustering

Global Clustering

  • Population average measure of spatial similarity

  • Importance of effect assessed by scale of statistic relative to range or sampling distribution.

Local Clustering

  • Intensity of similarity relative to surrounding areas.

  • Can be used to identify hotspots and coldspots.

  • Meaningfulness often assessed in terms of how different they are from other small units in the same population.

Getis-Ord \(G_i\) statistic


Basically the proportion of all cases within a threshhold distance \(d\) of location \(i\).


  • \(d\) is the maximum distance to consider clustering

  • \(w_{ij}(d)=1\) if place \(i\) and place \(j\) are within \(d\) of each other, and 0 otherwise. (When \(i=j\), \(w_{ij}=0\))

  • \(x_j\) is the variable of interest

  • Yields an estimate of both strength of clustering and approximate statistical significance.

Lets us go from this…

Tornado incidence from (1)

To this…

Tornado hot and cold spots identified in (1)


Frazier AE, Hemingway BL, Brasher JP. Land surface heterogeneity and tornado occurrence: An analysis of Tornado Alley and Dixie Alley. Geomatics, Natural Hazards and Risk [electronic article]. 2019;10(1):1475–1492. ( (Accessed January 22, 2020)