Igor Hut
12 January, 2017
- Install and load required R packages
- Methods for correlation analyses
- Compute correlation in R
- R functions
- Preliminary considerations
- Preleminary test to check the test assumptions
- Pearson correlation test
- Kendall rank correlation test
- Spearman rank correlation coefficient
- How to interpret correlation coefficient
- What is a correlation matrix?
- Compute correlation matrix in R
- Plain correlation matrix
- Correlation matrix with significance levels (p-value)
- Custom function for convinient formatting of the correlation matrix
- Visualization of a correlation matrix
- Use symnum() function: Symbolic number coding
- Use the corrplot() function: Draw a correlogram
- Correlogram layouts:
- Reordering the correlation matrix
- Changing the color and direction of text labels in the correlogram
- Combining correlogram with the significance test
- Fine tuning customization of the correlogram
- Use chart.Correlation(): Draw scatter plots
- Use heatmap()
The following content is mostly compiled (with some original additions on my side) from the material that can be found at http://www.sthda.com/, as well as in the vignette for the corrplot R package - An Introduction to corrplot Package. The sole purpose of this text is to put all the info into one document in an easy to search format. Since I’m a huge fan of Hadley Wickham’s work I’ll insist on solutions based in “tidyverse” whenewer possible…
Install and load required R packages
We’ll use the ggpubr R package for an easy ggplot2-based data visualization, corrplot package to plot correlograms, Hmisc to calculate correlation matrices containing both cor. coefs. and p-values,corrplot for plotting correlograms, and of course tidyverse for all the data wrangling, plotting and alike:
require(ggpubr)require(tidyverse)require(Hmisc)require(corrplot)Methods for correlation analyses
There are different methods to perform correlation analysis:
Pearson correlation (r), which measures a linear dependence between two variables (x and y). It’s also known as a parametric correlation test because it depends to the distribution of the data. It can be used only when x and y are from normal distribution. The plot of y = f(x) is named the linear regression curve.
Kendall \(\tau\) and Spearman \(\rho\), which are rank-based correlation coefficients (non-parametric)
The most commonly used method is the Pearson correlation method
Compute correlation in R
R functions
Correlation coefficients can be computed in R by using the functions cor() and cor.test():
cor()computes the correlation coefficientcor.test()test for association/correlation between paired samples. It returns both the correlation coefficient and the significance level(or p-value) of the correlation.
The simplified formats are:
cor(x, y, method = c("pearson", "kendall", "spearman"))cor.test(x, y, method=c("pearson", "kendall", "spearman"))where:
- x, y: numeric vectors with the same length
- method: correlation method
If the data contain missing values, the following R code can be used to handle missing values by case-wise deletion:
cor(x, y, method = "pearson", use = "complete.obs")Preliminary considerations
We’ll use the well known built-in mtcars R dataset.
head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1We’d like to compute the correlation between
mpgandwtvariables.
First let’s visualise our data by the means of a scatter plot. We’ll be using ggpubr R package
library(ggpubr)my_data <- mtcarsmy_data$cyl <- factor(my_data$cyl)str(my_data)## 'data.frame': 32 obs. of 11 variables:## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...## $ cyl : Factor w/ 3 levels "4","6","8": 2 2 1 2 3 2 3 1 1 2 ...## $ disp: num 160 160 108 258 360 ...## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...## $ qsec: num 16.5 17 18.6 19.4 17 ...## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...## $ am : num 1 1 1 0 0 0 0 0 0 0 ...## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...ggscatter(my_data, x = "wt", y = "mpg", add = "reg.line", conf.int = TRUE, cor.coef = TRUE, cor.method = "pearson", xlab = "Weight (1000 lbs)", ylab = "Miles/ (US) gallon")
Preleminary test to check the test assumptions
Is the relation between variables linear? Yes, from the plot above, the relationship can be, closely enough, modeled as linear. In the situation where the scatter plots show curved patterns, we are dealing with nonlinear association between the two variables.
- Are the data from each of the 2 variables (x, y) following a normal distribution?
