# scan.test

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##### Spatial Scan Test

Performs the Spatial Scan Test for clustering in a spatial point pattern, or for clustering of one type of point in a bivariate spatial point pattern.

Keywords
htest, spatial
##### Usage
scan.test(X, r, ...,
method = c("poisson", "binomial"),
nsim = 19,
baseline = NULL,
case = 2,
alternative = c("greater", "less", "two.sided"),
verbose = TRUE)
##### Arguments
X
A point pattern (object of class "ppp").
r
Radius of circle to use. A single number.
...
Optional. Arguments passed to as.mask to determine the spatial resolution of the computations.
method
Either "poisson" or "binomial" specifying the type of likelihood.
nsim
Number of simulations for computing Monte Carlo p-value.
baseline
Baseline for the Poisson intensity, if method="poisson". A pixel image or a function.
case
Which type of point should be interpreted as a case, if method="binomial". Integer or character string.
alternative
Alternative hypothesis: "greater" if the alternative postulates that the mean number of points inside the circle will be greater than expected under the null.
verbose
Logical. Whether to print progress reports.
##### Details

The spatial scan test (Kulldorf, 1997) is applied to the point pattern X.

In a nutshell,

• Ifmethod="poisson"then a significant result would mean that there is a circle of radiusr, located somewhere in the spatial domain of the data, which contains a significantly higher than expected number of points ofX. That is, the patternXexhibits spatial clustering.
• Ifmethod="binomial"thenXmust be a bivariate (two-type) point pattern. By default, the first type of point is interpreted as a control (non-event) and the second type of point as a case (event). A significant result would mean that there is a circle of radiusrwhich contains a significantly higher than expected number of cases. That is, the cases are clustered together, conditional on the locations of all points.

Following is a more detailed explanation.

• Ifmethod="poisson"then the scan test based on Poisson likelihood is performed (Kulldorf, 1997). The datasetXis treated as an unmarked point pattern. By default (ifbaselineis not specified) the null hypothesis is complete spatial randomness CSR (i.e. a uniform Poisson process). The alternative hypothesis is a Poisson process with one intensity$\beta_1$inside some circle of radiusrand another intensity$\beta_0$outside the circle. Ifbaselineis given, then it should be a pixel image or afunction(x,y). The null hypothesis is an inhomogeneous Poisson process with intensity proportional tobaseline. The alternative hypothesis is an inhomogeneous Poisson process with intensitybeta1 * baselineinside some circle of radiusr, andbeta0 * baselineoutside the circle.
• Ifmethod="binomial"then the scan test based on binomial likelihood is performed (Kulldorf, 1997). The datasetXmust be a bivariate point pattern, i.e. a multitype point pattern with two types. The null hypothesis is that all permutations of the type labels are equally likely. The alternative hypothesis is that some circle of radiusrhas a higher proportion of points of the second type, than expected under the null hypothesis.

The result of scan.test is a hypothesis test (object of class "htest") which can be plotted to report the results. The component p.value contains the $p$-value.

The result of scan.test can also be plotted (using the plot method for the class "scan.test"). The plot is a pixel image of the Likelihood Ratio Test Statistic (2 times the log likelihood ratio) as a function of the location of the centre of the circle. This pixel image can be extracted from the object using as.im.

##### Value

• An object of class "htest" (hypothesis test) which also belongs to the class "scan.test". Printing this object gives the result of the test. Plotting this object displays the Likelihood Ratio Test Statistic as a function of the location of the centre of the circle.

##### References

Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics --- Theory and Methods 26, 1481--1496.

relrisk

• scan.test
##### Examples
nsim <- if(interactive()) 19 else 2
data(redwood)
scan.test(redwood, 0.1, method="poisson", nsim=nsim)
data(chorley)
scan.test(chorley, 1, method="binomial", case="larynx", nsim=nsim)
Documentation reproduced from package spatstat, version 1.29-0, License: GPL (>= 2)

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