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🔗 Methods for Correlation Analysis

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correlation

correlation is aneasystats package focusedon correlation analysis. It’s lightweight, easy to use, and allows forthe computation of many different kinds of correlations, such aspartial correlations,Bayesian correlations,multilevelcorrelations,polychoric correlations,biweight,percentagebend orSheperd’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,Bayesianpartial multilevel correlation).

Citation

You can cite the package as follows:

Makowski, D., Ben-Shachar, M. S., Patil, I., & Lüdecke, D. (2020).Methods and algorithms for correlation analysis in R.Journal of OpenSource Software,5(51), 2306.https://doi.org/10.21105/joss.02306

Makowski, D., Wiernik, B. M., Patil, I., Lüdecke, D., & Ben-Shachar, M.S. (2022).correlation: Methods for correlation analysis [Rpackage].https://CRAN.R-project.org/package=correlation (Originalwork published 2020)

Installation

Thecorrelation package is available on CRAN, while its latestdevelopment version is available on R-universe (fromrOpenSci).

Type	Source	Command
Release	CRAN	`install.packages("correlation")`
Development	R-universe	`install.packages("correlation", repos = "https://easystats.r-universe.dev")`

Once you have downloaded the package, you can then load it using:

library("correlation")

Tip
Instead oflibrary(bayestestR), uselibrary(easystats). This willmake all features of the easystats-ecosystem available.
To stay updated, useeasystats::install_latest().

Documentation

Check out packagewebsitefor documentation.

Features

Thecorrelation package can compute many different types ofcorrelation, 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 rankcorrelation
✅Point-Biserial and biserial correlation
✅Winsorized correlation
✅Polychoric correlation
✅Tetrachoric correlation
✅Multilevel correlation

An overview and description of these correlations types isavailablehere.Moreover, many of these correlation types are available aspartialor within aBayesian framework.

Examples

The main function iscorrelation(),which builds on top ofcor_test()and comes with a number of possible options.

Correlation details and matrix

results<- correlation(iris)results## # Correlation Matrix (pearson-method)#### Parameter1   |   Parameter2 |     r |         95% CI | t(148) |         p## -------------------------------------------------------------------------## Sepal.Length |  Sepal.Width | -0.12 | [-0.27,  0.04] |  -1.44 | 0.152## 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.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***## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] |  43.39 | < .001***#### p-value adjustment method: Holm (1979)## Observations: 150

The output is not a square matrix, but a(tidy) dataframe with allcorrelations tests per row. One can also obtain amatrix 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 matrixusing:

summary(results,redundant=TRUE)## # Correlation Matrix (pearson-method)#### Parameter    | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width## ----------------------------------------------------------------------## Sepal.Length |              |       -0.12 |      0.87*** |     0.82***## Sepal.Width  |        -0.12 |             |     -0.43*** |    -0.37***## Petal.Length |      0.87*** |    -0.43*** |              |     0.96***## Petal.Width  |      0.82*** |    -0.37*** |      0.96*** |#### p-value adjustment method: Holm (1979)

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

Correlation tests

Thecor_test() function, for pairwise correlations, is also veryconvenient for making quick scatter plots.

plot(cor_test(iris,"Sepal.Width","Sepal.Length"))

Grouped dataframes

Thecorrelation() function also supportsstratified correlations,all within thetidyverse 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 aBayesian framework.

correlation(iris,bayesian=TRUE)## # Correlation Matrix (pearson-method)#### Parameter1   |   Parameter2 |   rho |         95% CI |      pd | % in ROPE## --------------------------------------------------------------------------## Sepal.Length |  Sepal.Width | -0.11 | [-0.27,  0.04] |  92.70% |    42.83%## Sepal.Length | Petal.Length |  0.86 | [ 0.82,  0.90] | 100%*** |        0%## Sepal.Length |  Petal.Width |  0.81 | [ 0.75,  0.86] | 100%*** |        0%## Sepal.Width  | Petal.Length | -0.41 | [-0.55, -0.28] | 100%*** |        0%## Sepal.Width  |  Petal.Width | -0.35 | [-0.49, -0.22] | 100%*** |        0%## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] | 100%*** |        0%#### Parameter1   |         Prior |          BF## ------------------------------------------## Sepal.Length | Beta (3 +- 3) |       0.509## Sepal.Length | Beta (3 +- 3) | 2.14e+43***## Sepal.Length | Beta (3 +- 3) | 2.62e+33***## Sepal.Width  | Beta (3 +- 3) | 3.49e+05***## Sepal.Width  | Beta (3 +- 3) | 5.29e+03***## Petal.Length | Beta (3 +- 3) | 1.24e+80***#### Observations: 150

Tetrachoric, Polychoric, Biserial, Biweight…

Thecorrelation package also supports different types of methods,which can deal with correlationsbetween 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 supportspartial correlations (as well as Bayesian partialcorrelations).

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 asGaussianGraphical Models (GGM), an increasingly popular tool in psychology. AGGM 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 (seeBhushan etal.,2019).

library(see)# for plottinglibrary(ggraph)# needs to be loadedplot(correlation(mtcars,partial=TRUE))+  scale_edge_color_continuous(low="#000004FF",high="#FCFDBFFF")

Multilevel Correlations

It also provide some cutting-edge methods, such as Multilevel (partial)correlations. These are are partial correlations based on linearmixed-effects models that include the factors asrandom effects.They can be see as correlationsadjusted 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 thepartial argument is set toFALSE, it will try toconvert the partial coefficient into regular ones.These can beconverted 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 thepackage, please followthisguide. Forquestions about the functionality, you may either contact us via emailor also file an issue.