Python 中的 Clark evans 聚集指数
Clark evans aggregation index in Python
Clark-Evans index是空间分析中衡量点聚集的最基本统计之一。但是，我在 Python 中找不到任何实现。所以我从上面的超链接改编了 R 代码。我想问一下 统计数据和 p 值对于这种不规则的研究区域是否正确:
函数
import numpy as np
import os, math
from shapely.geometry import Polygon, Point
from sklearn.neighbors import KDTree
from statistics import NormalDist
def clarkEvans (X, Y, roi):
""" Clark evans index takes point x,y coordinates and a polygon for cell shape (roi) and outputs Clark-Evans index:
R ~1 suggests spatial randomness, while R<<1 suggests clustering and R>>1 suggests ordering"""
# Import cell boundries from roi file
pgon = Polygon(roi)
# Calculate intensity from points/area
areaW = pgon.area
npts = len(X)
intensity = npts/areaW
if npts <2:
return(np.nan)
tmp_df = list(zip(X, Y))
# Get nearest neighbours for each observation
kdt = KDTree(tmp_df, leaf_size=30, metric='euclidean') # This is very good for large datasets, but maybe bad for small ones?
dists, ids = kdt.query(tmp_df, k=2)
dists = [x[1] for x in dists]
# Clark-Evans Index (mean NN distances/mean NN distances under poisson)
Dobs = np.mean(dists)
Dpoison = 1/(2 * math.sqrt(intensity))
Rnaive = Dobs/Dpoison
# Calculate p-value under normal distribution
SE = math.sqrt(((4 - math.pi) * areaW)/(4 * math.pi))/npts
Z = (Dobs - Dpoison)/SE
# Diff between observed and expected NN distances should have Normal Distribution according to Central Limit Theorem (CLT)
p_val = NormalDist().pdf(Z) # p_val for clustering
# Return the ClarkEvans Index and p-value
return(round(Rnaive,3), round(p_val, 3))
输出
图中是我的 Clark-Evans 指数被应用到两个不同的数据集并绘制成图。两种模式的索引相似，其中一种模式似乎更明显地聚集在一起。 p 值似乎发生了变化，我认为第二个图会有一个显着的 p 值，因为它是聚类的。
输入数据
# The xy coordinates of observations plus the point vertices of the study area (roi)
x1 = [123, 105, 71, 109, 96, 49, 86, 80, 120, 98, 59, 100, 118, 69, 84, 21, 95, 77, 158, 118, 87, 77, 87, 77, 82, 106, 120, 125, 61, 24, 53, 106, 52, 103, 89, 99, 111, 58, 97, 83, 51, 45, 64, 112, 114, 73, 55, 111, 110, 102, 116, 107, 84, 97, 118, 96, 116, 45, 102, 145, 126, 50, 103, 98, 20, 79, 113, 99, 90, 143, 36, 120, 106, 91, 95, 15, 122, 69, 28, 71, 66, 119, 78, 75, 113, 44, 85, 60, 88, 68, 116, 40, 59, 105, 65, 94, 79, 95, 120, 67, 78, 59, 89, 84, 111, 78, 72, 156, 162, 134, 157, 120, 126, 86, 58, 137, 32, 91, 68, 119, 112, 70, 120, 62, 118, 114, 66, 55, 99, 72, 91, 109, 53, 94, 71, 145, 146, 106, 15, 83, 104, 61, 129, 51, 58, 59, 113, 107, 94, 94, 69, 118, 74, 124, 107, 99, 66, 115, 159, 71, 115, 122, 76, 68, 79, 107, 81, 104, 87, 106, 