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correlation

correlation is an easystats package focused on correlation analysis. It’s lightweight, easy to use, and allows for the computation of many different kinds of correlations, such as partial correlations, Bayesian correlations, multilevel correlations, polychoric correlations, biweight, percentage bend or Sheperd’s Pi correlations (types of robust correlation), distance correlation (a type of non-linear correlation) and more, also allowing for combinations between them (for instance, Bayesian partial multilevel correlation).

You can reference the package and its documentation as follows:

  • Makowski, D., Ben-Shachar, M. S., Patil, I., & Lüdecke, D. (2019). Methods and Algorithms for Correlation Analysis in R. Journal of Open Source Software, 5(51), 2306. 10.21105/joss.02306

Installation

Run the following:

install.packages("devtools")
devtools::install_github("easystats/correlation")
library("correlation")

Documentation

Click on the buttons above to access the package documentation and the easystats blog, and check-out these vignettes:

Features

The correlation package can compute many different types of correlation, including:

  • Pearson’s correlation
  • Spearman’s rank correlation
  • Kendall’s rank correlation
  • Biweight midcorrelation
  • Distance correlation
  • Percentage bend correlation
  • Shepherd’s Pi correlation
  • Blomqvist’s coefficient
  • Hoeffding’s D
  • Gamma correlation
  • Gaussian rank correlation
  • Point-Biserial and biserial correlation
  • Polychoric correlation
  • Tetrachoric correlation
  • Multilevel correlation

An overview and description of these correlations types is available here. Moreover, many of these correlation types are available as partial or within a Bayesian framework.

Examples

The main function is correlation(), which builds on top of cor_test() and comes with a number of possible options.

Correlation details and matrix

results <- correlation(iris)
results
## Parameter1   |   Parameter2 |     r |         95% CI |     t |  df |      p |  Method | n_Obs
## ---------------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.12 | [-0.27,  0.04] | -1.44 | 148 | 0.152  | Pearson |   150
## Sepal.Length | Petal.Length |  0.87 | [ 0.83,  0.91] | 21.65 | 148 | < .001 | Pearson |   150
## Sepal.Length |  Petal.Width |  0.82 | [ 0.76,  0.86] | 17.30 | 148 | < .001 | Pearson |   150
## Sepal.Width  | Petal.Length | -0.43 | [-0.55, -0.29] | -5.77 | 148 | < .001 | Pearson |   150
## Sepal.Width  |  Petal.Width | -0.37 | [-0.50, -0.22] | -4.79 | 148 | < .001 | Pearson |   150
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] | 43.39 | 148 | < .001 | Pearson |   150

The output is not a square matrix, but a (tidy) dataframe with all correlations tests per row. One can also obtain a matrix using:

summary(results)
## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |     0.82*** |      0.87*** |       -0.12
## Sepal.Width  |    -0.37*** |     -0.43*** |            
## Petal.Length |     0.96*** |              |

Note that one can also obtain the full, square and redundant matrix using:

summary(results, redundant=TRUE)
## Parameter    | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width
## ----------------------------------------------------------------------
## Sepal.Length |      1.00*** |       -0.12 |      0.87*** |     0.82***
## Sepal.Width  |        -0.12 |     1.00*** |     -0.43*** |    -0.37***
## Petal.Length |      0.87*** |    -0.43*** |      1.00*** |     0.96***
## Petal.Width  |      0.82*** |    -0.37*** |      0.96*** |     1.00***
library(dplyr)
library(see)

results %>% 
  summary(redundant=TRUE) %>% 
  plot()

Grouped dataframes

The function also supports stratified correlations, all within the tidyverse workflow!