- Use Shapiro-Wilk normality test \(\rightarrow\) R function:
shapiro.test() - and look at the normality plot \(\rightarrow\) R function:
ggpubr::ggqqplot()
- Use Shapiro-Wilk normality test \(\rightarrow\) R function:
- Shapiro-Wilk test can be performed as follow:
- Null hypothesis: the data are normally distributed
- Alternative hypothesis: the data are not normally distributed
# Shapiro-Wilk normality test for mpgshapiro.test(my_data$mpg) # => p = 0.1229## ## Shapiro-Wilk normality test## ## data: my_data$mpg## W = 0.94756, p-value = 0.1229# Shapiro-Wilk normality test for wtshapiro.test(my_data$wt) # => p = 0.09## ## Shapiro-Wilk normality test## ## data: my_data$wt## W = 0.94326, p-value = 0.09265As can be seen from the output, the two p-values are greater than the predetermined significance level of 0.05 implying that the distribution of the data are not significantly different from normal distribution. In other words, we can assume the normality.
- One more option for checking the normality of the data distribution is visual inspection of the Q-Q plots (quantile-quantile plots). Q-Q plot draws the correlation between a given sample and the theoretical normal distribution.
Again, we’ll use the ggpubr R package to obtain “pretty”, i.e.publishing-ready, Q-Q plots.
library("ggpubr")# Check for the normality of "mpg""ggqqplot(my_data$mpg, ylab = "MPG")
# Check for the normality of "wt""ggqqplot(my_data$wt, ylab = "WT")
From the Q-Q normality plots, we can assume that both samples may come from populations that, closely enough, follow normal distributions.
It is important to note that if the data does not follow the normal distribution, at least closely enough, it’s recommended to use the non-parametric correlation, including Spearman and Kendall rank-based correlation tests.
Pearson correlation test
Example:
res <- cor.test(my_data$wt, my_data$mpg, method = "pearson")res## ## Pearson's product-moment correlation## ## data: my_data$wt and my_data$mpg## t = -9.559, df = 30, p-value = 1.294e-10## alternative hypothesis: true correlation is not equal to 0## 95 percent confidence interval:## -0.9338264 -0.7440872## sample estimates:## cor ## -0.8676594So what’s happening here? First of all let’s clarify the meaning of this printout:
tis the t-test statistic value(t = -9.559),dfis the degrees of freedom(df= 30),p-valueis the significance level of the t-test(p-value =\(1.29410^{-10}\)).conf.intis the confidence interval of the correlation coefficient at 95%(conf.int = [-0.9338, -0.7441]);sample estimatesis the correlation coefficient(Cor.coeff = -0.87).
Interpretation of the results: As can be see from the results above the p-value of the test is \(1.29410^{-10}\), which is less than the significance level \(\alpha = 0.05\). We can conclude that wt and mpg are significantly correlated with a correlation coefficient of -0.87 and p-value of \(1.29410^{-10}\).
Access to the values returned by cor.test() function
The function cor.test() returns a list containing the following components:
str(res)## List of 9## $ statistic : Named num -9.56## ..- attr(*, "names")= chr "t"## $ parameter : Named int 30## ..- attr(*, "names")= chr "df"## $ p.value : num 1.29e-10## $ estimate : Named num -0.868## ..- attr(*, "names")= chr "cor"## $ null.value : Named num 0## ..- attr(*, "names")= chr "correlation"## $ alternative: chr "two.sided"## $ method : chr "Pearson's product-moment correlation"## $ data.name : chr "my_data$wt and my_data$mpg"## $ conf.int : atomic [1:2] -0.934 -0.744## ..- attr(*, "conf.level")= num 0.95## - attr(*, "class")= chr "htest"Of these we are most interested with:
p.value: the p-value of the testestimate: the correlation coefficient
# Extract the p.valueres$p.value## [1] 1.293959e-10# Extract the correlation coefficientres$estimate## cor ## -0.8676594Kendall rank correlation test
The Kendall rank correlation coefficient or Kendall’s \(\tau\) statistic is used to estimate a rank-based measure of association. This test may be used if the data do not necessarily come from a bivariate normal distribution.
res2 <- cor.test(my_data$mpg, my_data$wt, method = "kendall")## Warning in cor.test.default(my_data$mpg, my_data$wt, method = "kendall"):## Cannot compute exact p-value with tiesres2## ## Kendall's rank correlation tau## ## data: my_data$mpg and my_data$wt## z = -5.7981, p-value = 6.706e-09## alternative hypothesis: true tau is not equal to 0## sample estimates:## tau ## -0.7278321Here tau is the Kendall correlation coefficient, so The correlation coefficient between mpg and wy is -0.7278 and the p-value is \(6.70610^{-9}\).