105, 112, 111, 79, 54, 108, 62, 115, 36, 74, 84, 75, 64, 92, 64, 82, 77, 56, 75, 69, 88, 105, 96, 61, 84, 106, 31, 53, 173, 102, 99, 124, 87, 70, 25, 19, 122, 101, 126, 60, 94, 78, 97, 64, 45, 92, 114, 87, 96, 160, 88, 66, 40, 124, 103, 60, 129, 120, 35, 95, 56, 76, 116, 65, 7, 103, 160, 63, 134, 101, 56, 50, 89, 92, 99, 89, 120, 47, 58, 47, 74, 124, 8, 93, 121, 53, 66, 63, 90, 114, 91, 71, 123, 55, 142, 97, 69, 141, 92, 76, 69, 74, 66, 90, 81, 96, 110, 61, 58, 62, 50, 125, 106, 115, 79, 94, 118, 117, 64, 99, 55, 53, 93, 57, 116, 61, 125, 10, 119, 74, 64, 77, 127, 115, 59, 53, 99, 81, 68, 101, 43, 122, 129, 109, 108, 84, 103, 59, 105, 76, 122, 101, 101, 108, 79, 75, 60, 111, 97, 104, 82, 67, 96, 70, 96, 104, 103, 66, 89, 114, 121, 119, 104, 93, 156, 108, 88, 98, 52, 112, 65, 99, 107, 90, 107, 115, 73, 106, 100, 120, 128, 66, 116, 69, 113, 69, 103, 62, 124, 110, 124, 72, 76, 115, 73, 84, 95, 100, 51, 61, 82, 97, 106, 68, 112, 69, 115, 67, 80, 72, 63, 123, 92, 101, 61, 69, 103, 112, 70, 59, 91, 90, 102, 111, 41, 101, 90, 33, 122, 161, 161]
y1 = [37, 51, 35, 67, 94, 114, 62, 24, 64, 92, 55, 11, 74, 38, 79, 77, 90, 77, 70, 70, 41, 46, 81, 83, 81, 65, 63, 43, 56, 95, 26, 8, 68, 82, 44, 78, 77, 72, 45, 68, 83, 99, 100, 58, 91, 89, 115, 34, 46, 68, 79, 71, 41, 43, 48, 83, 67, 69, 42, 55, 63, 69, 47, 67, 102, 72, 33, 77, 67, 1, 123, 59, 69, 47, 73, 79, 89, 48, 55, 97, 56, 92, 121, 70, 48, 47, 114, 62, 84, 78, 54, 55, 79, 76, 62, 63, 83, 71, 74, 83, 50, 67, 84, 81, 75, 59, 12, 77, 97, 6, 26, 55, 10, 74, 58, 59, 77, 76, 77, 68, 60, 50, 53, 89, 76, 87, 67, 86, 86, 73, 79, 74, 62, 54, 67, 58, 23, 76, 95, 63, 38, 76, 117, 18, 52, 46, 98, 62, 44, 36, 86, 52, 74, 51, 85, 100, 75, 73, 63, 38, 64, 91, 47, 70, 77, 88, 70, 88, 88, 39, 52, 45, 79, 56, 74, 60, 59, 69, 116, 44, 55, 48, 70, 83, 66, 87, 78, 73, 58, 76, 46, 50, 43, 81, 102, 45, 115, 88, 80, 34, 55, 55, 97, 103, 112, 122, 111, 97, 90, 81, 22, 36, 87, 86, 48, 39, 42, 83, 57, 16, 100, 89, 115, 75, 69, 86, 69, 69, 74, 39, 52, 23, 63, 49, 92, 96, 71, 105, 10, 75, 84, 80, 30, 30, 59, 52, 32, 119, 107, 74, 79, 101, 106, 99, 77, 66, 89, 83, 102, 94, 97, 78, 91, 93, 16, 11, 33, 16, 78, 50, 30, 26, 79, 34, 32, 86, 64, 40, 63, 51, 58, 52, 92, 98, 35, 36, 34, 47, 86, 88, 60, 80, 92, 96, 94, 94, 98, 111, 49, 54, 56, 36, 72, 94, 92, 102, 105, 32, 40, 30, 73, 59, 107, 39, 46, 40, 53, 57, 93, 92, 63, 59, 65, 68, 81, 69, 56, 53, 53, 85, 56, 55, 93, 45, 40, 68, 101, 93, 29, 44, 93, 93, 46, 67, 38, 34, 97, 93, 72, 90, 62, 68, 32, 31, 74, 71, 59, 38, 51, 95, 73, 82, 5, 53, 50, 34, 49, 43, 82, 77, 65, 88, 87, 89, 30, 38, 45, 36, 79, 89, 88, 100, 98, 45, 41, 20, 35, 51, 77, 64, 60, 63, 33, 44, 78, 82, 83, 70, 74, 78, 41, 61, 71, 40, 124, 82, 67, 121, 5, 65, 66]
