Title:  Methods for Correlation Analysis 

Description:  Lightweight package for computing different kinds of correlations, such as partial correlations, Bayesian correlations, multilevel correlations, polychoric correlations, biweight correlations, distance correlations and more. Part of the 'easystats' ecosystem. References: Makowski et al. (2020) <doi:10.21105/joss.02306>. 
Authors:  Dominique Makowski [aut, inv] (<https://orcid.org/0000000153759967>, @Dom_Makowski), Brenton M. Wiernik [aut, cre] (<https://orcid.org/0000000195606336>, @bmwiernik), Indrajeet Patil [aut] (<https://orcid.org/0000000319956531>, @patilindrajeets), Daniel Lüdecke [aut] (<https://orcid.org/0000000288953206>, @strengejacke), Mattan S. BenShachar [aut] (<https://orcid.org/0000000242874801>, @mattansb), Rémi Thériault [aut] (<https://orcid.org/0000000343156788>, @rempsyc), Mark White [rev], Maximilian M. Rabe [rev] 
Maintainer:  Brenton M. Wiernik <[email protected]> 
License:  MIT + file LICENSE 
Version:  0.8.5.1 
Built:  20240729 08:21:21 UTC 
Source:  https://github.com/easystats/correlation 
Return the upper or lower triangular part of the correlation matrix.
cor_lower(x, diag = FALSE, ...)
cor_lower(x, diag = FALSE, ...)
x 
A correlation object. 
diag 
Should the diagonal be included? 
... 
Other arguments to be passed to or from other functions. 
x < correlation(mtcars, redundant = TRUE) # Generate full matrix x < cor_lower(x) if (require("ggplot2")) { ggplot(x, aes(x = Parameter2, y = Parameter1, fill = r)) + geom_tile() } # Sorted x < correlation(mtcars, redundant = TRUE) # Generate full matrix x < cor_sort(x) x < cor_lower(x) if (require("ggplot2")) { ggplot(x, aes(x = Parameter2, y = Parameter1, fill = r)) + geom_tile() }
x < correlation(mtcars, redundant = TRUE) # Generate full matrix x < cor_lower(x) if (require("ggplot2")) { ggplot(x, aes(x = Parameter2, y = Parameter1, fill = r)) + geom_tile() } # Sorted x < correlation(mtcars, redundant = TRUE) # Generate full matrix x < cor_sort(x) x < cor_lower(x) if (require("ggplot2")) { ggplot(x, aes(x = Parameter2, y = Parameter1, fill = r)) + geom_tile() }
Make correlations positive definite using psych::cor.smooth
. If smoothing
is done, inferential statistics (pvalues, confidence intervals, etc.) are
removed, as they are no longer valid.
cor_smooth(x, method = "psych", verbose = TRUE, ...) is.positive_definite(x, tol = 10^12, ...) is_positive_definite(x, tol = 10^12, ...)
cor_smooth(x, method = "psych", verbose = TRUE, ...) is.positive_definite(x, tol = 10^12, ...) is_positive_definite(x, tol = 10^12, ...)
x 
A correlation matrix. 
method 
Smoothing method. Can be 
verbose 
Set to 
... 
Other arguments to be passed to or from other functions. 
tol 
The minimum eigenvalue to be considered as acceptable. 
set.seed(123) data < as.matrix(mtcars) # Make missing data so pairwise correlation matrix is nonpositive definite data[sample(seq_len(352), size = 60)] < NA data < as.data.frame(data) x < correlation(data) is.positive_definite(x) smoothed < cor_smooth(x)
set.seed(123) data < as.matrix(mtcars) # Make missing data so pairwise correlation matrix is nonpositive definite data[sample(seq_len(352), size = 60)] < NA data < as.data.frame(data) x < correlation(data) is.positive_definite(x) smoothed < cor_smooth(x)
Sort a correlation matrix based on hclust()
.
cor_sort(x, distance = "correlation", hclust_method = "complete", ...)
cor_sort(x, distance = "correlation", hclust_method = "complete", ...)
x 
A correlation matrix. 
distance 
How the distance between each variable should be calculated.
If 
hclust_method 
Argument passed down into the 
... 
