Kcross.inhom(spatstat)
Kcross.inhom()所属R语言包：spatstat
Inhomogeneous Cross K Function
非均匀交叉K功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
For a multitype point pattern, estimate the inhomogeneous version of the cross K function, which counts the expected number of points of type j within a given distance of a point of type i, adjusted for spatially varying intensity.
对于多类型的点模式，估计非均匀交叉K函数，它计算的预期数量的分型j给定距离内的一个点的类型i，调整版本在空间上的不同强度。
用法----------Usage----------
Kcross.inhom(X, i, j, lambdaI=NULL, lambdaJ=NULL, ..., r=NULL, breaks=NULL,
correction = c("border", "isotropic", "Ripley", "translate"),
sigma=NULL, varcov=NULL,
lambdaIJ=NULL)
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of the inhomogeneous cross type K function Kij(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
所观察到的点图案，从其中的估计的非均匀交叉型K函数Kij(r)将被计算。它必须是一个多类型的点模式（一个标记点图案的标记是一个因素）。请参阅“详细信息”下。
参数：i
The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).
X距离的测量点的类型（标记值）。一个字符串（或东西都将被转换为一个字符串）。默认的第一级marks(X)。
参数：j
The type (mark value) of the points in X to which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level of marks(X).
距离的测量点X的类型（标记值）。一个字符串（或东西都将被转换为一个字符串）。默认的第二个层次的marks(X)。
参数：lambdaI
Optional. Values of the the estimated intensity of the sub-process of points of type i. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the type i points in X, or a function(x,y) which can be evaluated to give the intensity value at any location.
可选。值的估计强度的的类型i点的子流程。无论是像素的图像（对象的类"im"），于各类型的i点X或function(x,y)可以含有的强度值的一个数值向量评价，得到的强度值在任何位置。
参数：lambdaJ
Optional. Values of the the estimated intensity of the sub-process of points of type j. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the type j points in X, or a function(x,y) which can be evaluated to give the intensity value at any location.
可选。值的估计强度的的类型j点的子流程。无论是像素的图像（对象的类"im"），于各类型的j点X或function(x,y)可以含有的强度值的一个数值向量评价，得到的强度值在任何位置。
参数：r
Optional. Numeric vector giving the values of the argument r at which the cross 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。数字矢量提供的参数的值r在交叉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
Optional. An alternative to the argument r. Not normally invoked by the user. See the Details section.
可选。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：...
Ignored.
忽略。
参数：sigma
Standard deviation of isotropic Gaussian smoothing kernel, used in computing leave-one-out kernel estimates of lambdaI, lambdadot if they are omitted.
用于计算标准差的高斯平滑核，留一出lambdaI，lambdadot，如果省略了它们的内核估计。
参数：varcov
Variance-covariance matrix of anisotropic Gaussian kernel, used in computing leave-one-out kernel estimates of lambdaI, lambdadot if they are omitted. Incompatible with sigma.
方差 - 协方差矩阵的的各向异性高斯内核，用于计算留一出内核的估计lambdaI，lambdadot，如果他们被省略了。不相容的sigma。
参数：lambdaIJ
Optional. A matrix containing estimates of the product of the intensities lambdaI and lambdaJ for each pair of points of types i and j respectively.
可选。一个矩阵包含了产品的强度估计lambdaI和lambdaJ点的类型i和j分别为每对。
Details
详细信息----------Details----------
This is a generalisation of the function Kcross to include an adjustment for spatially inhomogeneous intensity, in a manner similar to the function Kinhom.
这是一个一般化的功能Kcross包括空间非均匀的强度调整，以类似的方式，在给函数Kinhom。
The inhomogeneous cross-type K function is described by Moller and Waagepetersen (2003, pages 48-49 and 51-53).
非齐次十字型K函数所描述的穆勒和Waagepetersen的（2003年，页48-49和51-53）。
Briefly, given a multitype point process, suppose the sub-process of points of type j has intensity function lambda[j](u) at spatial locations u. Suppose we place a mass of 1/lambda[j](z) at each point z of type j. Then the expected total mass per unit area is 1. The inhomogeneous “cross-type” K function K[ij]inhom(r) equals the expected total mass within a radius r of a point of the process of type i.
简单地说，一个多类型点的过程中，假设子进程的的类型j点有强度功能lambda[j](u)在空间位置u。假设我们把一个质量1/lambda[j](z)的每个点z类型j。那么预期的每单位面积的总质量为1。不均匀的“十字型”K函数K[ij]inhom(r)等于预期的半径范围内的总质量r一个点类型i的过程中。
If the process of type i points were independent of the process of type j points, then K[ij]inhom(r) would equal pi * r^2. Deviations between the empirical Kij curve and the theoretical curve pi * r^2 suggest dependence between the points of types i and j.