roi1 = [[152.5078125, 3.7060546875], [158.8408203125, 12.455078125], [165.5126953125, 25.3154296875], [170.796875, 38.787109375], [171.013671875, 46.02734375], [172.6083984375, 53.0615234375], [172.6083984375, 63.9306640625], [174.419921875, 70.9169921875], [174.419921875, 85.41015625], [175.947265625, 92.4296875], [175.7998046875, 103.2626953125], [169.52734375, 116.3212890625], [166.9765625, 118.89453125], [159.7451171875, 119.2177734375], [152.7265625, 121.01953125], [138.2333984375, 121.029296875], [131.21875, 122.8408203125], [73.248046875, 122.8408203125], [66.2119140625, 124.5546875], [58.966796875, 124.65234375], [51.9990234375, 126.4638671875], [23.013671875, 126.4638671875], [19.42578125, 125.958984375], [16.5361328125, 123.7734375], [10.20703125, 115.0283203125], [0.5068359375, 95.57421875], [0.5537109375, 91.951171875], [9.0869140625, 80.318359375], [12.552734375, 73.9599609375], [18.884765625, 65.2119140625], [25.89453125, 56.994140625], [35.611328125, 41.7626953125], [42.345703125, 33.296875], [45.7568359375, 26.90625], [53.634765625, 14.7744140625], [58.1103515625, 9.078125], [64.916015625, 6.8984375], [86.654296875, 6.8984375], [93.6904296875, 5.291015625], [100.89453125, 4.57421875], [104.2763671875, 3.275390625], [122.3837890625, 3.025390625], [129.3935546875, 1.4638671875], [143.8857421875, 1.4638671875], [147.376953125, 0.4931640625]]
clarkEvans (x1, y1, roi1)
x2 = [94, 111, 79, 95, 86, 46, 30, 34, 53, 17, 44, 20, 42, 56, 23, 21, 50, 16, 50, 52, 47, 132, 44, 40, 43, 33, 29, 52, 24, 125, 86, 84]
y2 = [17, 71, 94, 88, 108, 132, 116, 115, 121, 132, 120, 121, 123, 116, 116, 139, 121, 124, 116, 140, 141, 33, 119, 118, 125, 130, 123, 122, 40, 23, 80, 107]
roi2 = [[129.4560546875, 3.6552734375], [132.3408203125, 5.84765625], [134.4638671875, 12.7744140625], [134.4638671875, 45.3828125], [132.65234375, 56.0302734375], [132.65234375, 66.8994140625], [131.4169921875, 70.3056640625], [130.7021484375, 77.5029296875], [129.029296875, 84.5419921875], [129.029296875, 88.1650390625], [127.2177734375, 95.1728515625], [127.16796875, 106.04296875], [125.40625, 113.0712890625], [125.40625, 116.6943359375], [123.896484375, 119.9873046875], [120.6533203125, 121.6025390625], [110.0654296875, 123.9130859375], [99.6181640625, 126.8427734375], [89.896484375, 