Openshaw's GAM
Description
Scan an area with Openshaw's Geographical Analysis Machine to look for clusters.
opgam is the main function, while gam.intern is called from there.
Usage
1 2 3 
Arguments
data 
A dataframe with the data, as described in DCluster manual page. 
thegrid 
A twocolumns matrix containing the points of the grid to be used. If it is null, a rectangular grid of step step is built. 
radius 
The radius of the circles used in the computations. 
step 
The step of the grid. 
alpha 
Significance level of the tests performed. 
iscluster 
Function used to decide whether the current circle is a possible cluster or not. It must have the same arguments and return the same object than gam.iscluster.default 
.
set.idxorder 
Whether an index for the ordering by distance to the center of the current ball is calculated or not. 
point 
Point where the curent ball is centred. 
rr 
rr=radius*radius . 
... 
Aditional arguments to be passed to iscluster. 
Details
The Geographical Analysis Machine was developed by Openshaw et al. to perform geographical studies of the relationship between different types of cancer and their proximity to nuclear plants.
In this method, a grid of a fixed step is built along the study region, and small balls of a given radius are created at each point of the grid. Local observed and expected number of cases and population are calculated and a function is used to assess whether the current ball is a cluster or not. For more information about this function see opgam.iscluster.default, which is the default function used.
If the obverved number of cases excess a critical value, which is calculated by a function passed as an argument, then that circle is marked as a possible cluster. At the end, all possible clusters are drawn on a map. Clusters may be easily identified then.
Notice that we have follow a pretty flexible approach, since userimplemented functions can be used to detect clusters, such as those related to ovedispersion (Pearson's Chi square statistic, PotthoffWhittinghill's statistic) or autocorrelation (Moran's I statistic and Geary's c statistic), or a bootstrap procedure, although it is not recommended because it can be VERY slow.
Value
A dataframe with five columns:
x 
Easting coordinate of the center of the cluster. 
y 
Northing coordinate of the center of the cluster. 
statistic 
Value of the statistic computed. 
cluster 
Is it a cluster (according to the criteria used)? It should be always TRUE. 
pvalue 
Significance of the cluster. 
References
Openshaw, S. and Charlton, M. and Wymer, C. and Craft, A. W. (1987). A mark I geographical analysis machine for the automated analysis of point data sets. International Journal of Geographical Information Systems 1, 335358.
Waller, Lance A. and Turnbull, Bruce W. and Clarck, Larry C. and Nasca, Philip (1994). Spatial Pattern Analyses to Detect Rare Disease Clusters. In 'Case Studies in Biometry'. Chapter 1, 323.
See Also
DCluster, opgam.iscluster.default
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  library(spdep)
data(nc.sids)
sids<data.frame(Observed=nc.sids$SID74)
sids<cbind(sids, Expected=nc.sids$BIR74*sum(nc.sids$SID74)/sum(nc.sids$BIR74))
sids<cbind(sids, x=nc.sids$x, y=nc.sids$y)
#GAM using the centroids of the areas in data
sidsgam<opgam(data=sids, radius=30, step=10, alpha=.002)
#Plot centroids
plot(sids$x, sids$y, xlab="Easting", ylab="Northing")
#Plot points marked as clusters
points(sidsgam$x, sidsgam$y, col="red", pch="*")
