Kmulti.inhom(spatstat)
Kmulti.inhom()所属R语言包：spatstat
Inhomogeneous Marked K-Function
非均匀标记K-功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
For a marked point pattern, estimate the inhomogeneous version of the multitype K function which counts the expected number of points of subset J within a given distance from a typical point in subset I, adjusted for spatially varying intensity.
一个显着的点模式，估计的多类型K函数计算的预期数量的子集点J给定距离内，从一个典型的点在子集I，调整不均匀的版本在空间上的不同强度。
用法----------Usage----------
Kmulti.inhom(X, I, J, lambdaI=NULL, lambdaJ=NULL,
...,
r=NULL, breaks=NULL,
correction=c("border", "isotropic", "Ripley", "translate"),
lambdaIJ=NULL,
sigma=NULL, varcov=NULL)
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of the inhomogeneous multitype K function KIJ(r) will be computed. It must be a marked point pattern. See under Details.
所观察到的点图案，从估计的非均匀多类型K函数KIJ(r)将被计算。它必须是一个显着的点模式。请参阅“详细信息”下。
参数：I
Subset index specifying the points of X from which distances are measured. See Details.
指定X距离的测量点的子集指数。查看详细信息。
参数：J
Subset index specifying the points in X to which distances are measured. See Details.
指定点的子集指数在X距离的测量。查看详细信息。
参数：lambdaI
Optional. Values of the estimated intensity of the sub-process X[I]. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the points in X[I], or a function(x,y) which can be evaluated to give the intensity value at any location.
可选。的强度估计的子流程X[I]的值。无论是像素的图像（对象的类"im"），包含在每个点的强度值在X[I]，或function(x,y)可以评价，得到的强度值的一个数值向量在任何位置。
参数：lambdaJ
Optional. Values of the estimated intensity of the sub-process X[J]. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the points in X[J], or a function(x,y) which can be evaluated to give the intensity value at any location.
可选。的强度估计的子流程X[J]的值。无论是像素的图像（对象的类"im"），包含在每个点的强度值在X[J]，或function(x,y)可以评价，得到的强度值的一个数值向量在任何位置。
参数：...
Ignored.
忽略。
参数：r
Optional. Numeric vector. The values of the argument r at which the multitype K function KIJ(r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r.
可选。数字矢量。的参数的值r多类型K函数KIJ(r)应进行评估。有一个合理的默认。我们强烈建议用户第一次不指定此参数。请参阅下面的重要条件r。
参数：breaks
An alternative to the argument r. Not normally invoked by the user. See the Details section.
替代到的参数r。通常不是由用户调用。查看详细信息“一节。
参数：correction
A character vector containing any selection of the options "border", "bord.modif", "isotropic", "Ripley", "translate", "none" or "best". It specifies the edge correction(s) to be applied.
字符向量含有任何选择的选项"border"，"bord.modif"，"isotropic"，"Ripley"，"translate"，"none"或"best" 。指定，边缘校正（S）。
参数：lambdaIJ
Optional. A matrix containing estimates of the product of the intensities lambdaI and lambdaJ for each pair of points, the first point
可选。一个矩阵包含了产品的强度lambdaI和lambdaJ每对点，第一点估计
参数：sigma,varcov
Optional arguments passed to density.ppp to control the smoothing bandwidth, when lambda is estimated by kernel smoothing.
可选参数传递给density.ppp控制的平滑带宽，当lambda核平滑估计。
Details
详细信息----------Details----------
The function Kmulti.inhom is the counterpart, for spatially-inhomogeneous marked point patterns, of the multitype K function Kmulti.
