An Introduction to corrplot package

Introduction

The corrplot package is a graphical display of a correlation matrix, confidence interval.
It also contains some algorithms to do matrix reordering. In addition, corrplot is good at details, including choosing color, text labels, color labels, layout, etc.

Visualization Methods

There are seven visualization methods (parameter method) in corrplot package, named "circle", "square", "ellipse", "number", "shade", "color", "pie".

data(mtcars)
M <- cor(mtcars)
corrplot(M, method = "circle")

corrplot(M, method = "square")

corrplot(M, method = "ellipse")

corrplot(M, method = "number")

corrplot(M, method = "shade")

corrplot(M, method = "color")

corrplot(M, method = "pie")

Layout

There are three layout types (parameter type), named "full" (default), "upper" or "lower", display full matrix, lower triangular or upper triangular matrix.

corrplot(M, type = "upper")

corrplot(M, type = "lower")

corrplot.mixed() is a wrapped function for mixed visualization style.

corrplot.mixed(M)

corrplot.mixed(M, lower = "ellipse", upper = "circle")

corrplot.mixed(M, lower = "square", upper = "circle")

Reorder A Correlation Matrix

Matrix reorder is very important for mining the hiden structure and pattern in the matrix. There are four methods in corrplot (parameter order), named "AOE", "FPC", "hclust", "alphabet". More algorithms can be found in seriation package.

You can also reorder the matrix “manually” via function corrMatOrder().

• "AOE" is for the angular order of the eigenvectors. It is calculated from the order of the angles. \( a_i \),

\[ a_i = \begin{cases} \tan (e_{i2}/e_{i1}), & \text{if $e_{i1}>0$;} \newline \tan (e_{i2}/e_{i1}) + \pi, & \text{otherwise.} \end{cases} \]

where \( e_1 \) and \( e_2 \) are the largest two eigenvalues of the correlation matrix. See Michael Friendly (2002) for details.

• "FPC" for the first principal component order.

• "hclust" for hierarchical clustering order, and "hclust.method" for the agglomeration method to be used . "hclust.method" should be one of "ward", "single", "complete", "average", "mcquitty", "median" or "centroid".

• "alphabet" for alphabetical order.

corrplot(M, order = "AOE")

corrplot(M, order = "hclust")

corrplot(M, order = "FPC")

corrplot(M, order = "alphabet")

If using "hclust", corrplot() can draw rectangles around the chart of corrrlation matrix based on the results of hierarchical clustering.

corrplot(M, order = "hclust", addrect = 2)

corrplot(M, order = "hclust", addrect = 3)

Using Different Color Spectrum

We can also specify the color system, colorRampPalette() is very convenient for generating color spectrum.

col1 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "white", "cyan", 
    "#007FFF", "blue", "#00007F"))
col2 <- colorRampPalette(c("#67001F", "#B2182B", "#D6604D", "#F4A582", "#FDDBC7", 
    "#FFFFFF", "#D1E5F0", "#92C5DE", "#4393C3", "#2166AC", "#053061"))
col3 <- colorRampPalette(c("red", "white", "blue"))
col4 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "#7FFF7F", 
    "cyan", "#007FFF", "blue", "#00007F"))
wb <- c("white", "black")
## using these color spectrums
corrplot(M, order = "hclust", addrect = 2, col = col1(100))

corrplot(M, order = "hclust", addrect = 2, col = col2(50))

corrplot(M, order = "hclust", addrect = 2, col = col3(20))

corrplot(M, order = "hclust", addrect = 2, col = col4(10))

corrplot(M, order = "hclust", addrect = 2, col = wb, bg = "gold2")

Color Legend and Text Legend

Parameter cl.* is for color legend, and tl.* if for text legend.

Here are some examples.

## remove color legend and text legend
corrplot(M, order = "AOE", cl.pos = "n", tl.pos = "n")

## bottom color legend, diagonal text legend, rotate text label
corrplot(M, order = "AOE", cl.pos = "b", tl.pos = "d", tl.srt = 60)

## a wider color legend with numbers right aligned
corrplot(M, order = "AOE", cl.ratio = 0.2, cl.align = "r")

Deal with the Non-correlation Matrix

corrplot(abs(M), order = "AOE", col = col3(200), cl.lim = c(0, 1))

## visualize a matrix in [-100, 100]
ran <- round(matrix(runif(225, -100, 100), 15))
corrplot(ran, is.corr = FALSE, method = "square")

## a beautiful color legend
corrplot(ran, is.corr = FALSE, method = "ellipse", cl.lim = c(-100, 100))

Combine with the Significance Test

cor.mtest <- function(mat, conf.level = 0.95) {
    mat <- as.matrix(mat)
    n <- ncol(mat)
    p.mat <- lowCI.mat <- uppCI.mat <- matrix(NA, n, n)
    diag(p.mat) <- 0
    diag(lowCI.mat) <- diag(uppCI.mat) <- 1
    for (i in 1:(n - 1)) {
        for (j in (i + 1):n) {
            tmp <- cor.test(mat[, i], mat[, j], conf.level = conf.level)
            p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
            lowCI.mat[i, j] <- lowCI.mat[j, i] <- tmp$conf.int[1]
            uppCI.mat[i, j] <- uppCI.mat[j, i] <- tmp$conf.int[2]
        }
    }
    return(list(p.mat, lowCI.mat, uppCI.mat))
}
res1 <- cor.mtest(mtcars, 0.95)
res2 <- cor.mtest(mtcars, 0.99)
## specialized the insignificant value according to the significant level
corrplot(M, p.mat = res1[[1]], sig.level = 0.2)

corrplot(M, p.mat = res1[[1]], sig.level = 0.05)

corrplot(M, p.mat = res1[[1]], sig.level = 0.01)

## leave blank on no significant coefficient
corrplot(M, p.mat = res1[[1]], insig = "blank")

## add p-values on no significant coefficient
corrplot(M, p.mat = res1[[1]], insig = "p-value")

## add all p-values
corrplot(M, p.mat = res1[[1]], insig = "p-value", sig.level = -1)

## add cross on no significant coefficient
corrplot(M, p.mat = res1[[1]], order = "hclust", insig = "pch", addrect = 3)

Visualize Confidence Interval

## plot confidence interval(0.95, 0.95, 0.99), 'rect' method
corrplot(M, low = res1[[2]], upp = res1[[3]], order = "hclust", rect.col = "navy", 
    plotC = "rect", cl.pos = "n")

corrplot(M, p.mat = res1[[1]], low = res1[[2]], upp = res1[[3]], order = "hclust", 
    pch.col = "red", sig.level = 0.01, addrect = 3, rect.col = "navy", plotC = "rect", 
    cl.pos = "n")

Here is an animation to show the relation between significant level and confidence interval.

for (i in seq(0.1, 0, -0.005)) {
    tmp <- cor.mtest(mtcars, 1 - i)
    corrplot(M, p.mat = tmp[[1]], low = tmp[[2]], upp = tmp[[3]], order = "hclust", 
        pch.col = "red", sig.level = i, plotC = "rect", cl.pos = "n", mar = c(0, 
            0, 1, 0), title = substitute(alpha == x, list(x = format(i, digits = 3, 
            nsmall = 3))))
}