Other arguments to be passed to or from other functions. 
x < correlation(mtcars) cor_sort(as.matrix(x)) cor_sort(x, hclust_method = "ward.D2") # It can also reorder the long form output cor_sort(summary(x, redundant = TRUE)) # As well as from the summary
x < correlation(mtcars) cor_sort(as.matrix(x)) cor_sort(x, hclust_method = "ward.D2") # It can also reorder the long form output cor_sort(summary(x, redundant = TRUE)) # As well as from the summary
This function performs a correlation test between two variables.
You can easily visualize the result using plot()
(see examples here).
cor_test( data, x, y, method = "pearson", ci = 0.95, bayesian = FALSE, bayesian_prior = "medium", bayesian_ci_method = "hdi", bayesian_test = c("pd", "rope", "bf"), include_factors = FALSE, partial = FALSE, partial_bayesian = FALSE, multilevel = FALSE, ranktransform = FALSE, winsorize = FALSE, verbose = TRUE, ... )
cor_test( data, x, y, method = "pearson", ci = 0.95, bayesian = FALSE, bayesian_prior = "medium", bayesian_ci_method = "hdi", bayesian_test = c("pd", "rope", "bf"), include_factors = FALSE, partial = FALSE, partial_bayesian = FALSE, multilevel = FALSE, ranktransform = FALSE, winsorize = FALSE, verbose = TRUE, ... )
data 
A data frame. 
x , y

Names of two variables present in the data. 
method 
A character string indicating which correlation coefficient is
to be used for the test. One of 
ci 
Confidence/Credible Interval level. If 
bayesian 
If 
bayesian_prior 
For the prior argument, several named values are
recognized: 
bayesian_ci_method , bayesian_test

See arguments in

include_factors 
If 
partial 
Can be 
partial_bayesian 
If partial correlations under a Bayesian framework
are needed, you will also need to set 
multilevel 
If 
ranktransform 
If 
winsorize 
Another way of making the correlation more "robust" (i.e.,
limiting the impact of extreme values). Can be either 
verbose 
Toggle warnings. 
... 
Additional arguments (e.g., 
Pearson's correlation: This is the most common correlation method. It corresponds to the covariance of the two variables normalized (i.e., divided) by the product of their standard deviations.
Spearman's rank correlation: A nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). Confidence Intervals (CI) for Spearman's correlations are computed using the Fieller et al. (1957) correction (see Bishara and Hittner, 2017).
Kendall's rank correlation: In the normal case, the Kendall correlation is preferred than the Spearman correlation because of a smaller gross error sensitivity (GES) and a smaller asymptotic variance (AV), making it more robust and more efficient. However, the interpretation of Kendall's tau is less direct than that of Spearman's rho, in the sense that it quantifies the difference between the percentage of concordant and discordant pairs among all possible pairwise events. Confidence Intervals (CI) for Kendall's correlations are computed using the Fieller et al. (1957) correction (see Bishara and Hittner, 2017).
Biweight midcorrelation: A measure of similarity that is medianbased, instead of the traditional meanbased, thus being less sensitive to outliers. It can be used as a robust alternative to other similarity metrics, such as Pearson correlation (Langfelder & Horvath, 2012).
Distance correlation: Distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.
Percentage bend correlation: Introduced by Wilcox (1994), it
is based on a downweight of a specified percentage of marginal observations
deviating from the median (by default, 20%
).
Shepherd's Pi correlation: Equivalent to a Spearman's rank correlation after outliers removal (by means of bootstrapped Mahalanobis distance).
Blomqvist’s coefficient: The Blomqvist’s coefficient (also referred to as Blomqvist's Beta or medial correlation; Blomqvist, 1950) is a medianbased nonparametric correlation that has some advantages over measures such as Spearman's or Kendall's estimates (see Shmid & Schimdt, 2006).
Hoeffding’s D: The Hoeffding’s D statistics is a nonparametric rank based measure of association that detects more general departures from independence (Hoeffding 1948), including nonlinear associations. Hoeffding’s D varies between 0.5 and 1 (if there are no tied ranks, otherwise it can have lower values), with larger values indicating a stronger relationship between the variables.
