参考文献：

https://www.bilibili.com/video/BV1LQRnYcECS/?spm_id_from=333.337.search-card.all.click&vd_source=80131b0637928aecfc4f4ea0c4fe5ad5

https://mp.weixin.qq.com/s/cWAhrMg1W2X0z38RZ_K5Ag

加载必要的包

library(corrplot)

library(ggplot2)

设置随机种子以保证结果可重现

set.seed(123)

创建模拟数据 - 生成9个变量（A到I）的100个观测值

n <- 100

A <- rnorm(n)

B <- A + rnorm(n, sd = 0.5)

C <- -0.4*A + rnorm(n, sd = 0.8) # 与A负相关

D <- rnorm(n)

E <- 0.7*B + rnorm(n, sd = 0.6)

F <- 0.3*D + rnorm(n, sd = 0.9)

G <- 0.5*E + 0.3*F + rnorm(n, sd = 0.7)

H <- rnorm(n)

I <- -0.4*A + 0.3*H + rnorm(n, sd = 0.8) # 与A负相关

创建数据框

data <- data.frame(A, B, C, D, E, F, G, H, I)

计算相关性矩阵

cor_matrix <- cor(data)

手动调整一些相关性以匹配描述中的模式

确保某些变量有较强的负相关性

cor_matrix $"A", "C"$ <- -0.46

cor_matrix $"C", "A"$ <- -0.46

cor_matrix $"A", "I"$ <- -0.44

cor_matrix $"I", "A"$ <- -0.44

cor_matrix $"C", "E"$ <- -0.42

cor_matrix $"E", "C"$ <- -0.42

增强一些正相关性

cor_matrix $"B", "E"$ <- 0.75

cor_matrix $"E", "B"$ <- 0.75

cor_matrix $"E", "G"$ <- 0.68

cor_matrix $"G", "E"$ <- 0.68

方法1: 使用corrplot包创建高级相关性矩阵图

corrplot(cor_matrix,

method = "color", # 使用颜色表示相关性

type = "upper", # 只显示上三角

order = "original", # 保持原始顺序

diag = TRUE, # 显示对角线

tl.cex = 0.8, # 标签字体大小

tl.col = "black", # 标签颜色

number.cex = 0.7, # 数字字体大小

addCoef.col = "black", # 系数颜色

col = colorRampPalette(c("red", "white", "green"))(100), # 颜色渐变

mar = c(0, 0, 1, 0), # 边距

title = "9×9 相关性矩阵热图")

方法2: 使用ggplot2创建更基础的热图

library(reshape2) # 用于数据重塑

将相关性矩阵转换为长格式

melted_cor <- melt(cor_matrix)

创建ggplot热图

ggplot(data = melted_cor, aes(x = Var1, y = Var2, fill = value)) +

geom_tile(color = "white") +

scale_fill_gradient2(low = "red", high = "green", mid = "yellow",

midpoint = 0, limit = c(-1, 1), space = "Lab",

name="相关性") +

geom_text(aes(label = sprintf("%.2f", value)), size = 3) +

theme_minimal() +

theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1)) +

labs(title = "9×9 相关性矩阵热图", x = "", y = "") +

coord_fixed()

方法3: 使用基础R的热图函数

heatmap(cor_matrix,

col = colorRampPalette(c("red", "white", "green"))(100),

symm = TRUE, # 对称矩阵

margins = c(10, 10),

main = "相关性矩阵热图")

打印数值矩阵

print("相关性矩阵数值:")

print(round(cor_matrix, 2))

分析显著的相关性

cat("\n显著的正相关性 (r > 0.5):\n")

high_pos <- which(cor_matrix > 0.5 & cor_matrix < 1, arr.ind = TRUE)

for(i in 1:nrow(high_pos)) {

if(high_pos $i,1$ < high_pos $i,2$ ) { # 避免重复

cat(sprintf("%s - %s: %.2f\n",

rownames(cor_matrix) $high_pos\[i,1$ ],

colnames(cor_matrix) $high_pos\[i,2$ ],

cor_matrix $high_pos\[i,1$ , high_pos $i,2$ ]))

}

cat("\n显著的负相关性 (r < -0.3):\n")

high_neg <- which(cor_matrix < -0.3, arr.ind = TRUE)

for(i in 1:nrow(high_neg)) {

if(high_neg $i,1$ < high_neg $i,2$ ) { # 避免重复

cat(sprintf("%s - %s: %.2f\n",

rownames(cor_matrix) $high_neg\[i,1$ ],

colnames(cor_matrix) $high_neg\[i,2$ ],

cor_matrix $high_neg\[i,1$ , high_neg $i,2$ ]))

}

保存相关性矩阵为CSV文件

write.csv(cor_matrix, "correlation_matrix.csv")

保存图形

png("correlation_plot.png", width = 800, height = 800)

corrplot(cor_matrix,

method = "color",

type = "upper",

diag = TRUE,

tl.cex = 0.8,

tl.col = "black",

number.cex = 0.7,

addCoef.col = "black",