131.7041015625], [83.8388671875, 135.638671875], [77.03515625, 138.134765625], [73.4228515625, 138.40625], [56.181640625, 143.8408203125], [45.568359375, 142.029296875], [31.076171875, 142.029296875], [27.4736328125, 141.6455078125], [20.626953125, 139.302734375], [15.5029296875, 134.1787109375], [11.0546875, 128.5234375], [4.537109375, 115.5849609375], [0.40625, 98.0078125], [0.513671875, 72.646484375], [4.927734375, 55.0859375], [11.4091796875, 42.123046875], [15.333984375, 36.0859375], [21.94921875, 27.4912109375], [34.7587890625, 14.6806640625], [43.416015625, 8.205078125], [57.9013671875, 7.970703125], [61.28125, 6.666015625], [71.9052734375, 4.541015625], [82.7705078125, 4.34765625], [89.7578125, 2.5361328125], [107.873046875, 2.5361328125], [114.8916015625, 1.015625], [122.126953125, 0.724609375]]
clarkEvans (x2, y2, roi2)
使用原始 R 函数产生相似但不相等的结果：
clarkevans.test(X, alternative = "clustered")
>R= 0.87719, p-value = 9.542e-07 # First dataset
>R= 0.83365, p-value = 0.03591 # Second dataset
我不确定统计数据和 p 值计算是否有效，因为我的研究区域形状不规则。变量 SE 是用 pi 计算的，这看起来像是在估计圆形研究区域中的随机分布。我应该做 Monte Carlo 模拟吗？有没有办法避免这种情况？
干杯！
我以前没有使用过 Clark-Evans (CE) 索引，但是阅读了您链接到的信息并研究了您的代码后，我的解释是：
- 数据集 2 的索引值小于数据集 1 的索引值。这正确地反映了聚集度的视觉差异，即较小的索引值与更聚集的数据相关联。
- 说两个 CE 索引值相似可能没有意义，除了特殊情况，例如观察到两个 CE 索引值都小于 1 或都大于 1，或者如果 A < B < C 则AB 比 AC 更相似。
- p 值和指数值衡量的是不同的东西。指标值衡量聚集度（如果小于 1）或规律性（如果大于 1）。 p 值（相反）衡量数据比偶然预期更聚集或比偶然预期更规律的确定性。 p 值尤其对样本量以及点的分布敏感。
- 在计算 SE 时使用 pi 反映了点之间的欧几里得距离假设（而不是城市街区距离）。也就是说，点的最近邻点是径向距离最小的点。在计算 SE 时使用 pi 不会对感兴趣区域的形状做出任何假设。
- 特别是对于小型数据集（如 Dataset2），您需要追踪有关边界效应对索引值或 p 值的潜在影响的信息。
更具推测性，我想知道使用凸包来帮助确定感兴趣区域而不是主观地这样做是否有用。
Clark-Evans index是空间分析中衡量点聚集的最基本统计之一。但是，我在 Python 中找不到任何实现。所以我从上面的超链接改编了 R 代码。我想问一下 统计数据和 p 值对于这种不规则的研究区域是否正确:
函数
import numpy as np
import os, math
from shapely.geometry import Polygon, Point
from sklearn.neighbors import KDTree
from statistics import NormalDist
def clarkEvans (X, Y, roi):
""" Clark evans index takes point x,y coordinates and a polygon for cell shape (roi) and outputs Clark-Evans index:
R ~1 suggests spatial randomness, while R<<1 suggests clustering and R>>1 suggests ordering"""
# Import cell boundries from roi file
pgon = Polygon(roi)
# Calculate intensity from points/area
areaW = pgon.area
npts = len(X)
intensity = npts/areaW
if npts <2:
return(np.nan)
tmp_df = list(zip(X, Y))
# Get nearest neighbours for each observation
kdt = KDTree(tmp_df, leaf_size=30, metric='euclidean') # This is very good for large datasets, but maybe bad for small ones?
