segregation.test(X, ...)## S3 method for class 'ppp':
segregation.test(X, \dots, nsim = 19,
permute = TRUE, verbose = TRUE, Xname)
"ppp"
with factor-valued marks).relrisk.ppp
to control the smoothing parameter or bandwidth selection.rlabel
. If TRUE
(the
default), randomisation is performed by randomly permuting the
labels of X
. If FALSE
, randomisation is performing
byX
."htest"
representing the result of the test.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.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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