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 user-implemented
functions can be used to detect clusters, such as those related to
ovedispersion (Pearson's Chi square statistic, Potthoff-Whittinghill'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.