# alltypes

0th

Percentile

##### Calculate Summary Statistic for All Types in a Multitype Point Pattern

Given a marked point pattern, this computes the estimates of a selected summary function ($F$,$G$, $J$, $K$ etc) of the pattern, for all possible combinations of marks, and returns these functions in an array.

Keywords
spatial, nonparametric
##### Usage
alltypes(X, fun="K", ..., dataname=NULL,verb=FALSE,envelope=FALSE)
##### Arguments
X
The observed point pattern, for which summary function estimates are required. An object of class "ppp" or "lpp".
fun
The summary function. Either an Rfunction, or a character string indicating the summary function required. Options for strings are "F", "G", "J", "K", "L", "pcf",
...
Arguments passed to the summary function (and to the function envelope if appropriate)
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. 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.
envelope
Logical value. If envelope is true, then simulation envelopes of the summary function will also be computed. See Details.
##### Details

This routine is a convenient way to analyse the dependence between types in a multitype point pattern. It computes the estimates of a selected summary function of the pattern, for all possible combinations of marks. It returns these functions in an array (an object of class "fasp") amenable to plotting by plot.fasp().

The argument fun specifies the summary function that will be evaluated for each type of point, or for each pair of types. It may be either an Rfunction or a character string. 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 $X_i$. See Fest for explanation of the empty space function. The estimate is computed by applying Fest to $X_i$ with the optional arguments ....

If fun is "Gcross", "Jcross", "Kcross" or "Lcross", the routine calculates, for each pair of types $(i,j)$, an estimate of the i-toj'' cross-type function $G_{ij}(r)$, $J_{ij}(r)$, $K_{ij}(r)$ or $L_{ij}(r)$ respectively describing the dependence between $X_i$ and $X_j$. See Gcross, Jcross, Kcross or Lcross respectively for explanation of these functions. The estimate is computed by applying the relevant function (Gcross etc) to X using each possible value of the arguments i,j, together with the optional arguments .... If fun is "pcf" the routine calculates the cross-type pair correlation function pcfcross between each pair of types.

If fun is "Gdot", "Jdot", "Kdot" or "Ldot", the routine calculates, for each type $i$, an estimate of the i-to-any'' dot-type function $G_{i\bullet}(r)$, $J_{i\bullet}(r)$ or $K_{i\bullet}(r)$ or $L_{i\bullet}(r)$ respectively describing the dependence between $X_i$ and $X$. See Gdot, Jdot, Kdot or Ldot respectively for explanation of these functions. The estimate is computed by applying the relevant function (Gdot etc) to X using each possible value of the argument i, together with the optional arguments ....

The letters "G", "J", "K" and "L" are interpreted as abbreviations for Gcross, Jcross, Kcross and Lcross respectively, assuming the point pattern is marked. If the point pattern is unmarked, the appropriate function Fest, Jest, Kest or Lest is invoked instead.

If envelope=TRUE, then as well as computing the value of the summary function for each combination of types, the algorithm also computes simulation envelopes of the summary function for each combination of types. The arguments ... are passed to the function envelope to control the number of simulations, the random process generating the simulations, the construction of envelopes, and so on.

##### Value

• A function array (an object of class "fasp", see fasp.object). This can be plotted using plot.fasp.

If the pattern is not marked, the resulting array'' has dimensions $1 \times 1$. Otherwise the following is true:

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 applying Fest to the points of type i only.

If fun is "Gdot", "Jdot", "Kdot" or "Ldot", the function array again has dimensions $m \times 1$. The entry at position [i,1] in this array is the result of Gdot(X, i), Jdot(X, i) Kdot(X, i) or Ldot(X, i) respectively.

If fun is "Gcross", "Jcross", "Kcross" or "Lcross" (or their abbreviations "G", "J", "K" or "L"), 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 function Gcross, Jcross, Kcross orLcross to the pair of types (i,j). The diagonal [i,i] entry of the function array is the result of applying the univariate function Gest, Jest, Kest or Lest to the points of type i only.

If envelope=FALSE, then each function entry fns[[i]] retains the format of the output of the relevant estimating routine Fest, Gest, Jest, Kest, Lest, Gcross, Jcross ,Kcross, Lcross, Gdot, Jdot, Kdot or Ldot The default formulae for plotting these functions are cbind(km,theo) ~ r for F, G, and J functions, and cbind(trans,theo) ~ r for K and L functions.

If envelope=TRUE, then each function entry fns[[i]] has the same format as the output of the envelope command.

##### Note

Sizeable amounts of memory may be needed during the calculation.

plot.fasp, fasp.object, Fest, Gest, Jest, Kest, Lest, Gcross, Jcross, Kcross, Lcross, Gdot, Jdot, Kdot, envelope.

• alltypes
##### Examples
# bramblecanes (3 marks).
data(bramblecanes)
<testonly>bramblecanes <- bramblecanes[c(seq(1, 744, by=20), seq(745, 823, by=4))]</testonly>
bF <- alltypes(bramblecanes,"F",verb=TRUE)
plot(bF)
plot(alltypes(bramblecanes,"G"))
plot(alltypes(bramblecanes,"Gdot"))

# Swedishpines (unmarked).
data(swedishpines)
<testonly>swedishpines <- swedishpines[1:25]</testonly>
plot(alltypes(swedishpines,"K"))

data(amacrine)
plot(alltypes(amacrine, "pcf"), ylim=c(0,1.3))

# 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")

# envelopes
bKE <- alltypes(bramblecanes,"K",envelope=TRUE,nsim=19)
bFE <- alltypes(bramblecanes,"F",envelope=TRUE,nsim=19,global=TRUE)

# extract one entry
as.fv(bKE[1,1])
Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)

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