Somers’ D: The Somers’ D statistics is a nonparametric rank based measure of association between a binary variable and a continuous variable, for instance, in the context of logistic regression the binary outcome and the predicted probabilities for each outcome. Usually, Somers' D is a measure of ordinal association, however, this implementation it is limited to the case of a binary outcome.
PointBiserial and biserial correlation: Correlation coefficient used when one variable is continuous and the other is dichotomous (binary). PointBiserial is equivalent to a Pearson's correlation, while Biserial should be used when the binary variable is assumed to have an underlying continuity. For example, anxiety level can be measured on a continuous scale, but can be classified dichotomously as high/low.
Gamma correlation: The GoodmanKruskal gamma statistic is similar to Kendall's Tau coefficient. It is relatively robust to outliers and deals well with data that have many ties.
Winsorized correlation: Correlation of variables that have been formerly Winsorized, i.e., transformed by limiting extreme values to reduce the effect of possibly spurious outliers.
Gaussian rank Correlation: The Gaussian rank correlation estimator is a simple and wellperforming alternative for robust rank correlations (Boudt et al., 2012). It is based on the Gaussian quantiles of the ranks.
Polychoric correlation: Correlation between two theorized normally distributed continuous latent variables, from two observed ordinal variables.
Tetrachoric correlation: Special case of the polychoric correlation applicable when both observed variables are dichotomous.
Partial correlations are estimated as the correlation between two
variables after adjusting for the (linear) effect of one or more other
variable. The correlation test is then run after having partialized the
dataset, independently from it. In other words, it considers partialization
as an independent step generating a different dataset, rather than belonging
to the same model. This is why some discrepancies are to be expected for the
t and pvalues, CIs, BFs etc (but not the correlation coefficient)
compared to other implementations (e.g., ppcor
). (The size of these
discrepancies depends on the number of covariates partialledout and the
strength of the linear association between all variables.) Such partial
correlations can 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).
Multilevel correlations are a special case of partial correlations where
the variable to be adjusted for is a factor and is included as a random
effect in a mixed model (note that the remaining continuous variables of the
dataset will still be included as fixed effects, similarly to regular partial
correlations). The model is a random intercept model, i.e. the multilevel
correlation is adjusted for (1  groupfactor)
.That said, there is an
important difference between using cor_test()
and correlation()
: If you
set multilevel=TRUE
in correlation()
but partial
is set to FALSE
(as
per default), then a backtransformation from partial to nonpartial
correlation will be attempted (through pcor_to_cor()
).
However, this is not possible when using cor_test()
so that if you set
multilevel=TRUE
in it, the resulting correlations are partial one. Note
that for Bayesian multilevel correlations, if partial = FALSE
, the back
transformation will also recompute pvalues based on the new r scores,
and will drop the Bayes factors (as they are not relevant anymore). To keep
Bayesian scores, set partial = TRUE
.
Kendall and Spearman correlations when bayesian=TRUE
: These are technically
Pearson Bayesian correlations of rank transformed data, rather than pure
Bayesian rank correlations (which have different priors).
