:link: Methods for Correlation Analysis
correlationis 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:
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")
Click on the buttons above to access the package documentation and the easystats blog, and check-out these vignettes:
The correlation package can compute many different types of correlation, including:
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.
correlation(), which builds on top of
cor_test()and comes with a number of possible options.
resultsThe 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: 50Bayesian 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: 150Tetrachoric, Polychoric, Biserial, Biweight…
The
correlationpackage 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: 150Partial 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 loadedmtcars %>% 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
partialargument is set toFALSE, 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*** | |