Gcross(spatstat)
Gcross()所属R语言包：spatstat
Multitype Nearest Neighbour Distance Function (i-to-j)
多类型最近邻距离函数（I--J）
译者：生物统计家园网 机器人LoveR
描述----------Description----------
For a multitype point pattern, estimate the distribution of the distance from a point of type i to the nearest point of type j.
对于多类型的点模式，估计分布的距离的最近点的类型i从类型j点。
用法----------Usage----------
Gcross(X, i, j, r=NULL, breaks=NULL, ..., correction=c("rs", "km", "han"))
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of the cross type distance distribution function Gij(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，从其中一个估计的交叉型距离分布函数Gij(r)将被计算出来的。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：r
Optional. Numeric vector. The values of the argument r at which the distribution function Gij(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的分布函数Gij(r)应该进行评估。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：...
Ignored.
忽略。
参数：correction
Optional. Character string specifying the edge correction(s) to be used. Options are "none", "rs", "km", "hanisch" and "best".
可选。字符的字符串指定的边缘校正（s）到被使用。选项"none"，"rs"，"km"，"hanisch"和"best"。
Details
详细信息----------Details----------
This function Gcross and its companions Gdot and Gmulti are generalisations of the function Gest to multitype point patterns.
此功能Gcross和它的同伴Gdot和Gmulti的功能Gest多类型，点模式的概括。
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.
一个多类型的模式是一个空间格局分为有限数量的可能的“颜色”或“类型”的点。在spatstat包，多类型图案表示作为一个单一的点图案在该点进行标记的对象，并连接到每个点的标记值确定该点的类型。
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$marks must be a factor. The arguments i and j will be interpreted as levels of the factor X$marks. (Warning: this means that an integer value i=3 will be interpreted as the number 3, not the 3rd smallest level).
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$marks必须是一个因素。的参数i和j将被解释为水平的因素X$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）。
The “cross-type” (type i to type j) nearest neighbour distance distribution function of a multitype point process is the cumulative distribution function Gij(r) of the distance from a typical random point of the process with type i the nearest point of type j.
“十字型”（类型i输入“j）最近邻距离分布函数的多类型点过程中的累积分布函数Gij(r)一个典型的随机点的距离的类型i最近点的类型j。
An estimate of Gij(r) is a useful summary statistic in exploratory data analysis of a multitype point pattern. If the process of type i points were independent of the process of type j points, then Gij(r) would equal Fj(r), the empty space function of the type j points. For a multitype Poisson point process where the type i points have intensity lambda[i], we have
Gij(r)的估计是一个多类型模式的探索性数据分析的一个有用的摘要统计。如果类型的过程i点是独立类型j点的过程中，那么Gij(r)将等于Fj(r)，空的空间的类型的功能j 点。对于进行多的泊松点的过程类型i点有强度lambda[i]，我们有
Deviations between the empirical and theoretical Gij curves may suggest dependence between the points of types i and j.
之间的偏差的理论和实证Gij曲线可能会建议点之间的类型i和j的依赖。
This algorithm estimates the distribution function Gij(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 X$window) may have arbitrary shape. Biases due to edge effects are treated in the same manner as in Gest.
该算法估计分布函数Gij(r)点模式X。它假定X可以被视为一个实现了一个固定的（的空间均匀）随机空间点在飞机上，观察到一个有限的窗口。窗口（中指定XX$window的）可以有任意形状的。边缘效应产生的偏差的处理中相同的方式，当在Gest。
The argument r is the vector of values for the distance r at which Gij(r) should be evaluated. It is also used to determine the breakpoints (in the sense of hist) for the computation of histograms of distances. The reduced-sample and Kaplan-Meier estimators are computed from histogram counts. In the case of the Kaplan-Meier estimator this introduces a discretisation error which is controlled by the fineness of the breakpoints.
参数r是向量的值的距离r，Gij(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。减少了样品和Kaplan-Meier估计从直方图数量计算。在Kaplan-Meier法估计的情况下，引入了离散误差控制细度的断点。
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. Furthermore, the successive entries of r must be finely spaced.