library(correlation) cor_test(iris, "Sepal.Length", "Sepal.Width") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "spearman") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "kendall") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "biweight") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "distance") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "percentage") if (require("wdm", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", method = "blomqvist") } if (require("Hmisc", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", method = "hoeffding") } cor_test(iris, "Sepal.Length", "Sepal.Width", method = "gamma") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "gaussian") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "shepherd") if (require("BayesFactor", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", bayesian = TRUE) } # Robust (these two are equivalent) cor_test(iris, "Sepal.Length", "Sepal.Width", method = "spearman") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "pearson", ranktransform = TRUE) # Winsorized cor_test(iris, "Sepal.Length", "Sepal.Width", winsorize = 0.2) # Tetrachoric if (require("psych", quietly = TRUE) && require("rstanarm", quietly = TRUE)) { data < iris data$Sepal.Width_binary < ifelse(data$Sepal.Width > 3, 1, 0) data$Petal.Width_binary < ifelse(data$Petal.Width > 1.2, 1, 0) cor_test(data, "Sepal.Width_binary", "Petal.Width_binary", method = "tetrachoric") # Biserial cor_test(data, "Sepal.Width", "Petal.Width_binary", method = "biserial") # Polychoric data$Petal.Width_ordinal < as.factor(round(data$Petal.Width)) data$Sepal.Length_ordinal < as.factor(round(data$Sepal.Length)) cor_test(data, "Petal.Width_ordinal", "Sepal.Length_ordinal", method = "polychoric") # When one variable is continuous, will run 'polyserial' correlation cor_test(data, "Sepal.Width", "Sepal.Length_ordinal", method = "polychoric") } # Partial cor_test(iris, "Sepal.Length", "Sepal.Width", partial = TRUE) if (require("lme4", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", multilevel = TRUE) } if (require("rstanarm", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", partial_bayesian = TRUE) }
library(correlation) cor_test(iris, "Sepal.Length", "Sepal.Width") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "spearman") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "kendall") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "biweight") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "distance") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "percentage") if (require("wdm", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", method = "blomqvist") } if (require("Hmisc", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", method = "hoeffding") } cor_test(iris, "Sepal.Length", "Sepal.Width", method = "gamma") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "gaussian") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "shepherd") if (require("BayesFactor", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", bayesian = TRUE) } # Robust (these two are equivalent) cor_test(iris, "Sepal.Length", "Sepal.Width", method = "spearman") cor_test(iris, "Sepal.Length", "Sepal.Width", method = "pearson", ranktransform = TRUE) # Winsorized cor_test(iris, "Sepal.Length", "Sepal.Width", winsorize = 0.2) # Tetrachoric if (require("psych", quietly = TRUE) && require("rstanarm", quietly = TRUE)) { data < iris data$Sepal.Width_binary < ifelse(data$Sepal.Width > 3, 1, 0) data$Petal.Width_binary < ifelse(data$Petal.Width > 1.2, 1, 0) cor_test(data, "Sepal.Width_binary", "Petal.Width_binary", method = "tetrachoric") # Biserial cor_test(data, "Sepal.Width", "Petal.Width_binary", method = "biserial") # Polychoric data$Petal.Width_ordinal < as.factor(round(data$Petal.Width)) data$Sepal.Length_ordinal < as.factor(round(data$Sepal.Length)) cor_test(data, "Petal.Width_ordinal", "Sepal.Length_ordinal", method = "polychoric") # When one variable is continuous, will run 'polyserial' correlation cor_test(data, "Sepal.Width", "Sepal.Length_ordinal", method = "polychoric") } # Partial cor_test(iris, "Sepal.Length", "Sepal.Width", partial = TRUE) if (require("lme4", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", multilevel = TRUE) } if (require("rstanarm", quietly = TRUE)) { cor_test(iris, "Sepal.Length", "Sepal.Width", partial_bayesian = TRUE) }
This function returns a formatted character of correlation statistics.
cor_text(x, show_ci = TRUE, show_statistic = TRUE, show_sig = TRUE, ...)
cor_text(x, show_ci = TRUE, show_statistic = TRUE, show_sig = TRUE, ...)
x 
A dataframe with correlation statistics. 
show_ci , show_statistic , show_sig

Toggle on/off different parts of the text. 
... 
Other arguments to be passed to or from other functions. 
rez < cor_test(mtcars, "mpg", "wt") cor_text(rez) cor_text(rez, show_statistic = FALSE, show_ci = FALSE, stars = TRUE) rez < correlation(mtcars) cor_text(rez)
rez < cor_test(mtcars, "mpg", "wt") cor_text(rez) cor_text(rez, show_statistic = FALSE, show_ci = FALSE, stars = TRUE) rez < correlation(mtcars) cor_text(rez)
Get statistics, pvalues and confidence intervals (CI) from correlation coefficients.
cor_to_ci(cor, n, ci = 0.95, method = "pearson", correction = "fieller", ...) cor_to_p(cor, n, method = "pearson")
cor_to_ci(cor, n, ci = 0.95, method = "pearson", correction = "fieller", ...) cor_to_p(cor, n, method = "pearson")
cor 
A correlation matrix or coefficient. 
n 
The sample size (number of observations). 
ci 
Confidence/Credible Interval level. If 
method 
A character string indicating which correlation coefficient is
to be used for the test. One of 
correction 
Only used if method is 'spearman' or 'kendall'. Can be 'fieller' (default; Fieller et al., 1957), 'bw' (only for Spearman) or 'none'. Bonett and Wright (2000) claim their correction ('bw') performs better, though the Bishara and Hittner (2017) paper favours the Fieller correction. Both are generally very similar. 
