对每一种聚类算法的结果我们都会遇到一个真实的问题：就是这个结果能否反映真实的生态情况。我们已经看到内部准则（如轮廓法或其他聚类质量指数） 都仅仅是依赖物种数据，还不足以选择最佳聚类结果。选择最终的聚类结果有时也需要基于生态学解释。生态学解释可视为样方聚类的外部验证。
利用外部独立的解释变量验证聚类结果（作为响应数据）可以用判别式分析。当然也可以将样方分组当做因子对解释变量（作为响应数据）进行方差分析，了解解释变量在各组间是否有显著差异。
# 加载所需的程序包
library(ade4)
library(vegan) # 应该先加载ade4后加载vegan以避免冲突
library(gclus)
library(cluster)
library(RColorBrewer)
library(labdsv)
library(mvpart)
library(MVPARTwrap) # MVPARTwrap这个程序包必须从本地zip文件安装
# 导入CSV格式的数据
rm(list = ls())
setwd("D:\\Users\\Administrator\\Desktop\\RStudio\\数量生态学\\DATA")
spe <- read.csv("DoubsSpe.csv", row.names=1)
env <- read.csv("DoubsEnv.csv", row.names=1)
spa <- read.csv("DoubsSpa.csv", row.names=1)
# 删除无物种数据的样方8
spe <- spe[-8,]
env <- env[-8,]
spa <- spa[-8,]
# 物种多度数据：先计算样方之间的弦距离矩阵，然后进行单连接聚合聚类
# **************************************************************
spe.norm <- decostand(spe, "normalize")
spe.ch <- vegdist(spe.norm, "euc")
spe.ch.single <- hclust(spe.ch, method="single")
# 预转化后物种数据k-均值划分
# ****************************
spe.kmeans <- kmeans(spe.norm, centers=4, nstart=100)
下面的案例展示一样方聚类簇为因子去对解释变量进行方差分析。首先检验某一环境变量是否符合方差分析假设（残差正态性和方差齐性），然后用传统的单因素方差分析或非参数的Kruskal-Wallis检验解释变量在组间是否有显著差异。
# 基于k-均值划分结果（分4组）的样方聚类簇与4个环境变量的关系
# *************************************************************
attach(env)
# 定量环境变量箱线图
# 海拔、坡度、氧含量和铵浓度
par(mfrow=c(2,2))
boxplot(sqrt(alt) ~ spe.kmeans$cluster, main="海拔", las=1,
ylab="sqrt(alt)", col=2:5, varwidth=TRUE)
boxplot(log(pen) ~ spe.kmeans$cluster, main="坡度", las=1,
ylab="log(pen)", col=2:5, varwidth=TRUE)
boxplot(oxy ~ spe.kmeans$cluster, main="氧含量", las=1,
ylab="oxy", col=2:5, varwidth=TRUE)
boxplot(sqrt(amm) ~ spe.kmeans$cluster, main="铵浓度", las=1,
ylab="sqrt(amm)", col=2:5, varwidth=TRUE)
> # 检验方差分析的假设
> # 检验残差的正态性
> shapiro.test(resid(lm(sqrt(alt) ~ as.factor(spe.kmeans$cluster))))
Shapiro-Wilk normality test
data: resid(lm(sqrt(alt) ~ as.factor(spe.kmeans$cluster)))
W = 0.96238, p-value = 0.3756
> shapiro.test(resid(lm(log(pen) ~ as.factor(spe.kmeans$cluster))))
Shapiro-Wilk normality test
data: resid(lm(log(pen) ~ as.factor(spe.kmeans$cluster)))
W = 0.95182, p-value = 0.204
> shapiro.test(resid(lm(log(pen) ~ as.factor(spe.kmeans$cluster))))
Shapiro-Wilk normality test
data: resid(lm(log(pen) ~ as.factor(spe.kmeans$cluster)))
W = 0.95182, p-value = 0.204
> shapiro.test(resid(lm(oxy ~ as.factor(spe.kmeans$cluster))))
Shapiro-Wilk normality test
data: resid(lm(oxy ~ as.factor(spe.kmeans$cluster)))
W = 0.93941, p-value = 0.09674
> shapiro.test(resid(lm(sqrt(amm) ~ as.factor(spe.kmeans$cluster))))
Shapiro-Wilk normality test
data: resid(lm(sqrt(amm) ~ as.factor(spe.kmeans$cluster)))
W = 0.95398, p-value = 0.2319
> #检验结果表明sqrt(alt)、log(pen)、oxy和sqrt(amm)的残差是正态分布。
> #也尝试为其他的环境变量寻找好的标准化转化。
> # 检验方差齐性
> bartlett.test(sqrt(alt), as.factor(spe.kmeans$cluster))
Bartlett test of homogeneity of variances
data: sqrt(alt) and as.factor(spe.kmeans$cluster)
Bartlett's K-squared = 16.953, df = 3, p-value = 0.0007227
> bartlett.test(log(pen), as.factor(spe.kmeans$cluster))
