Corrlation

Corrlation

set.seed(0)
x <- 1:20 + rnorm(20,sd=5)
y <- 1:20 + rnorm(20,sd=5)
type <- rep(LETTERS[1:2],each=10)

# Make a data frame with the variables
dat <- data.frame(x=x, y=y,type=type)

cor(dat$x,dat$y,method = c("pearson", "kendall", "spearman")[1])
# 0.608
pearson <-  function(x, y) var(x, y) / (sd(x) * sd(y))
pearson(dat$x,dat$y)
#  0.608063
cor.test(dat$x,dat$y,method="pearson")
#   Pearson's product-moment correlation
# 
# data:  dat$x and dat$y
# t = 3.2496, df = 18, p-value = 0.00445
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
#  0.2264849 0.8278307
# sample estimates:
#      cor
# 0.608063
cor(dat$x,dat$y,method = c("pearson", "kendall", "spearman")[3])
cor(rank(dat$x),rank(dat$y),method = c("pearson", "kendall", "spearman")[1])
# 0.6015038

## https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient
cor(dat$x,dat$y,method = c("pearson", "kendall", "spearman")[2])
cor(rank(dat$x),rank(dat$y),method = c("pearson", "kendall", "spearman")[2])
# 0.4526316

kendall <- function(x,y){
    cd = 0
    l <- length(x)
    if (!identical(length(x),length(y))){
      stop("Not equal length vectors")
    }
    for (i in 1:(l-1)){
      for (j in i:l){
          cd = cd + sign(x[i] - x[j]) * sign(y[i] - y[j])
      }}
    return((cd/(l*(l-1)/2)))
}
kendall(dat$x,dat$y)
# 0.4526316

library(corrplot)
corrplot(corr = cor(dat[,-3]), method="number", col="black", cl.pos="n")

corrplot(corr, method = c(“circle”, “square”, “ellipse”, “number”, “shade”, “color”, “pie”)(可视化的方法，圆形、方形、椭圆形、数值、阴影、颜色或饼图)
type = c(“full”, “lower”, “upper”)(展示的方式，可以是完全的、下三角或上三角)
add = FALSE
col = NULL(图形展示的颜色，默认以均匀的颜色展示), bg = “white”(背景色), title = “”(标题)
is.corr = TRUE(FALSE,则为非相关系数的可视化), diag = TRUE(展示对角线上的相关系数)
outline = FALSE(绘制圆形、方形或椭圆形的轮廓), mar = c(0, 0, 0, 0)(图形的四边间距)
addgrid.col = NULL(当选择的方法为颜色或阴影时，默认的网格线颜色为白色，否则为灰色)
addCoef.col = NULL(为相关系数添加颜色，默认不添加相关系数，只有方法为number时，该参数才起作用)
addCoefasPercent = FALSE(是否将相关系数转换为百分比格式)
order = c(“original”,“AOE”, “FPC”, “hclust”, “alphabet”)(原始顺序(original)、特征向量角序(AOE)、第一主成分顺序(FPC)、层次聚类顺序(hclust)
hclust.method = c(“complete”, “ward”,“ward.D”, “ward.D2”, “single”, “average”, “mcquitty”, “median”, “centroid”)(hclust的聚类方法)
addrect = NULL(hclust的矩形框), rect.col = “black”(矩形框的颜色), rect.lwd = 2(矩形框的线宽)
tl.pos = NULL(指定文本标签的位置，type=full时，在左边和顶部(lt)，type=lower时,在左边和对角线(ld),type=upper时,在顶部和对角线，d表示对角线，n表示不添加文本标签)
tl.cex = 1(文本标签的大小), tl.col = “red”(文本标签的颜色), tl.offset = 0.4, tl.srt = 90
cl.pos = NULL(图例（颜色）位置，当type=upper或full时，图例在右表(r)，当type=lower时，图例在底部，不需要图例时，只需指定该参数为n)
cl.lim = NULL, cl.length = NULL, cl.cex = 0.8,cl.ratio = 0.15, cl.align.text = “c”, cl.offset = 0.5
number.cex = 1, number.font = 2, number.digits = NULL,
addshade = c(“negative”,“positive”, “all”)(若method=shade，则negtive/positive和all，对相关系数加阴影, 正相关系数的阴影是45度，负相关系数的阴影是135度)
shade.lwd = 1(阴影的线宽), shade.col = “white”(阴影线的颜色), p.mat = NULL, sig.level = 0.05
insig = c(“pch”, “p-value”, “blank”, “n”, “label_sig”),pch = 4, pch.col = “black”, pch.cex = 3
plotCI = c(“n”, “square”,“circle”, “rect”), lowCI.mat = NULL, uppCI.mat = NULL, na.label = “?”,
na.label.col = “black”, win.asp = 1, …)

pairs(mtcars[,1:7])

require(GGally)
ggpairs(mtcars[,1:7])

library(car)
scatterplotMatrix(mtcars[,1:7],
                   diagonal="histogram",
                   smooth=FALSE)

## Warning in applyDefaults(diagonal, defaults = list(method =
## "adaptiveDensity"), : unnamed diag arguments, will be ignored

corr <- cor(mtcars[,1:7])
corrplot(corr = corr, method = 'color', order ="AOE", addCoef.col="grey",tl.col = "black",tl.cex = 1,cl.pos = "n")

corrplot(corr = corr, col = "yellow", order="AOE", outline=FALSE, cl.pos="n",bg="gold")

corrplot(corr = corr,order="AOE",type="upper",tl.pos="d")
corrplot(corr = corr,add=TRUE, type="lower", method="number",order="AOE",diag=F,tl.pos="n", cl.pos="n")

corrplot(corr = corr, order="hclust", addrect = 3, rect.col = "black",cl.pos = "n",tl.cex = 1.2)

library(ellipse)
colorfun <- colorRamp(c("#4CAF50","white","#F57C00"), space="rgb")
plotcorr(corr, col=rgb(colorfun((corr+1)/2), maxColorValue=255),numbers = F,
         mar = c(0.1, 0.1, 0.1, 0.1))