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

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

An object of class `"htest"`

representing the result of the test.

- 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`

.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

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
$$
T = \sum_i \sum_m \left( \widehat p(m \mid x_i) - \overline p_m
\right)^2
$$
where \(\widehat p(m \mid x_i)\) is the
leave-one-out kernel smoothing estimate of the probability that the
\(i\)-th data point has type \(m\), and
\(\overline p_m\) 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.

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.

`relrisk`

```
segregation.test(hyytiala, 5)
if(interactive()) segregation.test(hyytiala, hmin=0.05)
```

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