DCluster (version 0.2-2)

opgam: 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

opgam(data, thegrid=NULL, radius=Inf, step=NULL,  alpha, iscluster=opgam.iscluster.default, set.idxorder=TRUE, ...)
opgam.intern(point, data, rr, set.idxorder, iscluster, alpha, ...)

Arguments

data

A dataframe with the data, as described in DCluster manual page.

thegrid

A two-columns 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.

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.

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 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.

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, 335-358.

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, 3-23.

See Also

DCluster, opgam.iscluster.default

Examples

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="*")