# alltypes

##### 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"`

. - 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`

-to`j`

'' 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`

or`Lcross`

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.

##### See Also

`plot.fasp`

,
`fasp.object`

,
`Fest`

,
`Gest`

,
`Jest`

,
`Kest`

,
`Lest`

,
`Gcross`

,
`Jcross`

,
`Kcross`

,
`Lcross`

,
`Gdot`

,
`Jdot`

,
`Kdot`

,
`envelope`

.

##### 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 1.21-0, License: GPL (>= 2)*