Bartlett test of homogeneity of variances
data: log(pen) and as.factor(spe.kmeans$cluster)
Bartlett's K-squared = 2.9832, df = 3, p-value = 0.3942
> bartlett.test(oxy, as.factor(spe.kmeans$cluster))
Bartlett test of homogeneity of variances
data: oxy and as.factor(spe.kmeans$cluster)
Bartlett's K-squared = 1.8258, df = 3, p-value = 0.6093
> bartlett.test(sqrt(amm), as.factor(spe.kmeans$cluster))
Bartlett test of homogeneity of variances
data: sqrt(amm) and as.factor(spe.kmeans$cluster)
Bartlett's K-squared = 5.7203, df = 3, p-value = 0.126
> #变量sqrt(alt)的方差不齐，所以参数检验的方差分析不适用
> #可被参数检验的变量的方差分析
> summary(aov(log(pen) ~ as.factor(spe.kmeans$cluster)))
Df Sum Sq Mean Sq F value Pr(>F)
as.factor(spe.kmeans$cluster) 3 18.05 6.018 7.283 0.00114 **
Residuals 25 20.66 0.826
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(aov(oxy ~ as.factor(spe.kmeans$cluster)))
Df Sum Sq Mean Sq F value Pr(>F)
as.factor(spe.kmeans$cluster) 3 103.54 34.51 26.27 6.75e-08 ***
Residuals 25 32.84 1.31
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(aov(sqrt(amm) ~ as.factor(spe.kmeans$cluster)))
Df Sum Sq Mean Sq F value Pr(>F)
as.factor(spe.kmeans$cluster) 3 2.6126 0.8709 49.55 1.15e-10 ***
Residuals 25 0.4394 0.0176
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #坡度、含氧量和铵浓度在不同聚类簇之间是否差异显著？
> # 变量alt的Kruskal-Wallis检验
> kruskal.test(alt ~ as.factor(spe.kmeans$cluster))
Kruskal-Wallis rank sum test
data: alt by as.factor(spe.kmeans$cluster)
Kruskal-Wallis chi-squared = 21.526, df = 3, p-value = 8.186e-05
> #海拔在不同聚类簇之间是否有显著差异？
> detach(env)
双类型比较（列联表分析）
> # 两种聚类的列联表
> # ******************
> # 基于环境变量（见第2章）的样方聚类
> env2 <- env[,-1]
> env.de <- vegdist(scale(env2), "euc")
> env.kmeans <- kmeans(env.de, centers=4, nstart=100)
> env.KM.4 <- env.kmeans$cluster
> # 比较两种聚类的结果
> table(as.factor(spe.kmeans$cluster), as.factor(env.kmeans$cluster))
1 2 3 4
1 0 4 7 1
2 1 0 0 2
3 5 3 0 0
4 0 4 2 0
> #两种聚类结果是否相同？
> # 用卡方检验分析两种聚类之间的差异
> chisq.test(as.factor(spe.kmeans$cluster), as.factor(env.kmeans$cluster))
Pearson's Chi-squared test
data: as.factor(spe.kmeans$cluster) and as.factor(env.kmeans$cluster)
X-squared = 30.227, df = 9, p-value = 0.0004014
Warning message:
In chisq.test(as.factor(spe.kmeans$cluster), as.factor(env.kmeans$cluster)) :
Chi-squared近似算法有可能不准
> # 改用置换的方法进行卡方检验分析
> chisq.test(as.factor(spe.kmeans$cluster), as.factor(env.kmeans$cluster),
+ simulate.p.value=TRUE)
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
data: as.factor(spe.kmeans$cluster) and as.factor(env.kmeans$cluster)
X-squared = 30.227, df = NA, p-value = 0.0004998
> # k-均值样方聚类簇平均多度
> # ***********************
> groups <- as.factor(spe.kmeans$cluster)
> as.factor(spe.kmeans$cluster)
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 1 1 4 1 1 4 1 1 1 1 1 1 4 4 4 4 3 3 3 2 2 2 3 3 3 3 3
Levels: 1 2 3 4
> as.factor(env.kmeans$cluster)
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
4 3 3 3 3 3 3 3 3 2 2 2 2 3 2 2 2 2 2 2 2 4 1 4 1 1 1 1 1
Levels: 1 2 3 4
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