Spearman rank correlation coefficient
Spearman’s \(\rho\) statistic is also used to estimate a rank-based measure of association. This test may be used if the data do not come from a bivariate normal distribution.
res3 <- cor.test(my_data$wt, my_data$mpg, method = "spearman")## Warning in cor.test.default(my_data$wt, my_data$mpg, method = "spearman"):## Cannot compute exact p-value with tiesres3## ## Spearman's rank correlation rho## ## data: my_data$wt and my_data$mpg## S = 10292, p-value = 1.488e-11## alternative hypothesis: true rho is not equal to 0## sample estimates:## rho ## -0.886422Here, rho is the Spearman’s correlation coefficient, so the correlation coefficient between mpg and wt is -0.8864 and the p-value is \(1.48810^{-11}\).
How to interpret correlation coefficient
Value of the correlation coefficient can vary between -1 and 1:
- -1 indicates a strong negative correlation : this means that every time x increases, y decreases
- 0 means that there is no association between the two variables (x and y)
- 1 indicates a strong positive correlation : this means that y increases with x
What is a correlation matrix?
Previously, we described how to perform correlation test between two variables. In the following sections we’ll see how a correlation matrix can be computed and visualized. The correlation matrix is used to investigate the dependence between multiple variables at the same time. The result is a table containing the correlation coefficients between each variable and the others.
Compute correlation matrix in R
We have already mentioned the cor() function, at the intoductory part of this document dealing with the correlation test for a bivariate case. It be used to compute a correlation matrix. A simplified format of the function is :
cor(x, method = c("pearson", "kendall", "spearman")) Here:
xis numeric matrix or a data frame.method: indicates the correlation coefficient to be computed. The default is “pearson”" correlation coefficient which measures the linear dependence between two variables. As already explained “kendall” and “spearman” correlation methods are non-parametric rank-based correlation tests.
If your data contain missing values, the following R code can be used to handle missing values by case-wise deletion:
cor(x, method = "pearson", use = "complete.obs")Plain correlation matrix
Example:
library(dplyr)my_data <- select(mtcars, mpg, disp, hp, drat, wt, qsec)head(my_data)## mpg disp hp drat wt qsec## Mazda RX4 21.0 160 110 3.90 2.620 16.46## Mazda RX4 Wag 21.0 160 110 3.90 2.875 17.02## Datsun 710 22.8 108 93 3.85 2.320 18.61## Hornet 4 Drive 21.4 258 110 3.08 3.215 19.44## Hornet Sportabout 18.7 360 175 3.15 3.440 17.02## Valiant 18.1 225 105 2.76 3.460 20.22#Let's compute the correlation matrixcor_1 <- round(cor(my_data), 2)cor_1## mpg disp hp drat wt qsec## mpg 1.00 -0.85 -0.78 0.68 -0.87 0.42## disp -0.85 1.00 0.79 -0.71 0.89 -0.43## hp -0.78 0.79 1.00 -0.45 0.66 -0.71## drat 0.68 -0.71 -0.45 1.00 -0.71 0.09## wt -0.87 0.89 0.66 -0.71 1.00 -0.17## qsec 0.42 -0.43 -0.71 0.09 -0.17 1.00Unfortunately, the function cor() returns only the correlation coefficients between variables. In the next section, we will use Hmisc R package to calculate the correlation p-values.
Correlation matrix with significance levels (p-value)
The function rcorr() (in Hmisc package) can be used to compute the significance levels for pearson and spearman correlations. It returns both the correlation coefficients and the p-value of the correlation for all possible pairs of columns in the data table.
Simplified format:
rcorr(x, type = c("pearson","spearman"))x should be a matrix. The correlation type can be either pearson or spearman.