... 
Additional arguments (e.g., 
A list containing a pvalue and the statistic or the CI bounds.
Bishara, A. J., & Hittner, J. B. (2017). Confidence intervals for correlations when data are not normal. Behavior research methods, 49(1), 294309.
cor.test(iris$Sepal.Length, iris$Sepal.Width) cor_to_p(0.1175698, n = 150) cor_to_p(cor(iris[1:4]), n = 150) cor_to_ci(0.1175698, n = 150) cor_to_ci(cor(iris[1:4]), n = 150) cor.test(iris$Sepal.Length, iris$Sepal.Width, method = "spearman", exact = FALSE) cor_to_p(0.1667777, n = 150, method = "spearman") cor_to_ci(0.1667777, ci = 0.95, n = 150) cor.test(iris$Sepal.Length, iris$Sepal.Width, method = "kendall", exact = FALSE) cor_to_p(0.07699679, n = 150, method = "kendall")
cor.test(iris$Sepal.Length, iris$Sepal.Width) cor_to_p(0.1175698, n = 150) cor_to_p(cor(iris[1:4]), n = 150) cor_to_ci(0.1175698, n = 150) cor_to_ci(cor(iris[1:4]), n = 150) cor.test(iris$Sepal.Length, iris$Sepal.Width, method = "spearman", exact = FALSE) cor_to_p(0.1667777, n = 150, method = "spearman") cor_to_ci(0.1667777, ci = 0.95, n = 150) cor.test(iris$Sepal.Length, iris$Sepal.Width, method = "kendall", exact = FALSE) cor_to_p(0.07699679, n = 150, method = "kendall")
Convert a correlation to covariance
cor_to_cov(cor, sd = NULL, variance = NULL, tol = .Machine$double.eps^(2/3))
cor_to_cov(cor, sd = NULL, variance = NULL, tol = .Machine$double.eps^(2/3))
cor 
A correlation matrix, or a partial or a semipartial correlation matrix. 
sd , variance

A vector that contains the standard deviations, or the variance, of the variables in the correlation matrix. 
tol 
Relative tolerance to detect zero singular values. 
A covariance matrix.
cor < cor(iris[1:4]) cov(iris[1:4]) cor_to_cov(cor, sd = sapply(iris[1:4], sd)) cor_to_cov(cor, variance = sapply(iris[1:4], var))
cor < cor(iris[1:4]) cov(iris[1:4]) cor_to_cov(cor, sd = sapply(iris[1:4], sd)) cor_to_cov(cor, variance = sapply(iris[1:4], var))
Convert a correlation matrix to a (semi)partial correlation matrix. Partial correlations are a measure of the correlation between two variables that remains after controlling for (i.e., "partialling" out) all the other relationships. They can be used for graphical Gaussian models, as they represent the direct interactions between two variables, conditioned on all remaining variables. This means that the squared partial correlation between a predictor X1 and a response variable Y can be interpreted as the proportion of (unique) variance accounted for by X1 relative to the residual or unexplained variance of Y that cannot be accounted by the other variables.
cor_to_pcor(cor, tol = .Machine$double.eps^(2/3)) pcor_to_cor(pcor, tol = .Machine$double.eps^(2/3)) cor_to_spcor(cor = NULL, cov = NULL, tol = .Machine$double.eps^(2/3))
cor_to_pcor(cor, tol = .Machine$double.eps^(2/3)) pcor_to_cor(pcor, tol = .Machine$double.eps^(2/3)) cor_to_spcor(cor = NULL, cov = NULL, tol = .Machine$double.eps^(2/3))
cor 
A correlation matrix, or a partial or a semipartial correlation matrix. 
tol 
Relative tolerance to detect zero singular values. 
pcor 
A correlation matrix, or a partial or a semipartial correlation matrix. 
cov 
A covariance matrix (or a vector of the SD of the variables). Required for semipartial correlations. 