iris %>% 
  select(Species, Sepal.Length, Sepal.Width, Petal.Width) %>% 
  group_by(Species) %>% 
  correlation()
## Group      |   Parameter1 |  Parameter2 |    r |        95% CI |    t | df |      p |  Method | n_Obs
## -----------------------------------------------------------------------------------------------------
## setosa     | Sepal.Length | Sepal.Width | 0.74 | [ 0.59, 0.85] | 7.68 | 48 | < .001 | Pearson |    50
## setosa     | Sepal.Length | Petal.Width | 0.28 | [ 0.00, 0.52] | 2.01 | 48 | 0.101  | Pearson |    50
## setosa     |  Sepal.Width | Petal.Width | 0.23 | [-0.05, 0.48] | 1.66 | 48 | 0.104  | Pearson |    50
## versicolor | Sepal.Length | Sepal.Width | 0.53 | [ 0.29, 0.70] | 4.28 | 48 | < .001 | Pearson |    50
## versicolor | Sepal.Length | Petal.Width | 0.55 | [ 0.32, 0.72] | 4.52 | 48 | < .001 | Pearson |    50
## versicolor |  Sepal.Width | Petal.Width | 0.66 | [ 0.47, 0.80] | 6.15 | 48 | < .001 | Pearson |    50
## virginica  | Sepal.Length | Sepal.Width | 0.46 | [ 0.20, 0.65] | 3.56 | 48 | 0.002  | Pearson |    50
## virginica  | Sepal.Length | Petal.Width | 0.28 | [ 0.00, 0.52] | 2.03 | 48 | 0.048  | Pearson |    50
## virginica  |  Sepal.Width | Petal.Width | 0.54 | [ 0.31, 0.71] | 4.42 | 48 | < .001 | Pearson |    50

Bayesian Correlations

It is very easy to switch to a Bayesian framework.

correlation(iris, bayesian = TRUE)
## Parameter1   |   Parameter2 |   rho |         95% CI |     pd | % in ROPE |    BF |              Prior |           Method | n_Obs
## ---------------------------------------------------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.11 | [-0.24,  0.02] | 92.03% |    41.93% |  0.51 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150
## Sepal.Length | Petal.Length |  0.86 | [ 0.83,  0.89] |   100% |        0% | > 999 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150
## Sepal.Length |  Petal.Width |  0.81 | [ 0.76,  0.85] |   100% |        0% | > 999 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150
## Sepal.Width  | Petal.Length | -0.41 | [-0.52, -0.31] |   100% |        0% | > 999 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150
## Sepal.Width  |  Petal.Width | -0.35 | [-0.47, -0.24] |   100% |     0.07% | > 999 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] |   100% |        0% | > 999 | Cauchy (0 +- 0.33) | Bayesian Pearson |   150

Tetrachoric, Polychoric, Biserial, Biweight…

The correlation package also supports different types of methods, which can deal with correlations between factors!

correlation(iris, include_factors = TRUE, method = "auto")
## Parameter1         |         Parameter2 |     r |         95% CI |      t |  df |      p |         Method | n_Obs
## -----------------------------------------------------------------------------------------------------------------
## Sepal.Length       |        Sepal.Width | -0.12 | [-0.27,  0.04] |  -1.44 | 148 | 0.452  |        Pearson |   150
## Sepal.Length       |       Petal.Length |  0.87 | [ 0.83,  0.91] |  21.65 | 148 | < .001 |        Pearson |   150
## Sepal.Length       |        Petal.Width |  0.82 | [ 0.76,  0.86] |  17.30 | 148 | < .001 |        Pearson |   150
## Sepal.Length       |     Species.setosa | -0.72 | [-0.79, -0.63] | -12.53 | 148 | < .001 | Point-biserial |   150
## Sepal.Length       | Species.versicolor |  0.08 | [-0.08,  0.24] |   0.97 | 148 | 0.452  | Point-biserial |   150
## Sepal.Length       |  Species.virginica |  0.64 | [ 0.53,  0.72] |  10.08 | 148 | < .001 | Point-biserial |   150
## Sepal.Width        |       Petal.Length | -0.43 | [-0.55, -0.29] |  -5.77 | 148 | < .001 |        Pearson |   150
## Sepal.Width        |        Petal.Width | -0.37 | [-0.50, -0.22] |  -4.79 | 148 | < .001 |        Pearson |   150
## Sepal.Width        |     Species.setosa |  0.60 | [ 0.49,  0.70] |   9.20 | 148 | < .001 | Point-biserial |   150
## Sepal.Width        | Species.versicolor | -0.47 | [-0.58, -0.33] |  -6.44 | 148 | < .001 | Point-biserial |   150
## Sepal.Width        |  Species.virginica | -0.14 | [-0.29,  0.03] |  -1.67 | 148 | 0.392  | Point-biserial |   150
## Petal.Length       |        Petal.Width |  0.96 | [ 0.95,  0.97] |  43.39 | 148 | < .001 |        Pearson |   150
## Petal.Length       |     Species.setosa | -0.92 | [-0.94, -0.89] | -29.13 | 148 | < .001 | Point-biserial |   150
## Petal.Length       | Species.versicolor |  0.20 | [ 0.04,  0.35] |   2.51 | 148 | 0.066  | Point-biserial |   150
## Petal.Length       |  Species.virginica |  0.72 | [ 0.63,  0.79] |  12.66 | 148 | < .001 | Point-biserial |   150
## Petal.Width        |     Species.setosa | -0.89 | [-0.92, -0.85] | -23.41 | 148 | < .001 | Point-biserial |   150
## Petal.Width        | Species.versicolor |  0.12 | [-0.04,  0.27] |   1.44 | 148 | 0.452  | Point-biserial |   150
## Petal.Width        |  Species.virginica |  0.77 | [ 0.69,  0.83] |  14.66 | 148 | < .001 | Point-biserial |   150
## Species.setosa     | Species.versicolor | -0.88 | [-0.91, -0.84] | -22.35 | 148 | < .001 |    Tetrachoric |   150
## Species.setosa     |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.35 | 148 | < .001 |    Tetrachoric |   150
## Species.versicolor |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.35 | 148 | < .001 |    Tetrachoric |   150

