R: Spatial Scan Test

scan.test {spatstat} | R Documentation

## Spatial Scan Test

### Description

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.

### 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 beta1 inside some circle of radius `r` and another intensity beta0 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.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

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

### See Also

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

### Examples

       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)

[Package spatstat version 1.63-3 Index]