如果该过程的类型i点独立类型j点的过程中，那么K[ij]inhom(r)将等于pi * r^2。的经验Kij曲线和理论曲线之间的偏差pi * r^2建议点之间的类型i和j的依赖。
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$marks must be a factor.
参数X必须是点模式（类的对象"ppp"）或任何数据到as.ppp是可以接受的。它必须是一个显着的点图案，并标记矢量X$marks必须是一个因素。
The arguments i and j will be interpreted as levels of the factor X$marks. (Warning: this means that an integer value i=3 will be interpreted as the number 3, not the 3rd smallest level). If i and j are missing, they default to the first and second level of the marks factor, respectively.
的参数i和j将被解释为水平的因素X$marks。 （警告：这意味着一个整数值i=3将被解释为3号，而不是第三最小的水平）。如果i和j缺少，它们默认为第一级和第二级的标记因素，分别。
The argument lambdaI supplies the values of the intensity of the sub-process of points of type i. It may be either
的参数lambdaI提供子流程的类型i点的强度值。它可以是
a pixel image (object of class "im") which gives the values of the type i intensity at all locations in the window containing X;
像素图像（对象类"im"）的值在所有位置的窗口，其中包含的类型i强度X;
a numeric vector containing the values of the type i intensity evaluated only at the data points of type i. The length of this vector must equal the number of type i points in X.
一个数值向量包含的类型i的值强度进行评估，只有在数据类型i点。这个向量的长度必须等于类型i点X。
which can be evaluated to give values of the intensity at any locations.
它可以在任何地方进行评价，得到的强度的值。
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 should contain estimated values of the intensity of the sub-process of points of type j. It may be either a pixel image, a function, a numeric vector, or omitted.
同样lambdaJ应该包含的子进程的类型j点的强度估计值。它可以是一个像素的图像，一个函数，一个数值向量，或省略。
The optional argument lambdaIJ is for advanced use only. It is a matrix containing estimated values of the products of these two intensities for each pair of data points of types i and j respectively.
可选参数lambdaIJ是使用先进的。它是一种含有这两个强度的产品，为每个类型i和j分别对数据点的估计值的矩阵。
The argument r is the vector of values for the distance r at which Kij(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.
参数r是向量的值的距离r，Kij(r)应该进行评估。 r的值，必须增加非负数和最大r值必须超过包含在窗口中的最大的光盘的半径。
The argument correction chooses the edge correction as explained e.g. in Kest.
参数correction选择的边缘校正的解释，例如在Kest。
The pair correlation function can also be applied to the result of Kcross.inhom; see pcf.
对相关功能也可以应用到的结果Kcross.inhom看pcf。
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。
警告----------Warnings----------
The arguments i and j are always interpreted as levels of the factor X$marks. They are converted to character strings if they are not already character strings. The value i=1 does not refer to the first level of the factor.
的参数i和j总是被解释为水平的因素X$marks。它们被转换为字符串，如果他们不已经字符串。值i=1不是指第一级的因素。
（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----------
Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
参见----------See Also----------
Kcross, Kinhom, Kdot.inhom, Kmulti.inhom, pcf
Kcross，Kinhom，Kdot.inhom，Kmulti.inhom，pcf
实例----------Examples----------
# Lansing Woods data[蓝星伍兹数据]
data(lansing)
lansing <- lansing[seq(1,lansing$n, by=10)]
ma <- split(lansing)$maple
wh <- split(lansing)$whiteoak
# method (1): estimate intensities by nonparametric smoothing[方法（1）：平滑非参数估计强度]
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdaW <- density.ppp(wh, sigma=0.15, at="points")
K <- Kcross.inhom(lansing, "whiteoak", "maple", lambdaW, lambdaM)
# method (2): leave-one-out[方法（2）：留一出]
K <- Kcross.inhom(lansing, "whiteoak", "maple", sigma=0.15)
# method (3): fit parametric intensity model[方法（3）：合适的参数强度模型]
fit <- ppm(lansing, ~marks * polynom(x,y,2))
# evaluate fitted intensities at data points[评估合身的强度，数据点]
# (these are the intensities of the sub-processes of each type)[（这些每种类型的子流程的强度）]
inten <- fitted(fit, dataonly=TRUE)
# split according to types of points[分裂根据类型的点]
lambda <- split(inten, lansing$marks)
K <- Kcross.inhom(lansing, "whiteoak", "maple",
lambda$whiteoak, lambda$maple)
# synthetic example: type A points have intensity 50,[合成例如：键入一个点的强度为50，]
# type B points have intensity 100 * x[B型点的强度为100 * X]
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
K <- Kcross.inhom(X, "A", "B",
lambdaI=as.im(50, X$window), lambdaJ=lamB)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
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。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
|
发表于 2012-9-30 13:39:04