dists, ids = kdt.query(tmp_df, k=2)
dists = [x[1] for x in dists]
# Clark-Evans Index (mean NN distances/mean NN distances under poisson)
Dobs = np.mean(dists)
Dpoison = 1/(2 * math.sqrt(intensity))
Rnaive = Dobs/Dpoison
# Calculate p-value under normal distribution
SE = math.sqrt(((4 - math.pi) * areaW)/(4 * math.pi))/npts
Z = (Dobs - Dpoison)/SE
# Diff between observed and expected NN distances should have Normal Distribution according to Central Limit Theorem (CLT)
p_val = NormalDist().pdf(Z) # p_val for clustering
# Return the ClarkEvans Index and p-value
return(round(Rnaive,3), round(p_val, 3))
输出
图中是我的 Clark-Evans 指数被应用到两个不同的数据集并绘制成图。两种模式的索引相似，其中一种模式似乎更明显地聚集在一起。 p 值似乎发生了变化，我认为第二个图会有一个显着的 p 值，因为它是聚类的。
输入数据
# The xy coordinates of observations plus the point vertices of the study area (roi)
x1 = [123, 105, 71, 109, 96, 49, 86, 80, 120, 98, 59, 100, 118, 69, 84, 21, 95, 77, 158, 118, 87, 77, 87, 77, 82, 106, 120, 125, 61, 24, 53, 106, 52, 103, 89, 99, 111, 58, 97, 83, 51, 45, 64, 112, 114, 73, 55, 111, 110, 102, 116, 107, 84, 97, 118, 96, 116, 45, 102, 145, 126, 50, 103, 98, 20, 79, 113, 99, 90, 143, 36, 120, 106, 91, 95, 15, 122, 69, 28, 71, 66, 119, 78, 75, 113, 44, 85, 60, 88, 68, 116, 40, 59, 105, 65, 94, 79, 95, 120, 67, 78, 59, 89, 84, 111, 78, 72, 156, 162, 134, 157, 120, 126, 86, 58, 137, 32, 91, 68, 119, 112, 70, 120, 62, 118, 114, 66, 55, 99, 72, 91, 109, 53, 94, 71, 145, 146, 106, 15, 83, 104, 61, 129, 51, 58, 59, 113, 107, 94, 94, 69, 118, 74, 124, 107, 99, 66, 115, 159, 71, 115, 122, 76, 68, 79, 107, 81, 104, 87, 106, 105, 112, 111, 79, 54, 108, 62, 115, 36, 74, 84, 75, 64, 92, 64, 82, 77, 56, 75, 69, 88, 105, 96, 61, 84, 106, 31, 53, 173, 102, 99, 124, 87, 70, 25, 19, 122, 101, 126, 60, 94, 78, 97, 64, 45, 92, 114, 87, 96, 160, 88, 66, 40, 124, 103, 60, 129, 120, 35, 95, 56, 76, 116, 65, 7, 103, 160, 63, 134, 101, 56, 50, 89, 92, 99, 89, 120, 47, 58, 47, 74, 124, 8, 93, 121, 53, 66, 63, 90, 114, 91, 71, 123, 55, 142, 97, 69, 141, 92, 76, 69, 74, 66, 90, 81, 96, 110, 61, 58, 62, 50, 125, 106, 115, 79, 94, 118, 117, 64, 99, 55, 53, 93, 57, 116, 61, 125, 10, 119, 74, 64, 77, 127, 115, 59, 53, 99, 81, 68, 101, 43, 122, 129, 109, 108, 84, 103, 59, 105, 76, 122, 101, 101, 108, 79, 75, 60, 111, 97, 104, 82, 67, 96, 70, 96, 104, 103, 66, 89, 114, 121, 119, 104, 93, 156, 108, 88, 98, 52, 112, 65, 99, 107, 90, 107, 115, 73, 106, 100, 120, 128, 66, 116, 69, 113, 69, 103, 62, 124, 110, 124, 72, 76, 115, 73, 84, 95, 100, 51, 61, 82, 97, 106, 68, 112, 69, 115, 67, 80, 72, 63, 123, 92, 101, 61, 69, 103, 112, 70, 59, 91, 90, 102, 111, 41, 101, 90, 33, 122, 161, 161]
