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:link: Methods for Correlation Analysis

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correlation

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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

CRAN Build
Status codecov

Run the following to install the stable release of correlation from CRAN:

install.packages("correlation")

Or this one to install the latest development version:

install.packages("remotes")
remotes::install_github("easystats/correlation")

Documentation

Documentation Blog Features

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:

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

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)
## # Correlation Matrix (pearson-method)
## 
## 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*** |              |            
## 
## p-value adjustment method: Holm (1979)

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

summary(results, redundant=TRUE)
## # Correlation Matrix (pearson-method)
## 
## 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***
## 
## p-value adjustment method: Holm (1979)
library(dplyr)
library(see)

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

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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()
## # Correlation table (pearson-method)
## 
## Group      |   Parameter1 |  Parameter2 |    r |        95% CI | t(48) |         p
## ----------------------------------------------------------------------------------
## setosa     | Sepal.Length | Sepal.Width | 0.74 | [ 0.59, 0.85] |  7.68 | < .001***
## setosa     | Sepal.Length | Petal.Width | 0.28 | [ 0.00, 0.52] |  2.01 | 0.101    
## setosa     |  Sepal.Width | Petal.Width | 0.23 | [-0.05, 0.48] |  1.66 | 0.104    
## versicolor | Sepal.Length | Sepal.Width | 0.53 | [ 0.29, 0.70] |  4.28 | < .001***
## versicolor | Sepal.Length | Petal.Width | 0.55 | [ 0.32, 0.72] |  4.52 | < .001***
## versicolor |  Sepal.Width | Petal.Width | 0.66 | [ 0.47, 0.80] |  6.15 | < .001***
## virginica  | Sepal.Length | Sepal.Width | 0.46 | [ 0.20, 0.65] |  3.56 | 0.002**  
## virginica  | Sepal.Length | Petal.Width | 0.28 | [ 0.00, 0.52] |  2.03 | 0.048*   
## virginica  |  Sepal.Width | Petal.Width | 0.54 | [ 0.31, 0.71] |  4.42 | < .001***
## 
## p-value adjustment method: Holm (1979)
## Observations: 50

Bayesian Correlations

It is very easy to switch to a Bayesian framework.

correlation(iris, bayesian = TRUE)
## # Correlation table (pearson-method)
## 
## Parameter1   |   Parameter2 |   rho |         95% CI |      pd | % in ROPE |        BF |         Prior
## ------------------------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.11 | [-0.24,  0.01] |  92.38% |    42.83% |     0.509 | Beta (3 +- 3)
## Sepal.Length | Petal.Length |  0.86 | [ 0.82,  0.89] | 100%*** |        0% | > 1000*** | Beta (3 +- 3)
## Sepal.Length |  Petal.Width |  0.80 | [ 0.76,  0.85] | 100%*** |        0% | > 1000*** | Beta (3 +- 3)
## Sepal.Width  | Petal.Length | -0.41 | [-0.52, -0.31] | 100%*** |        0% | > 1000*** | Beta (3 +- 3)
## Sepal.Width  |  Petal.Width | -0.35 | [-0.46, -0.24] | 100%*** |     0.12% | > 1000*** | Beta (3 +- 3)
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] | 100%*** |        0% | > 1000*** | Beta (3 +- 3)
## 
## Observations: 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")
## # Correlation table (auto-method)
## 
## Parameter1         |         Parameter2 |     r |         95% CI | t(148) |         p
## -------------------------------------------------------------------------------------
## Sepal.Length       |        Sepal.Width | -0.12 | [-0.27,  0.04] |  -1.44 | 0.452    
## Sepal.Length       |       Petal.Length |  0.87 | [ 0.83,  0.91] |  21.65 | < .001***
## Sepal.Length       |        Petal.Width |  0.82 | [ 0.76,  0.86] |  17.30 | < .001***
## Sepal.Length       |     Species.setosa | -0.72 | [-0.79, -0.63] | -12.53 | < .001***
## Sepal.Length       | Species.versicolor |  0.08 | [-0.08,  0.24] |   0.97 | 0.452    
## Sepal.Length       |  Species.virginica |  0.64 | [ 0.53,  0.72] |  10.08 | < .001***
## Sepal.Width        |       Petal.Length | -0.43 | [-0.55, -0.29] |  -5.77 | < .001***
## Sepal.Width        |        Petal.Width | -0.37 | [-0.50, -0.22] |  -4.79 | < .001***
## Sepal.Width        |     Species.setosa |  0.60 | [ 0.49,  0.70] |   9.20 | < .001***
## Sepal.Width        | Species.versicolor | -0.47 | [-0.58, -0.33] |  -6.44 | < .001***
## Sepal.Width        |  Species.virginica | -0.14 | [-0.29,  0.03] |  -1.67 | 0.392    
## Petal.Length       |        Petal.Width |  0.96 | [ 0.95,  0.97] |  43.39 | < .001***
## Petal.Length       |     Species.setosa | -0.92 | [-0.94, -0.89] | -29.13 | < .001***
## Petal.Length       | Species.versicolor |  0.20 | [ 0.04,  0.35] |   2.51 | 0.066    
## Petal.Length       |  Species.virginica |  0.72 | [ 0.63,  0.79] |  12.66 | < .001***
## Petal.Width        |     Species.setosa | -0.89 | [-0.92, -0.85] | -23.41 | < .001***
## Petal.Width        | Species.versicolor |  0.12 | [-0.04,  0.27] |   1.44 | 0.452    
## Petal.Width        |  Species.virginica |  0.77 | [ 0.69,  0.83] |  14.66 | < .001***
## Species.setosa     | Species.versicolor | -0.88 | [-0.91, -0.84] | -22.43 | < .001***
## Species.setosa     |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.43 | < .001***
## Species.versicolor |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.43 | < .001***
## 
## p-value adjustment method: Holm (1979)
## Observations: 150

Partial Correlations

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

iris %>% 
  correlation(partial = TRUE) %>% 
  summary()
## # Correlation Matrix (pearson-method)
## 
## 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*** |              |            
## 
## p-value adjustment method: Holm (1979)

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()

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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()
## # Correlation Matrix (pearson-method)
## 
## 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*** |              |            
## 
## p-value adjustment method: Holm (1979)

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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