Example:
library("Hmisc")cor_2 <- rcorr(as.matrix(my_data))cor_2## mpg disp hp drat wt qsec## mpg 1.00 -0.85 -0.78 0.68 -0.87 0.42## disp -0.85 1.00 0.79 -0.71 0.89 -0.43## hp -0.78 0.79 1.00 -0.45 0.66 -0.71## drat 0.68 -0.71 -0.45 1.00 -0.71 0.09## wt -0.87 0.89 0.66 -0.71 1.00 -0.17## qsec 0.42 -0.43 -0.71 0.09 -0.17 1.00## ## n= 32 ## ## ## P## mpg disp hp drat wt qsec ## mpg 0.0000 0.0000 0.0000 0.0000 0.0171## disp 0.0000 0.0000 0.0000 0.0000 0.0131## hp 0.0000 0.0000 0.0100 0.0000 0.0000## drat 0.0000 0.0000 0.0100 0.0000 0.6196## wt 0.0000 0.0000 0.0000 0.0000 0.3389## qsec 0.0171 0.0131 0.0000 0.6196 0.3389The output of the function rcorr() is a list containing the following elements :
- r : the correlation matrix
- n : the matrix of the number of observations used in analyzing each pair of variables
- P : the p-values corresponding to the significance levels of correlations.
Extracting the p-values or the correlation coefficients from the output:
str(cor_2)## List of 3## $ r: num [1:6, 1:6] 1 -0.848 -0.776 0.681 -0.868 ...## ..- attr(*, "dimnames")=List of 2## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## $ n: int [1:6, 1:6] 32 32 32 32 32 32 32 32 32 32 ...## ..- attr(*, "dimnames")=List of 2## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## $ P: num [1:6, 1:6] NA 9.38e-10 1.79e-07 1.78e-05 1.29e-10 ...## ..- attr(*, "dimnames")=List of 2## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## .. ..$ : chr [1:6] "mpg" "disp" "hp" "drat" ...## - attr(*, "class")= chr "rcorr"# As you can see "cor_2" is a list so extracting these values is quite simple...# p-valuescor_2$P## mpg disp hp drat wt## mpg NA 9.380354e-10 1.787838e-07 1.776241e-05 1.293956e-10## disp 9.380354e-10 NA 7.142686e-08 5.282028e-06 1.222311e-11## hp 1.787838e-07 7.142686e-08 NA 9.988768e-03 4.145833e-05## drat 1.776241e-05 5.282028e-06 9.988768e-03 NA 4.784268e-06## wt 1.293956e-10 1.222311e-11 4.145833e-05 4.784268e-06 NA## qsec 1.708199e-02 1.314403e-02 5.766250e-06 6.195823e-01 3.388682e-01## qsec## mpg 1.708199e-02## disp 1.314403e-02## hp 5.766250e-06## drat 6.195823e-01## wt 3.388682e-01## qsec NA# Correlation matrixcor_2$r## mpg disp hp drat wt qsec## mpg 1.0000000 -0.8475513 -0.7761683 0.68117189 -0.8676594 0.41868404## disp -0.8475513 1.0000000 0.7909486 -0.71021390 0.8879799 -0.43369791## hp -0.7761683 0.7909486 1.0000000 -0.44875914 0.6587479 -0.70822340## drat 0.6811719 -0.7102139 -0.4487591 1.00000000 -0.7124406 0.09120482## wt -0.8676594 0.8879799 0.6587479 -0.71244061 1.0000000 -0.17471591## qsec 0.4186840 -0.4336979 -0.7082234 0.09120482 -0.1747159 1.00000000Custom function for convinient formatting of the correlation matrix
This section provides a simple function for formatting a correlation matrix into a table with 4 columns containing :
- Column 1 : row names (variable 1 for the correlation test)
- Column 2 : column names (variable 2 for the correlation test)
- Column 3 : the correlation coefficients
- Column 4 : the p-values of the correlations
flat_cor_mat <- function(cor_r, cor_p){ #This function provides a simple formatting of a correlation matrix #into a table with 4 columns containing : # Column 1 : row names (variable 1 for the correlation test) # Column 2 : column names (variable 2 for the correlation test) # Column 3 : the correlation coefficients # Column 4 : the p-values of the correlations library(tidyr) library(tibble) cor_r <- rownames_to_column(as.data.frame(cor_r), var = "row") cor_r <- gather(cor_r, column, cor, -1) cor_p <- rownames_to_column(as.data.frame(cor_p), var = "row") cor_p <- gather(cor_p, column, p, -1) cor_p_matrix <- left_join(cor_r, cor_p, by = c("row", "column")) cor_p_matrix}cor_3 <- rcorr(as.matrix(mtcars[, 1:7]))my_cor_matrix <- flat_cor_mat(cor_3$r, cor_3$P)head(my_cor_matrix)## row column cor p## 1 mpg mpg 1.0000000 NA## 2 cyl mpg -0.8521619 6.112697e-10## 3 disp mpg -0.8475513 9.380354e-10## 4 hp mpg -0.7761683 1.787838e-07## 5 drat mpg 0.6811719 1.776241e-05## 6 wt mpg -0.8676594 1.293956e-10Visualization of a correlation matrix
There are several different ways for visualizing a correlation matrix in R software:
symnum()functioncorrplot()function to plot a correlogram- scatter plots
- heatmap
We’ll run trough all of these, and then go a bit more into deatil with correlograms.
