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.
scan.test(X, r, ..., method = c("poisson", "binomial"), nsim = 19, baseline = NULL, case = 2, alternative = c("greater", "less", "two.sided"), verbose = TRUE)
- A point pattern (object of class
- Radius of circle to use. A single number or a numeric vector.
- Optional. Arguments passed to
as.maskto determine the spatial resolution of the computations.
"binomial"specifying the type of likelihood.
- Number of simulations for computing Monte Carlo p-value.
- Baseline for the Poisson intensity, if
method="poisson". A pixel image or a function.
- Which type of point should be interpreted as a case,
method="binomial". Integer or character string.
- Alternative hypothesis:
"greater"if the alternative postulates that the mean number of points inside the circle will be greater than expected under the null.
- Logical. Whether to print progress reports.
The spatial scan test (Kulldorf, 1997) is applied
to the point pattern
In a nutshell,
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
Xexhibits spatial clustering.
Xmust 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
rwhich 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.
method="poisson"then the scan test based on Poisson likelihood is performed (Kulldorf, 1997). The dataset
Xis treated as an unmarked point pattern. By default (if
baselineis 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
rand another intensity$\beta_0$outside the circle. If
baselineis 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 * baselineinside some circle of radius
beta0 * baselineoutside the circle.
method="binomial"then the scan test based on binomial likelihood is performed (Kulldorf, 1997). The dataset
Xmust 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
rhas 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
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
The Likelihood Ratio Test Statistic is computed by
- 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.
Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics --- Theory and Methods 26, 1481--1496.
nsim <- if(interactive()) 19 else 2 r <- if(interactive()) seq(0.5, 1, by=0.1) else c(0.5, 1) scan.test(redwood, 0.1 * r, method="poisson", nsim=nsim) scan.test(chorley, r, method="binomial", case="larynx", nsim=nsim)