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easystats/ correlation (0.7.1) 12 days ago
R TeX correlation bayesian robust
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easystats
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Description

: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).

Citation

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. https://doi.org/10.21105/joss.02306

Installation

CRAN Build Status codecov

Run the following to install the stable release 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:

✅ 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
✅ Winsorized 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 

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()



<!-- -->



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 Matrix (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 Matrix (pearson-method)
## 
## Parameter1   |   Parameter2 |   rho |         95% CI |      pd | % in ROPE |         Prior |        BF
## ------------------------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.11 | [-0.24,  0.02] |  91.03% |    43.55% | Beta (3 +- 3) |     0.509
## Sepal.Length | Petal.Length |  0.86 | [ 0.83,  0.90] | 100%*** |        0% | Beta (3 +- 3) | > 1000***
## Sepal.Length |  Petal.Width |  0.81 | [ 0.76,  0.85] | 100%*** |        0% | Beta (3 +- 3) | > 1000***
## Sepal.Width  | Petal.Length | -0.41 | [-0.51, -0.30] | 100%*** |        0% | Beta (3 +- 3) | > 1000***
## Sepal.Width  |  Petal.Width | -0.35 | [-0.46, -0.24] | 100%*** |     0.10% | Beta (3 +- 3) | > 1000***
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] | 100%*** |        0% | Beta (3 +- 3) | > 1000***
## 
## 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 Matrix (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()



<!-- -->



Multilevel Correlations



It also provide some cutting-edge methods, such as Multilevel (partial)
correlations. These are are partial correlations based on linear
mixed-effects 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*** |              |



Contributing and Support



In case you want to file an issue or contribute in another way to the
package, please follow this
guide. For
questions about the functionality, you may either contact us via email
or also file an issue.



Code of Conduct



Please note that this project is released with a Contributor Code of
Conduct.
By participating in this project you agree to abide by its terms.

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