函数Kmulti.inhom是对应的，空间不均匀性显着点模式，多类型K函数Kmulti。
Suppose X is a marked point process, with marks of any kind. Suppose X[I], X[J] are two sub-processes, possibly overlapping. Typically X[I] would consist of those points of X whose marks lie in a specified range of mark values, and similarly for X[J]. Suppose that lambdaI(u), lambdaJ(u) are the spatially-varying intensity functions of X[I] and X[J] respectively. Consider all the pairs of points (u,v) in the point process X such that the first point u belongs to X[I], the second point v belongs to X[J], and the distance between u and v is less than a specified distance r. Give this pair (u,v) the numerical weight 1/(lambdaI(u) lambdaJ(u)). Calculate the sum of these weights over all pairs of points as described. This sum (after appropriate edge-correction and normalisation) is the estimated inhomogeneous multitype K function.
假设X是一个标记点的过程中，任何形式的标志。假设X[I]，X[J]是两个子过程，可能有重叠。通常情况下X[I]将包括那些点X的标记趴在指定范围内的标记值，同样的X[J]。假设这lambdaI(u)，lambdaJ(u)是功能X[I]和X[J]分别在空间上变化的强度。考虑所有的点对(u,v)点过程X第一点u属于X[I]，第二点v属于X[J]，和u和v是少于一个指定的距离r之间的距离。给这对(u,v)数字权重1/(lambdaI(u) lambdaJ(u))。这些权重计算的总和超过所有对所描述的点。这个总和（适当的边缘校正和标准化后）是估计的的不均匀多类型K函数。
The argument X must be a point pattern (object of class "ppp") or any data that are acceptable to as.ppp.
参数X必须是点模式（类的对象"ppp"）或任何数据到as.ppp是可以接受的。
The arguments I and J specify two subsets of the point pattern. They may be any type of subset indices, for example, logical vectors of length equal to npoints(X), or integer vectors with entries in the range 1 to npoints(X), or negative integer vectors.
的参数I和J指定两个点模式的子集。它们可以是任何类型的子集的索引，例如，逻辑向量长度等于npoints(X)，或整数向量的条目中的取值范围为1到npoints(X)，或负整数向量。
Alternatively, I and J may be functions that will be applied to the point pattern X to obtain index vectors. If I is a function, then evaluating I(X) should yield a valid subset index. This option is useful when generating simulation envelopes using envelope.
另外，I和J可能是点模式X获得索引向量将被应用到的功能。如果I是一个函数，然后计算I(X)应该产生一个有效的子集指数。此选项是有用的时生成模拟信封使用envelope。
The argument lambdaI supplies the values of the intensity of the sub-process identified by index I. It may be either
参数lambdaI用品的强度指数I的过程中发现的值。它可以是
a pixel image (object of class "im") which gives the values of the intensity of X[I] at all locations in the window containing X;
像素图像（对象类"im"）的值的强度X[I]的窗口中包含的所有位置X;
a numeric vector containing the values of the intensity of X[I] evaluated only at the data points of X[I]. The length of this vector must equal the number of points in X[I].
包含的值的强度的一个数值向量X[I]只在评估的数据点X[I]。此向量的长度必须等于在X[I]的点的数量。
of the form function(x,y) which can be evaluated to give values of the intensity at any locations.
的形式function(x,y)可以进行评估，得到的强度的值在任何位置。
if lambdaI is omitted then it will be estimated using a leave-one-out kernel smoother.
如果lambdaI被忽略，那么它会使用一个离开的内核平滑估计。
If lambdaI is omitted, then it will be estimated using a "leave-one-out" kernel smoother, as described in Baddeley, Moller and Waagepetersen (2000). The estimate of lambdaI for a given point is computed by removing the point from the point pattern, applying kernel smoothing to the remaining points using density.ppp, and evaluating the smoothed intensity at the point in question. The smoothing kernel bandwidth is controlled by the arguments sigma and varcov, which are passed to density.ppp along with any extra arguments.
如果lambdaI被省略，那么它会被估计使用顺畅的假期一出“内核，中所描述巴德利，穆勒和Waagepetersen的的（2000年）。估计lambdaI除去点从点图案，对于一个给定的点的计算方法是，施加内核平滑使用density.ppp的其它点，和评价问题点的平滑强度。图像平滑用核的带宽的参数所控制的sigma和varcov，它被传递给density.ppp沿与任何额外的参数。
Similarly lambdaJ supplies the values of the intensity of the sub-process identified by index J.
