# 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 or a numeric vector.

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,

• If method="poisson" then a significant result would mean that there is a circle of radius r, located somewhere in the spatial domain of the data, which contains a significantly higher than expected number of points of X. That is, the pattern X exhibits spatial clustering.

• If method="binomial" then X must 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 radius r which 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.

• If method="poisson" then the scan test based on Poisson likelihood is performed (Kulldorf, 1997). The dataset X is treated as an unmarked point pattern. By default (if baseline is 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 radius r and another intensity $\beta_0$ outside the circle. If baseline is given, then it should be a pixel image or a function(x,y). The null hypothesis is an inhomogeneous Poisson process with intensity proportional to baseline. The alternative hypothesis is an inhomogeneous Poisson process with intensity beta1 * baseline inside some circle of radius r, and beta0 * baseline outside the circle.

• If method="binomial" then the scan test based on binomial likelihood is performed (Kulldorf, 1997). The dataset X must 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 radius r has 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.scan.test. The Likelihood Ratio Test Statistic is computed by scanLRTS.

##### 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.

plot.scan.test, as.im.scan.test, relrisk, scanLRTS

• scan.test
##### Examples
# NOT RUN {
nsim <- if(interactive()) 19 else 2
rr <- if(interactive()) seq(0.5, 1, by=0.1) else c(0.5, 1)
scan.test(redwood, 0.1 * rr, method="poisson", nsim=nsim)
scan.test(chorley, rr, method="binomial", case="larynx", nsim=nsim)
# }

Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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