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.
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.
Number of simulations for the Monte Carlo test.
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.
Logical value indicating whether to print progress reports.
Optional character string giving the name of the dataset X.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net 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.
Bithell, J.F. (1991) Estimation of relative risk functions. Statistics in Medicine 10, 1745--1751.
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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