# Correlation matrix : A quick start guide to analyze, format and visualize a correlation matrix using R software

- What is correlation matrix?
- Compute correlation matrix in R
- Online software to analyze and visualize a correlation matrix
- Summarry
- Infos

# What is correlation matrix?

**correlation test**between two variables. In this article, you’ll learn how to compute a

**correlation matrix**, which 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.

There are different methods for **correlation analysis** : **Pearson parametric correlation test**, **Spearman** and **Kendall** rank-based **correlation analysis**. These methods are discussed in the next sections.

The aim of this **R tutorial** is to show you how to compute and visualize a **correlation matrix in R**. We provide also an online software for computing and visualizing a correlation matrix.

# Compute correlation matrix in R

## R functions

As you may know, The **R** function **cor()** can be used to compute a **correlation matrix**. A simplified format of the function is :

`cor(x, method = c("pearson", "kendall", "spearman"))`

**x**: 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. kendall and spearman correlation methods are non-parametric**rank-based correlation test**.

If your data contain missing values, use the following R code to handle missing values by case-wise deletion.

`cor(x, method = "pearson", use = "complete.obs")`

## Import your data into R

**Prepare your data**as specified here: Best practices for preparing your data set for R**Save your data**in an external .txt tab or .csv files**Import your data into R**as follow:

```
# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())
```

Here, we’ll use a data derived from the built-in R data set *mtcars* as an example:

```
# Load data
data("mtcars")
my_data <- mtcars[, c(1,3,4,5,6,7)]
# print the first 6 rows
head(my_data, 6)
```

```
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
```

## Compute correlation matrix

```
res <- cor(my_data)
round(res, 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
```

In the table above **correlations coefficients** between the possible pairs of variables are shown.

Note that, if your data contain missing values, use the following R code to handle missing values by case-wise deletion.

`cor(my_data, use = "complete.obs")`

Unfortunately, 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**.

- Install
**Hmisc**package:

`install.packages("Hmisc")`

- Use
**rcorr**() function

```
library("Hmisc")
res2 <- rcorr(as.matrix(my_data))
res2
```

```
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 0.3389
```

The 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**.

If you want to extract the p-values or the correlation coefficients from the output, use this:

```
# Extract the correlation coefficients
res2$r
# Extract p-values
res2$P
```

## A simple function to format 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

The custom function below can be used :

```
# ++++++++++++++++++++++++++++
# flattenCorrMatrix
# ++++++++++++++++++++++++++++
# cormat : matrix of the correlation coefficients
# pmat : matrix of the correlation p-values
flattenCorrMatrix <- function(cormat, pmat) {
ut <- upper.tri(cormat)
data.frame(
row = rownames(cormat)[row(cormat)[ut]],
column = rownames(cormat)[col(cormat)[ut]],
cor =(cormat)[ut],
p = pmat[ut]
)
}
```

Example of usage :

```
library(Hmisc)
res2<-rcorr(as.matrix(mtcars[,1:7]))
flattenCorrMatrix(res2$r, res2$P)
```

```
row column cor p
1 mpg cyl -0.85216194 6.112697e-10
2 mpg disp -0.84755135 9.380354e-10
3 cyl disp 0.90203285 1.803002e-12
4 mpg hp -0.77616835 1.787838e-07
5 cyl hp 0.83244747 3.477856e-09
6 disp hp 0.79094857 7.142686e-08
7 mpg drat 0.68117189 1.776241e-05
8 cyl drat -0.69993812 8.244635e-06
9 disp drat -0.71021390 5.282028e-06
10 hp drat -0.44875914 9.988768e-03
11 mpg wt -0.86765939 1.293956e-10
12 cyl wt 0.78249580 1.217567e-07
13 disp wt 0.88797992 1.222311e-11
14 hp wt 0.65874785 4.145833e-05
15 drat wt -0.71244061 4.784268e-06
16 mpg qsec 0.41868404 1.708199e-02
17 cyl qsec -0.59124213 3.660527e-04
18 disp qsec -0.43369791 1.314403e-02
19 hp qsec -0.70822340 5.766250e-06
20 drat qsec 0.09120482 6.195823e-01
21 wt qsec -0.17471591 3.388682e-01
```

## Visualize correlation matrix

There are different ways for visualizing a **correlation matrix** in R software :

- symnum() function
- corrplot() function to plot a
**correlogram** - scatter plots
- heatmap

### Use symnum() function: Symbolic number coding

The R function symnum() replaces **correlation coefficients** by symbols according to the level of the correlation. It takes the **correlation matrix** as an argument :

**Simplified format**:

```
symnum(x, cutpoints = c(0.3, 0.6, 0.8, 0.9, 0.95),
symbols = c(" ", ".", ",", "+", "*", "B"),
abbr.colnames = TRUE)
```

**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 replace by”.“; etc …**symbols**: the symbols to use.**abbr.colnames**: logical value. If TRUE, colnames are abbreviated.