The semipartial correlation is similar to the partial correlation statistic. However, it represents (when squared) the proportion of (unique) variance accounted for by the predictor X1, relative to the total variance of Y. Thus, it might be seen as a better indicator of the "practical relevance" of a predictor, because it is scaled to (i.e., relative to) the total variability in the response variable.
The (semi) partial correlation matrix.
cor < cor(iris[1:4]) # Partialize cor_to_pcor(cor) cor_to_spcor(cor, cov = sapply(iris[1:4], sd)) # Inverse round(pcor_to_cor(cor_to_pcor(cor))  cor, 2) # Should be 0
cor < cor(iris[1:4]) # Partialize cor_to_pcor(cor) cor_to_spcor(cor, cov = sapply(iris[1:4], sd)) # Inverse round(pcor_to_cor(cor_to_pcor(cor))  cor, 2) # Should be 0
Easily output a correlation matrix and export it to Microsoft Excel, with the first row and column frozen, and correlation coefficients colourcoded based on effect size (0.00.2: small (no colour); 0.20.4: medium (pink/light blue); 0.41.0: large (red/dark blue)), following Cohen's suggestions for small (.10), medium (.30), and large (.50) correlation sizes.
cormatrix_to_excel(data, filename, overwrite = TRUE, print.mat = TRUE, ...)
cormatrix_to_excel(data, filename, overwrite = TRUE, print.mat = TRUE, ...)
data 
The data frame 
filename 
Desired filename (path can be added before hand but no need to specify extension). 
overwrite 
Whether to allow overwriting previous file. 
print.mat 
Logical, whether to also print the correlation matrix to console. 
... 
Parameters to be passed to 
A Microsoft Excel document, containing the colourcoded correlation matrix with significance stars, on the first sheet, and the colourcoded pvalues on the second sheet.
Adapted from @JanMarvin (JanMarvin/openxlsx2#286) and
the original rempsyc::cormatrix_excel
.
# Basic example suppressWarnings(cormatrix_to_excel(mtcars, select = c("mpg", "cyl", "disp", "hp", "carb"), filename = "cormatrix1" )) suppressWarnings(cormatrix_to_excel(iris, p_adjust = "none", filename = "cormatrix2" )) suppressWarnings(cormatrix_to_excel(airquality, method = "spearman", filename = "cormatrix3" ))
# Basic example suppressWarnings(cormatrix_to_excel(mtcars, select = c("mpg", "cyl", "disp", "hp", "carb"), filename = "cormatrix1" )) suppressWarnings(cormatrix_to_excel(iris, p_adjust = "none", filename = "cormatrix2" )) suppressWarnings(cormatrix_to_excel(airquality, method = "spearman", filename = "cormatrix3" ))
Performs a correlation analysis.
You can easily visualize the result using plot()
(see examples here).
correlation( data, data2 = NULL, select = NULL, select2 = NULL, rename = NULL, method = "pearson", p_adjust = "holm", ci = 0.95, bayesian = FALSE, bayesian_prior = "medium", bayesian_ci_method = "hdi", bayesian_test = c("pd", "rope", "bf"), redundant = FALSE, include_factors = FALSE, partial = FALSE, partial_bayesian = FALSE, multilevel = FALSE, ranktransform = FALSE, winsorize = FALSE, verbose = TRUE, standardize_names = getOption("easystats.standardize_names", FALSE), ... )
correlation( data, data2 = NULL, select = NULL, select2 = NULL, rename = NULL, method = "pearson", p_adjust = "holm", ci = 0.95, bayesian = FALSE, bayesian_prior = "medium", bayesian_ci_method = "hdi", bayesian_test = c("pd", "rope", "bf"), redundant = FALSE, include_factors = FALSE, partial = FALSE, partial_bayesian = FALSE, multilevel = FALSE, ranktransform = FALSE, winsorize = FALSE, verbose = TRUE, standardize_names = getOption("easystats.standardize_names", FALSE), ... )
data 
A data frame. 
data2 
An optional data frame. If specified, all pairwise correlations
between the variables in 
select , select2

(Ignored if 
rename 
In case you wish to change the names of the variables in
the output, these arguments can be used to specify these alternative names.
