segregation.test | R Documentation |
Performs a Monte Carlo test of spatial segregation of the types in a multitype point pattern.
segregation.test(X, ...)
## S3 method for class 'ppp'
segregation.test(X, ..., nsim = 19,
permute = TRUE, verbose = TRUE, Xname)
X |
Multitype point pattern (object of class |
... |
Additional arguments passed to |
nsim |
Number of simulations for the Monte Carlo test. |
permute |
Argument passed to |
verbose |
Logical value indicating whether to print progress reports. |
Xname |
Optional character string giving the name of the dataset |
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.
An object of class "htest"
representing the result of the test.
.
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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