同样lambdaJ用品的强度指数J的过程中发现的值。
The argument r is the vector of values for the distance r at which KIJ(r) should be evaluated. It is also used to determine the breakpoints (in the sense of hist) for the computation of histograms of distances.
参数r是向量的值的距离r，KIJ(r)应该进行评估。它也可以用来确定断点（在感hist）的直方图的距离的计算。
First-time users would be strongly advised not to specify r. However, if it is specified, r must satisfy r[1] = 0, and max(r) must be larger than the radius of the largest disc contained in the window.
用户第一次将强烈建议不指定r的。然而，如果它被指定，r必须满足r[1] = 0，和max(r)必须大于包含在窗口中的最大的光盘的半径。
Biases due to edge effects are treated in the same manner as in Kinhom. The edge corrections implemented here are
边缘效应产生的偏差的处理中相同的方式，当在Kinhom。这里实现的边缘修正
border the border method or “reduced sample” estimator (see Ripley, 1988). This is the least efficient (statistically) and the fastest to compute. It can be computed for a window of arbitrary shape.
毗邻边界的方法或“减少样本”估计（见里普利，1988年）。这是最有效的（统计），以最快的速度计算。它可以计算一个窗口的任意形状。
isotropic/Ripley Ripley's isotropic correction (see Ripley, 1988; Ohser, 1983). This is currently implemented only for rectangular windows.
各向同性/ Ripley旅游Ripley的各向同性修正（见里普利，1988; Ohser，1983年）。这是目前实施的矩形窗。
translate Translation correction (Ohser, 1983). Implemented for all window geometries.
翻译的翻译的校正（Ohser，1983）。实现所有窗口的几何形状。
The pair correlation function pcf can also be applied to the result of Kmulti.inhom.
对相关函数pcf也可以应用于结果Kmulti.inhom。
值----------Value----------
An object of class "fv" (see fv.object).
类的一个对象"fv"（见fv.object）。
Essentially a data frame containing numeric columns
本质上是一个数据框包含数字的列
参数：r
the values of the argument r at which the function KIJ(r) has been estimated
的参数的值的r在哪些函数KIJ(r)已估计
参数：theo
the theoretical value of KIJ(r) for a marked Poisson process, namely pi * r^2
理论值的KIJ(r)显着的泊松过程，即pi * r^2，
together with a column or columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function KIJ(r) obtained by the edge corrections named.
连同一列或多列名为"border"，"bord.modif"，"iso"和/或"trans"，根据选定的边修正。这些列包含的功能KIJ(r)命名的边缘修正的估计。
（作者）----------Author(s)----------
Adrian Baddeley
<a href="mailto:Adrian.Baddeley@csiro.au">Adrian.Baddeley@csiro.au</a>
<a href="http://www.maths.uwa.edu.au/~adrian/">http://www.maths.uwa.edu.au/~adrian/</a>
and Rolf Turner
<a href="mailto:r.turner@auckland.ac.nz">r.turner@auckland.ac.nz</a>
参考文献----------References----------
Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329–350.
参见----------See Also----------
Kmulti, Kdot.inhom, Kcross.inhom, pcf
Kmulti，Kdot.inhom，Kcross.inhom，pcf
实例----------Examples----------
# Finnish Pines data: marked by diameter and height[芬兰松树数据：直径和高度]
plot(finpines, which.marks="height")
I <- (marks(finpines)$height <= 2)
J <- (marks(finpines)$height > 3)
K <- Kmulti.inhom(finpines, I, J)
plot(K)
# functions determining subsets[功能确定的子集]
f1 <- function(X) { marks(X)$height <= 2 }
f2 <- function(X) { marks(X)$height > 3 }
K <- Kmulti.inhom(finpines, f1, f2)
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注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 13:40:12