Use symnum() function: Symbolic number coding
The R function symnum() is used to symbolically encode a given numeric or logical vector or array. It is particularly useful for visualization of structured matrices, e.g., correlation, sparse, or logical ones. In the case of a correlatino matrix it replaces correlation coefficients by symbols according to the level of the correlation.
Simplified format:
symnum(x, cutpoints = c(0.3, 0.6, 0.8, 0.9, 0.95), symbols = c(" ", ".", ",", "+", "*", "B"), abbr.colnames = TRUE)Here:
- x: the correlation matrix to visualize
- cutpoints: correlation coefficient cutpoints. The correlation coefficients between 0 and 0.3 are replaced by a space (" “); correlation coefficients between 0.3 and 0.6 are replaced by”.“; etc .
- symbols: the symbols to use.
- abbr.colnames: logical value. If TRUE, colnames are abbreviated.
Example:
cor_4 <- cor(mtcars[1:6])symnum(cor_4, abbr.colnames = FALSE)## mpg cyl disp hp drat wt## mpg 1 ## cyl + 1 ## disp + * 1 ## hp , + , 1 ## drat , , , . 1 ## wt + , + , , 1 ## attr(,"legend")## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1*As indicated in the legend, the correlation coefficients between 0 and 0.3 are replaced by a space (" “); correlation coefficients between 0.3 and 0.6 are replace by”.“; etc .*
Use the corrplot() function: Draw a correlogram
The function corrplot(), in the package of the same name, creates a graphical display of a correlation matrix, highlighting the most correlated variables in a data table.
In this plot, correlation coefficients are colored according to the value. Correlation matrix can be also reordered according to the degree of association between variables.
The simplified format of the function is:
corrplot(corr, method="circle")Here:
- corr: the correlation matrix to be visualized
- method: The visualization method to be used, there are seven different options: “circle”, “square”, “ellipse”, “number”, “shade”, “color”, “pie”.
Example:
M<-cor(mtcars)head(round(M,2))## mpg cyl disp hp drat wt qsec vs am gear carb## mpg 1.00 -0.85 -0.85 -0.78 0.68 -0.87 0.42 0.66 0.60 0.48 -0.55## cyl -0.85 1.00 0.90 0.83 -0.70 0.78 -0.59 -0.81 -0.52 -0.49 0.53## disp -0.85 0.90 1.00 0.79 -0.71 0.89 -0.43 -0.71 -0.59 -0.56 0.39## hp -0.78 0.83 0.79 1.00 -0.45 0.66 -0.71 -0.72 -0.24 -0.13 0.75## drat 0.68 -0.70 -0.71 -0.45 1.00 -0.71 0.09 0.44 0.71 0.70 -0.09## wt -0.87 0.78 0.89 0.66 -0.71 1.00 -0.17 -0.55 -0.69 -0.58 0.43#Visualize the correlation matrix# method = "circle""corrplot(M, method = "circle")
# method = "ellipse""corrplot(M, method = "ellipse")
# method = "pie"corrplot(M, method = "pie")
# method = "color"corrplot(M, method = "color")
Display the correlation coefficient:
corrplot(M, method = "number")
Correlogram layouts:
There are three general types of a correlogram layout :
- “full” (default) : display full correlation matrix
- “upper”: display upper triangular of the correlation matrix
- “lower”: display lower triangular of the correlation matrix
Examples:
# upper triangularcorrplot(M, type = "upper")
#lower triangularcorrplot(M, type = "lower")
Reordering the correlation matrix
The correlation matrix can be reordered according to the correlation coefficient. This is important to identify the hidden structure and pattern in the matrix. Use order = "hclust" argument for hierarchical clustering of correlation coefficients.