y1 = [37, 51, 35, 67, 94, 114, 62, 24, 64, 92, 55, 11, 74, 38, 79, 77, 90, 77, 70, 70, 41, 46, 81, 83, 81, 65, 63, 43, 56, 95, 26, 8, 68, 82, 44, 78, 77, 72, 45, 68, 83, 99, 100, 58, 91, 89, 115, 34, 46, 68, 79, 71, 41, 43, 48, 83, 67, 69, 42, 55, 63, 69, 47, 67, 102, 72, 33, 77, 67, 1, 123, 59, 69, 47, 73, 79, 89, 48, 55, 97, 56, 92, 121, 70, 48, 47, 114, 62, 84, 78, 54, 55, 79, 76, 62, 63, 83, 71, 74, 83, 50, 67, 84, 81, 75, 59, 12, 77, 97, 6, 26, 55, 10, 74, 58, 59, 77, 76, 77, 68, 60, 50, 53, 89, 76, 87, 67, 86, 86, 73, 79, 74, 62, 54, 67, 58, 23, 76, 95, 63, 38, 76, 117, 18, 52, 46, 98, 62, 44, 36, 86, 52, 74, 51, 85, 100, 75, 73, 63, 38, 64, 91, 47, 70, 77, 88, 70, 88, 88, 39, 52, 45, 79, 56, 74, 60, 59, 69, 116, 44, 55, 48, 70, 83, 66, 87, 78, 73, 58, 76, 46, 50, 43, 81, 102, 45, 115, 88, 80, 34, 55, 55, 97, 103, 112, 122, 111, 97, 90, 81, 22, 36, 87, 86, 48, 39, 42, 83, 57, 16, 100, 89, 115, 75, 69, 86, 69, 69, 74, 39, 52, 23, 63, 49, 92, 96, 71, 105, 10, 75, 84, 80, 30, 30, 59, 52, 32, 119, 107, 74, 79, 101, 106, 99, 77, 66, 89, 83, 102, 94, 97, 78, 91, 93, 16, 11, 33, 16, 78, 50, 30, 26, 79, 34, 32, 86, 64, 40, 63, 51, 58, 52, 92, 98, 35, 36, 34, 47, 86, 88, 60, 80, 92, 96, 94, 94, 98, 111, 49, 54, 56, 36, 72, 94, 92, 102, 105, 32, 40, 30, 73, 59, 107, 39, 46, 40, 53, 57, 93, 92, 63, 59, 65, 68, 81, 69, 56, 53, 53, 85, 56, 55, 93, 45, 40, 68, 101, 93, 29, 44, 93, 93, 46, 67, 38, 34, 97, 93, 72, 90, 62, 68, 32, 31, 74, 71, 59, 38, 51, 95, 73, 82, 5, 53, 50, 34, 49, 43, 82, 77, 65, 88, 87, 89, 30, 38, 45, 36, 79, 89, 88, 100, 98, 45, 41, 20, 35, 51, 77, 64, 60, 63, 33, 44, 78, 82, 83, 70, 74, 78, 41, 61, 71, 40, 124, 82, 67, 121, 5, 65, 66]
roi1 = [[152.5078125, 3.7060546875], [158.8408203125, 12.455078125], [165.5126953125, 25.3154296875], [170.796875, 38.787109375], [171.013671875, 46.02734375], [172.6083984375, 53.0615234375], [172.6083984375, 63.9306640625], [174.419921875, 70.9169921875], [174.419921875, 85.41015625], [175.947265625, 92.4296875], [175.7998046875, 103.2626953125], [169.52734375, 116.3212890625], [166.9765625, 118.89453125], [159.7451171875, 119.2177734375], [152.7265625, 121.01953125], [138.2333984375, 121.029296875], [131.21875, 122.8408203125], [73.248046875, 122.8408203125], [66.2119140625, 124.5546875], [58.966796875, 124.65234375], [51.9990234375, 126.4638671875], [23.013671875, 126.4638671875], [19.42578125, 125.958984375], [16.5361328125, 123.7734375], [10.20703125, 115.0283203125], [0.5068359375, 95.57421875], [0.5537109375, 91.951171875], [9.0869140625, 80.318359375], [12.552734375, 73.9599609375], [18.884765625, 65.2119140625], [25.89453125, 56.994140625], [35.611328125, 41.7626953125], [42.345703125, 33.296875], [45.7568359375, 26.90625], [53.634765625, 14.7744140625], [58.1103515625, 9.078125], [64.916015625, 6.8984375], [86.654296875, 6.8984375], [93.6904296875, 5.291015625], [100.89453125, 4.57421875], [104.2763671875, 3.275390625], [122.3837890625, 3.025390625], [129.3935546875, 1.4638671875], [143.8857421875, 1.4638671875], [147.376953125, 0.4931640625]]
