Description Usage Arguments Details Value Warnings Author(s) References See Also Examples

For a multitype point pattern,
estimate the multitype *J* function
summarising the interpoint dependence between
the type *i* points and the points of any type.

1 |

`X` |
The observed point pattern,
from which an estimate of the multitype |

`i` |
The type (mark value)
of the points in |

`eps` |
A positive number. The resolution of the discrete approximation to Euclidean distance (see below). There is a sensible default. |

`r` |
numeric vector. The values of the argument |

`breaks` |
This argument is for internal use only. |

`...` |
Ignored. |

`correction` |
Optional. Character string specifying the edge correction(s)
to be used. Options are |

This function `Jdot`

and its companions
`Jcross`

and `Jmulti`

are generalisations of the function `Jest`

to multitype point patterns.

A multitype point pattern is a spatial pattern of points classified into a finite number of possible “colours” or “types”. In the spatstat package, a multitype pattern is represented as a single point pattern object in which the points carry marks, and the mark value attached to each point determines the type of that point.

The argument `X`

must be a point pattern (object of class
`"ppp"`

) or any data that are acceptable to `as.ppp`

.
It must be a marked point pattern, and the mark vector
`X$marks`

must be a factor.
The argument `i`

will be interpreted as a
level of the factor `X$marks`

. (Warning: this means that
an integer value `i=3`

will be interpreted as the number 3,
**not** the 3rd smallest level.)

The “type *i* to any type” multitype *J* function
of a stationary multitype point process *X*
was introduced by Van lieshout and Baddeley (1999). It is defined by

*Ji.(r) = (1 - Gi.(r))/(1-F.(r))*

where *Gi.(r)* is the distribution function of
the distance from a type *i* point to the nearest other point
of the pattern, and *F.(r)* is the distribution
function of the distance from a fixed point in space to the nearest
point of the pattern.

An estimate of *Ji.(r)*
is a useful summary statistic in exploratory data analysis
of a multitype point pattern. If the pattern is
a marked Poisson point process, then
*Ji.(r) = 1*.
If the subprocess of type *i* points is independent
of the subprocess of points of all types not equal to *i*,
then *Ji.(r)* equals
*Jii(r)*, the ordinary *J* function
(see `Jest`

and Van Lieshout and Baddeley (1996))
of the points of type *i*.
Hence deviations from zero of the empirical estimate of
*Ji.-Jii*
may suggest dependence between types.

This algorithm estimates *Ji.(r)*
from the point pattern `X`

. It assumes that `X`

can be treated
as a realisation of a stationary (spatially homogeneous)
random spatial point process in the plane, observed through
a bounded window.
The window (which is specified in `X`

as `Window(X)`

)
may have arbitrary shape.
Biases due to edge effects are
treated in the same manner as in `Jest`

,
using the Kaplan-Meier and border corrections.
The main work is done by `Gmulti`

and `Fest`

.

The argument `r`

is the vector of values for the
distance *r* at which *Ji.(r)* should be evaluated.
The values of *r* must be increasing nonnegative numbers
and the maximum *r* value must exceed the radius of the
largest disc contained in the window.

An object of class `"fv"`

(see `fv.object`

).

Essentially a data frame containing six numeric columns

`J` |
the recommended
estimator of |

`r` |
the values of the argument |

`km` |
the Kaplan-Meier
estimator of |

`rs` |
the “reduced sample” or “border correction”
estimator of |

`han` |
the Hanisch-style
estimator of |

`un` |
the “uncorrected”
estimator of |

`theo` |
the theoretical value of |

The result also has two attributes `"G"`

and `"F"`

which are respectively the outputs of `Gdot`

and `Fest`

for the point pattern.

The argument `i`

is interpreted as
a level of the factor `X$marks`

. It is converted to a character
string if it is not already a character string.
The value `i=1`

does **not**
refer to the first level of the factor.

and \rolf

Van Lieshout, M.N.M. and Baddeley, A.J. (1996)
A nonparametric measure of spatial interaction in point patterns.
*Statistica Neerlandica* **50**, 344–361.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# Lansing woods data: 6 types of trees
woods <- lansing
Jh. <- Jdot(woods, "hickory")
plot(Jh.)
# diagnostic plot for independence between hickories and other trees
Jhh <- Jest(split(woods)$hickory)
plot(Jhh, add=TRUE, legendpos="bottom")
## Not run:
# synthetic example with two marks "a" and "b"
pp <- runifpoint(30) %mark% factor(sample(c("a","b"), 30, replace=TRUE))
J <- Jdot(pp, "a")
## End(Not run)
``` |

spatstat documentation built on Aug. 4, 2018, 1:04 a.m.

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