Example:
# correlogram with hclust reorderingcorrplot(M, order = "hclust")
# or exploit the symetry of the correlation matrix # correlogram with hclust reorderingcorrplot(M, type = "upper", order = "hclust")
Changing the color and direction of text labels in the correlogram
Examples:
# Change background color to lightgreen and color of the circles to darkorange and steel bluecorrplot(M, type = "upper", order = "hclust", col = c("darkorange", "steelblue"), bg = "lightgreen")
# use "colorRampPallete" to obtain contionus color scalescol <- colorRampPalette(c("darkorange", "white", "steelblue"))(20)corrplot(M, type = "upper", order = "hclust", col = col)
# Or use "RColorBrewer" packagelibrary(RColorBrewer)corrplot(M, type = "upper", order = "hclust", col = brewer.pal(n = 9, name = "PuOr"), bg = "darkgreen")
Use the tl.col argument for defining the text label color and tl.srt for text label string rotation.
Example:
corrplot(M, type = "upper", order = "hclust", tl.col = "darkblue", tl.srt = 45)
Combining correlogram with the significance test
# Mark the insignificant coefficients according to the specified p-value significance levelcor_5 <- rcorr(as.matrix(mtcars))M <- cor_5$rp_mat <- cor_5$Pcorrplot(M, type = "upper", order = "hclust", p.mat = p_mat, sig.level = 0.01)
# Leave blank on no significant coefficientcorrplot(M, type = "upper", order = "hclust", p.mat = p_mat, sig.level = 0.05, insig = "blank")
Fine tuning customization of the correlogram
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))corrplot(M, method = "color", col = col(200), type = "upper", order = "hclust", addCoef.col = "black", # Add coefficient of correlation tl.col = "darkblue", tl.srt = 45, #Text label color and rotation # Combine with significance level p.mat = p_mat, sig.level = 0.01, # hide correlation coefficient on the principal diagonal diag = FALSE )
I’d say this is more than enough for introductory exploration of correlograms. More information can be found in the, already mentioned, vignette for the corrplot R package - An Introduction to corrplot Package
Use chart.Correlation(): Draw scatter plots
The function chart.Correlation() from the package “PerformanceAnalytics”, can be used to display a chart of a correlation matrix. This is a very convinient way of exploring multivariate correlations.
library("PerformanceAnalytics")## Loading required package: xts## Loading required package: zoo## ## Attaching package: 'zoo'## The following objects are masked from 'package:base':## ## as.Date, as.Date.numeric## ## Attaching package: 'xts'## The following objects are masked from 'package:dplyr':## ## first, last## ## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':## ## legendmy_data <- mtcars[, c(1,3,4,5,6,7)]chart.Correlation(my_data, histogram = TRUE, pch = 19)
In the above plot:
- The distribution of each variable is shown on the diagonal.
- On the bottom of the diagonal : the bivariate scatter plots with a fitted line are displayed
- On the top of the diagonal : the value of the correlation plus the significance level as stars
- Each significance level is associated to a symbol : p-values(0, 0.001, 0.01, 0.05, 0.1, 1) <=> symbols(““,”“,””, “.”, " “)
Use heatmap()
I don’t really consider this method of correlation matrix visualization to be of practical value, but nevertheless here is a small example:
# Get some colorscol <- colorRampPalette(c("darkblue", "white", "darkorange"))(20)M <- cor(mtcars[1:7])heatmap(x = M, col = col, symm = TRUE)