clarkEvans (x1, y1, roi1)
x2 = [94, 111, 79, 95, 86, 46, 30, 34, 53, 17, 44, 20, 42, 56, 23, 21, 50, 16, 50, 52, 47, 132, 44, 40, 43, 33, 29, 52, 24, 125, 86, 84]
y2 = [17, 71, 94, 88, 108, 132, 116, 115, 121, 132, 120, 121, 123, 116, 116, 139, 121, 124, 116, 140, 141, 33, 119, 118, 125, 130, 123, 122, 40, 23, 80, 107]
roi2 = [[129.4560546875, 3.6552734375], [132.3408203125, 5.84765625], [134.4638671875, 12.7744140625], [134.4638671875, 45.3828125], [132.65234375, 56.0302734375], [132.65234375, 66.8994140625], [131.4169921875, 70.3056640625], [130.7021484375, 77.5029296875], [129.029296875, 84.5419921875], [129.029296875, 88.1650390625], [127.2177734375, 95.1728515625], [127.16796875, 106.04296875], [125.40625, 113.0712890625], [125.40625, 116.6943359375], [123.896484375, 119.9873046875], [120.6533203125, 121.6025390625], [110.0654296875, 123.9130859375], [99.6181640625, 126.8427734375], [89.896484375, 131.7041015625], [83.8388671875, 135.638671875], [77.03515625, 138.134765625], [73.4228515625, 138.40625], [56.181640625, 143.8408203125], [45.568359375, 142.029296875], [31.076171875, 142.029296875], [27.4736328125, 141.6455078125], [20.626953125, 139.302734375], [15.5029296875, 134.1787109375], [11.0546875, 128.5234375], [4.537109375, 115.5849609375], [0.40625, 98.0078125], [0.513671875, 72.646484375], [4.927734375, 55.0859375], [11.4091796875, 42.123046875], [15.333984375, 36.0859375], [21.94921875, 27.4912109375], [34.7587890625, 14.6806640625], [43.416015625, 8.205078125], [57.9013671875, 7.970703125], [61.28125, 6.666015625], [71.9052734375, 4.541015625], [82.7705078125, 4.34765625], [89.7578125, 2.5361328125], [107.873046875, 2.5361328125], [114.8916015625, 1.015625], [122.126953125, 0.724609375]]
clarkEvans (x2, y2, roi2)
使用原始 R 函数产生相似但不相等的结果：
clarkevans.test(X, alternative = "clustered")
>R= 0.87719, p-value = 9.542e-07 # First dataset
>R= 0.83365, p-value = 0.03591 # Second dataset
我不确定统计数据和 p 值计算是否有效，因为我的研究区域形状不规则。变量 SE 是用 pi 计算的，这看起来像是在估计圆形研究区域中的随机分布。我应该做 Monte Carlo 模拟吗？有没有办法避免这种情况？
干杯！
我以前没有使用过 Clark-Evans (CE) 索引，但是阅读了您链接到的信息并研究了您的代码后，我的解释是：
- 数据集 2 的索引值小于数据集 1 的索引值。这正确地反映了聚集度的视觉差异，即较小的索引值与更聚集的数据相关联。
- 说两个 CE 索引值相似可能没有意义，除了特殊情况，例如观察到两个 CE 索引值都小于 1 或都大于 1，或者如果 A < B < C 则AB 比 AC 更相似。
- p 值和指数值衡量的是不同的东西。指标值衡量聚集度（如果小于 1）或规律性（如果大于 1）。 p 值（相反）衡量数据比偶然预期更聚集或比偶然预期更规律的确定性。 p 值尤其对样本量以及点的分布敏感。
- 在计算 SE 时使用 pi 反映了点之间的欧几里得距离假设（而不是城市街区距离）。也就是说，点的最近邻点是径向距离最小的点。在计算 SE 时使用 pi 不会对感兴趣区域的形状做出任何假设。
- 特别是对于小型数据集（如 Dataset2），您需要追踪有关边界效应对索引值或 p 值的潜在影响的信息。
更具推测性，我想知道使用凸包来帮助确定感兴趣区域而不是主观地这样做是否有用。