Iest(X, ..., eps=NULL, r=NULL, breaks=NULL, correction=NULL)"ppp", or data
in any format acceptable to as.ppp().
r.
Jest.
Jest for information about the $J$ function.
The $I$ function is defined as
$$ %
I(r) = \sum_{i=1}^m p_i J_{ii}(r) %
- J_{\bullet\bullet}(r)$$
where $J$ is the $J$ function for
the entire point process ignoring the marks, while
$Jii$ is the $J$ function for the
process consisting of points of type $i$ only,
and $p[i]$ is the proportion of points which are of type $i$.The $I$ function is designed to measure dependence between points of different types, even if the points are not Poisson. Let $X$ be a stationary multitype point process, and write $X[i]$ for the process of points of type $i$. If the processes $X[i]$ are independent of each other, then the $I$-function is identically equal to $0$. Deviations $I(r) < 1$ or $I(r) > 1$ typically indicate negative and positive association, respectively, between types. See Van Lieshout and Baddeley (1999) for further information.
An estimate of $I$ derived from a multitype spatial point pattern dataset can be used in exploratory data analysis and formal inference about the pattern. The estimate of $I(r)$ is compared against the constant function $0$. Deviations $I(r) < 1$ or $I(r) > 1$ may suggest negative and positive association, respectively.
This algorithm estimates the $I$-function
from the multitype point pattern X.
It assumes that X can be treated
as a realisation of a stationary (spatially homogeneous)
random spatial marked point process in the plane, observed through
a bounded window.
The argument X is interpreted as a point pattern object
(of class "ppp", see ppp.object) and can
be supplied in any of the formats recognised by
as.ppp(). It must be a multitype point pattern
(it must have a marks vector which is a factor).
The function Jest is called to
compute estimates of the $J$ functions in the formula above.
In fact three different estimates are computed
using different edge corrections. See Jest for
information.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511--532.
Jest
data(amacrine)
Ic <- Iest(amacrine)
plot(Ic, main="Amacrine Cells data")
# values are below I= 0, suggesting negative association
# between 'on' and 'off' cells.
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