Partial Correlations

It also supports partial correlations (as well as Bayesian partial correlations).

iris %>% 
  correlation(partial = TRUE) %>% 
  summary()
## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |    -0.34*** |      0.72*** |     0.63***
## Sepal.Width  |     0.35*** |     -0.62*** |            
## Petal.Length |     0.87*** |              |

Gaussian Graphical Models (GGMs)

Such partial correlations can also be represented as Gaussian Graphical Models (GGM), an increasingly popular tool in psychology. A GGM traditionally include a set of variables depicted as circles (“nodes”), and a set of lines that visualize relationships between them, which thickness represents the strength of association (see Bhushan et al., 2019).

library(see) # for plotting
library(ggraph) # needs to be loaded

mtcars %>% 
  correlation(partial = TRUE) %>% 
  plot()

Multilevel Correlations

It also provide some cutting-edge methods, such as Multilevel (partial) correlations. These are are partial correlations based on linear mixed models that include the factors as random effects. They can be see as correlations adjusted for some group (hierarchical) variability.

iris %>% 
  correlation(partial = TRUE, multilevel = TRUE) %>% 
  summary()
## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |      -0.17* |      0.71*** |     0.43***
## Sepal.Width  |     0.39*** |       -0.18* |            
## Petal.Length |     0.38*** |              |

However, if the partial argument is set to FALSE, it will try to convert the partial coefficient into regular ones.These can be converted back to full correlations:

iris %>% 
  correlation(partial = FALSE, multilevel = TRUE) %>% 
  summary()
## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |     0.36*** |      0.76*** |     0.53***
## Sepal.Width  |     0.47*** |      0.38*** |            
## Petal.Length |     0.48*** |              |

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Version

Install

install.packages('correlation')

Monthly Downloads

30,328

Version

0.5.0

License

GPL-3

Maintainer

Dominique Makowski

Last Published

December 2nd, 2020

Functions in correlation (0.5.0)

is.cor

Check if matrix ressembles a correlation matrix
display.easycormatrix

Export tables into different output formats
cor_to_pcor

Correlation Matrix to (Semi) Partial Correlations
cor_test

Correlation test
correlation

Correlation Analysis
isSquare

Check if Square Matrix
cor_to_ci

Convert correlation to p-values and CIs
distance_mahalanobis

Mahalanobis distance and confidence interval (CI)
matrix_inverse

Matrix Inversion
reexports

Objects exported from other packages
cor_to_cov

Convert a correlation to covariance
simulate_simpson

Simpson's paradox dataset simulation
z_fisher

Fisher z-transformation
winsorize

Winsorize data