**Example of usage**:

`symnum(res, abbr.colnames = FALSE)`

```
mpg disp hp drat wt qsec
mpg 1
disp + 1
hp , , 1
drat , , . 1
wt + + , , 1
qsec . . , 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 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.

**Install corrplot**:

`install.packages("corrplot")`

**Use corrplot**() to create a**correlogram**:

The function **corrplot()** takes the **correlation matrix** as the first argument. The second argument (type=“upper”) is used to display only the upper triangular of the **correlation matrix**.

```
library(corrplot)
corrplot(res, type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45)
```

**Positive correlations** are displayed in blue and **negative correlations** in red color. Color intensity and the size of the circle are proportional to the **correlation coefficients**. In the right side of the **correlogram**, the legend color shows the **correlation coefficients** and the corresponding colors.

- The
**correlation matrix**is reordered according to the**correlation coefficient**using**“hclust”**method. **tl.col**(for text label color) and**tl.srt**(for text label string rotation) are used to change text colors and rotations.- Possible values for the argument
**type**are : “upper”, “lower”, “full”

Read more : visualize a correlation matrix using corrplot.

It’s also possible to **combine correlogram with the significance test**. We’ll use the result *res.cor2* generated in the previous section with **rcorr**() function [in **Hmisc** package]:

```
# Insignificant correlation are crossed
corrplot(res2$r, type="upper", order="hclust",
p.mat = res2$P, sig.level = 0.01, insig = "blank")
# Insignificant correlations are leaved blank
corrplot(res2$r, type="upper", order="hclust",
p.mat = res2$P, sig.level = 0.01, insig = "blank")
```

In the above plot, correlations with p-value > 0.01 are considered as insignificant. In this case the correlation coefficient values are leaved blank or crosses are added.

### Use chart.Correlation(): Draw scatter plots

The function *chart.Correlation()*[ in the package **PerformanceAnalytics**], can be used to display a chart of a correlation matrix.

**Install PerformanceAnalytics**:

`install.packages("PerformanceAnalytics")`

**Use chart.Correlation()**:

```
library("PerformanceAnalytics")
my_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()

```
# Get some colors
col<- colorRampPalette(c("blue", "white", "red"))(20)
heatmap(x = res, col = col, symm = TRUE)
```

**x**: the correlation matrix to be plotted**col**: color palettes**symm**: logical indicating if x should be treated symmetrically; can only be true when x is a square matrix.

# Online software to analyze and visualize a correlation matrix

Take me to the correlation matrix calculator

The software can be used as follow :

**Go to the web application**: correlation matrix calculator**Upload a .txt tab or a CSV file**containing your data (columns are variables). The supported file formats are described here. You can use the demo data available on the calculator web page by clicking on the corresponding link.- After uploading, an
**overview of a part of your file**is shown to check that the data are correctly imported. If the data are not correctly displayed, please make sure that the format of your file is OK here. **Click on the ‘Analyze’ button**and**select at least 2 variables**to calculate the correlation matrix. By default, all variables are selected.**Please, deselect the columns containing texts**. You can also**select the correlation methods**(Pearson, Spearman or Kendall). Default is the Pearson method.- Click the
**OK**button - Results : the output of the software includes :
- The correlation matrix
- The visualization of the correlation matrix as a correlogram
- A web link to export the results as .txt tab file

Note that, you can specify the alternative hypothesis to use for the correlation test by clicking on the button “Advanced options”.

Choose one of the 3 options :

- Two-sided
- Correlation < 0 for “less”
- Correlation > 0 for “greater”

**Two-sided**.

# Summarry

- Use
**cor**() function for simple**correlation analysis** - Use
**rcorr**() function from**Hmisc**package to compute**matrix of correlation coefficients**and**matrix of p-values**in single step. - Use
**symnum**(),**corrplot**()[from**corrplot**package],**chart.Correlation**() [from**PerformanceAnalytics**package], or**heatmap**() functions to visualize a**correlation matrix**.

# Infos

This analysis has been performed using **R software** (ver. 3.2.4).

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