R: Test of Spatial Segregation of Types

segregation.test {spatstat} | R Documentation

## Test of Spatial Segregation of Types

### Description

Performs a Monte Carlo test of spatial segregation of the types in a multitype point pattern.

### Usage

    segregation.test(X, ...)

    ## S3 method for class 'ppp'
    segregation.test(X, ..., nsim = 19,
           permute = TRUE, verbose = TRUE, Xname)

### Arguments

`X` | Multitype point pattern (object of class `"ppp"` with factor-valued marks).
`...` | Additional arguments passed to `relrisk.ppp` to control the smoothing parameter or bandwidth selection.
`nsim` | Number of simulations for the Monte Carlo test.
`permute` | Argument passed to `rlabel`. If `TRUE` (the default), randomisation is performed by randomly permuting the labels of `X`. If `FALSE`, randomisation is performing by resampling the labels with replacement.
`verbose` | Logical value indicating whether to print progress reports.
`Xname` | Optional character string giving the name of the dataset `X`.

### Details

The Monte Carlo test of spatial segregation of types, proposed by Kelsall and Diggle (1995) and Diggle et al (2005), is applied to the point pattern `X`. The test statistic is

T = sum[i] sum[m] (phat(m | x[i]) - pbar[m])^2

where phat(m | x[i]) is the leave-one-out kernel smoothing estimate of the probability that the i-th data point has type m, and pbar[m] is the average fraction of data points which are of type m. The statistic T is evaluated for the data and for `nsim` randomised versions of `X`, generated by randomly permuting or resampling the marks.

Note that, by default, automatic bandwidth selection will be performed separately for each randomised pattern. This computation can be very time-consuming but is necessary for the test to be valid in most conditions. A short-cut is to specify the value of the smoothing bandwidth `sigma` as shown in the examples.

### Value

An object of class `"htest"` representing the result of the test.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### References

Kelsall, J.E. and Diggle, P.J. (1995) Kernel estimation of relative risk. Bernoulli 1, 3–16.

Diggle, P.J., Zheng, P. and Durr, P. (2005) Non-parametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. Applied Statistics 54, 645–658.

### See Also

`relrisk`

### Examples

      segregation.test(hyytiala, 5)

      if(interactive()) segregation.test(hyytiala, hmin=0.05)

[Package spatstat version 1.63-3 Index]