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。此外，连续进入r必须进行精细的间隔。
The algorithm also returns an estimate of the hazard rate function, lambda(r), of Gij(r). This estimate should be used with caution as Gij(r) is not necessarily differentiable.
该算法也将返回的危险率函数的估计，lambda(r)，Gij(r)。这个估计应谨慎使用，因为Gij(r)不一定是微。
The naive empirical distribution of distances from each point of the pattern X to the nearest other point of the pattern, is a biased estimate of Gij. However this is also returned by the algorithm, as it is sometimes useful in other contexts. Care should be taken not to use the uncorrected empirical Gij as if it were an unbiased estimator of Gij.
天真的经验分布模式X最近的其他点的模式，每个点的距离，是一个有偏估计Gij。然而，这也由该算法返回，有时是有用的，因为它是在其他情况下。应注意不要使用未校正的经验Gij如果它是一个无偏估计Gij。
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 six numeric columns
本质上是一个数据框包含6个数字列
参数：r
the values of the argument r at which the function Gij(r) has been estimated
的参数的值的r在哪些函数Gij(r)已估计
参数：rs
the “reduced sample” or “border correction” estimator of Gij(r)
“减少样品”或“边界校正”估计Gij(r)
参数：han
the Hanisch-style estimator of Gij(r)
Hanisch式估计Gij(r)
参数：km
the spatial Kaplan-Meier estimator of Gij(r)
Kaplan-Meier生存的空间估计Gij(r)
参数：hazard
the hazard rate lambda(r) of Gij(r) by the spatial Kaplan-Meier method
危险率lambda(r)Gij(r)的空间Kaplan-Meier法
参数：raw
the uncorrected estimate of Gij(r), i.e. the empirical distribution of the distances from each point of type i to the nearest point of type j
未校正的估计Gij(r)，即经验分布的距离，每个点类型i到最近点类型j
参数：theo
the theoretical value of Gij(r) for a marked Poisson process with the same estimated intensity (see below).
Gij(r)显着的泊松过程的估计强度（见下文）的理论值。
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。
The function Gij does not necessarily have a density.
的功能Gij不一定具有的密度。
The reduced sample estimator of Gij is pointwise approximately unbiased, but need not be a valid distribution function; it may not be a nondecreasing function of r. Its range is always within [0,1].
减少样本估计Gij逐点约是公正的，但不必是一个有效的分布函数，它可能不会是一个非减函数的r。它的范围是总是在[0,1]。
The spatial Kaplan-Meier estimator of Gij is always nondecreasing but its maximum value may be less than 1.
的空间的Kaplan-Meier估计的Gij总是非降，但其最大的值可以是小于1。
（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----------
John Wiley and Sons, 1991.
Academic Press, 1983.
Displaced amacrine cells in the retina of a rabbit : analysis of a bivariate spatial point pattern. J. Neurosci. Meth. 18, 115–125.
A bivariate spatial point pattern of ants' nests. Applied Statistics 32, 293–303
Methods for analysing spatial processes of several types of points. J. Royal Statist. Soc. Ser. B 44, 406–413.
Cambridge University Press, 1988.
Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.
Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511–532.
参见----------See Also----------
Gdot, Gest, Gmulti
Gdot，Gest，Gmulti
实例----------Examples----------
data(betacells)
# cat retina data[猫的视网膜数据]
G01 <- Gcross(betacells)
# equivalent to:[等效于：]
## Not run: [＃不运行：]
G01 <- Gcross(betacells, "off", "on")
## End(Not run)[＃（不执行）]
plot(G01)
# empty space function of `on' points[空的空间功能上点]
## Not run: [＃不运行：]
F1 <- Fest(split(betacells)$on, r = G01$r, eps=10.0)
lines(F1$r, F1$km, lty=3)
## End(Not run)[＃（不执行）]
# synthetic example [合成例]
pp <- runifpoispp(30)
pp <- pp %mark% factor(sample(0:1, pp$n, replace=TRUE))
G <- Gcross(pp, "0", "1") # note: "0" not 0[附注：“0”不为0时]
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。
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发表于 2012-9-30 13:31:07
