alltypes
Calculate Statistic for All Types in a Multitype Point Pattern
Given a marked point pattern, this computes the estimates of
a selected summary function ($F$,$G$, $J$ or $K$)
of the pattern, for all possible combinations of marks.
It returns these functions in
a list (an object of class "fasp"
) amenable to plotting
by plot.fasp()
.
- Keywords
- spatial
Usage
alltypes(pp, fun="K",dataname=NULL,verb=FALSE)
Arguments
- pp
- The observed point pattern, for which summary function
estimates are required. An object of class
"ppp"
. If the pattern is not marked, the resulting ``array'' is $1 \times 1$. - fun
- Character string indicating the summary function
required. Must be one of the letters
"F"
,"G"
,"J"
,"K"
. - dataname
- Character string giving an optional (alternative)
name to the point pattern, different from what is given
in the call. This name, if supplied, may be used by
plot.fasp()
in forming the title - verb
- Logical value, meaning ``verbose''. If verb is true then terse ``progress reports'' (just the values of the mark indices) are printed out when the calculations for that combination of marks are completed.
Details
This routine is a convenient way to analyse the dependence between
types in a multitype point pattern.
Suppose that the points have possible types $1,2,\ldots,m$
and let $X_i$ denote the pattern of points of type $i$ only.
If fun="F"
then this routine
calculates, for each possible type $i$,
an estimate of the Empty Space Function $F_i(r)$ of
$X_i$.
If fun
is "G"
, "J"
or "K"
,
the routine calculates, for each pair of types $(i,j)$,
an estimate of the cross-type function
$G_{ij}(r)$,
$J_{ij}(r)$ or
$K_{ij}(r)$ respectively describing the
dependence between
$X_i$ and $X_j$.
The real work is done by the functions Fest
, Gest
,
Kest
, Jest
,
Gcross
, Kcross
, and Jcross
.
One of the first four functions (according to
fun
) is invoked if the two marks under consideration are
equal. The latter three are invoked if the marks are distinct.
(There is no Fcross
; for the empty space function $F(r)$
there is no cross-type version.)
Value
- A function array (an object of class
"fasp"
, seefasp.object
). This can be plotted usingplot.fasp
.If
fun="F"
, the function array has dimensions $m \times 1$ where $m$ is the number of different marks in the point pattern. The entry at position[i,1]
in this array is the result of applyingFest
to the points of typei
only.If
fun
is"G"
,"J"
or"K"
, the function array has dimensions $m \times m$. The[i,j]
entry of the function array (for $i \neq j$) is the result of applying the functionGcross
,Jcross
orKcross
to the pair of types(i,j)
. The diagonal[i,i]
entry of the function array is the result of applying the univariate functionGest
,Jest
orKest
to the points of typei
only. Each function entryfns[[i]]
retains the format of the output of the relevant estimating routineFest
,Gest
,Jest
,Kest
,Gcross
,Jcross
, orKcross
.The default formulae for plotting these functions are
cbind(km,theo) ~ r
for F, G, and J, andcbind(trans,theo) ~ r
for K.
Note
Sizeable amounts of memory may be needed during the calculation.
See Also
plot.fasp
,
fasp.object
,
allstats
,
Fest
,
Gest
,
Jest
,
Kest
,
Gcross
,
Jcross
,
Kcross
Examples
library(spatstat)
# bramblecanes (3 marks).
data(bramblecanes)
X.F <- alltypes(bramblecanes,fun="F",verb=TRUE)
plot(X.F)
X.G <- alltypes(bramblecanes,fun="G",verb=TRUE)
X.J <- alltypes(bramblecanes,fun="J",verb=TRUE)
X.K <- alltypes(bramblecanes,fun="K",verb=TRUE)
<testonly># smaller dataset
bram <- bramblecanes[seq(1, bramblecanes$n, by=20), ]
X.F <- alltypes(bram,fun="F",verb=TRUE)
X.G <- alltypes(bram,fun="G",verb=TRUE)
X.J <- alltypes(bram,fun="J",verb=TRUE)
X.K <- alltypes(bram,fun="K",verb=TRUE)</testonly>
# Swedishpines (unmarked).
data(swedishpines)
X.F <- alltypes(swedishpines,fun="F")
X.G <- alltypes(swedishpines,fun="G")
X.J <- alltypes(swedishpines,fun="J")
X.K <- alltypes(swedishpines,fun="K")
# simulated data
pp <- runifpoint(350, owin(c(0,1),c(0,1)))
pp$marks <- factor(c(rep(1,50),rep(2,100),rep(3,200)))
X.F <- alltypes(pp,fun="F",verb=TRUE,dataname="Fake Data")
X.G <- alltypes(pp,fun="G",verb=TRUE,dataname="Fake Data")
X.J <- alltypes(pp,fun="J",verb=TRUE,dataname="Fake Data")
X.K <- alltypes(pp,fun="K",verb=TRUE,dataname="Fake Data")
# A setting where you might REALLY want to use dataname:
xxx <- alltypes(ppp(Melvin$x,Melvin$y,
window=as.owin(c(5,20,15,50)),marks=clyde),
fun="F",verb=TRUE,dataname="Melvin")