Note that the number of names should be equal to the number of columns
selected. Ignored if 
method 
A character string indicating which correlation coefficient is
to be used for the test. One of 
p_adjust 
Correction method for frequentist correlations. Can be one of

ci 
Confidence/Credible Interval level. If 
bayesian 
If 
bayesian_prior 
For the prior argument, several named values are
recognized: 
bayesian_ci_method , bayesian_test

See arguments in

redundant 
Should the data include redundant rows (where each given correlation is repeated two times). 
include_factors 
If 
partial 
Can be 
partial_bayesian 
If partial correlations under a Bayesian framework
are needed, you will also need to set 
multilevel 
If 
ranktransform 
If 
winsorize 
Another way of making the correlation more "robust" (i.e.,
limiting the impact of extreme values). Can be either 
verbose 
Toggle warnings. 
standardize_names 
This option can be set to 
... 
Additional arguments (e.g., 
Pearson's correlation: This is the most common correlation method. It corresponds to the covariance of the two variables normalized (i.e., divided) by the product of their standard deviations.
Spearman's rank correlation: A nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). Confidence Intervals (CI) for Spearman's correlations are computed using the Fieller et al. (1957) correction (see Bishara and Hittner, 2017).
Kendall's rank correlation: In the normal case, the Kendall correlation is preferred than the Spearman correlation because of a smaller gross error sensitivity (GES) and a smaller asymptotic variance (AV), making it more robust and more efficient. However, the interpretation of Kendall's tau is less direct than that of Spearman's rho, in the sense that it quantifies the difference between the percentage of concordant and discordant pairs among all possible pairwise events. Confidence Intervals (CI) for Kendall's correlations are computed using the Fieller et al. (1957) correction (see Bishara and Hittner, 2017).
Biweight midcorrelation: A measure of similarity that is medianbased, instead of the traditional meanbased, thus being less sensitive to outliers. It can be used as a robust alternative to other similarity metrics, such as Pearson correlation (Langfelder & Horvath, 2012).
Distance correlation: Distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.
Percentage bend correlation: Introduced by Wilcox (1994), it
is based on a downweight of a specified percentage of marginal observations
deviating from the median (by default, 20%
).
Shepherd's Pi correlation: Equivalent to a Spearman's rank correlation after outliers removal (by means of bootstrapped Mahalanobis distance).
Blomqvist’s coefficient: The Blomqvist’s coefficient (also referred to as Blomqvist's Beta or medial correlation; Blomqvist, 1950) is a medianbased nonparametric correlation that has some advantages over measures such as Spearman's or Kendall's estimates (see Shmid & Schimdt, 2006).
Hoeffding’s D: The Hoeffding’s D statistics is a nonparametric rank based measure of association that detects more general departures from independence (Hoeffding 1948), including nonlinear associations. Hoeffding’s D varies between 0.5 and 1 (if there are no tied ranks, otherwise it can have lower values), with larger values indicating a stronger relationship between the variables.
Somers’ D: The Somers’ D statistics is a nonparametric rank based measure of association between a binary variable and a continuous variable, for instance, in the context of logistic regression the binary outcome and the predicted probabilities for each outcome. Usually, Somers' D is a measure of ordinal association, however, this implementation it is limited to the case of a binary outcome.
PointBiserial and biserial correlation: Correlation coefficient used when one variable is continuous and the other is dichotomous (binary). PointBiserial is equivalent to a Pearson's correlation, while Biserial should be used when the binary variable is assumed to have an underlying continuity. For example, anxiety level can be measured on a continuous scale, but can be classified dichotomously as high/low.
Gamma correlation: The GoodmanKruskal gamma statistic is similar to Kendall's Tau coefficient. It is relatively robust to outliers and deals well with data that have many ties.
Winsorized correlation: Correlation of variables that have been formerly Winsorized, i.e., transformed by limiting extreme values to reduce the effect of possibly spurious outliers.
Gaussian rank Correlation: The Gaussian rank correlation estimator is a simple and wellperforming alternative for robust rank correlations (Boudt et al., 2012). It is based on the Gaussian quantiles of the ranks.
Polychoric correlation: Correlation between two theorized normally distributed continuous latent variables, from two observed ordinal variables.
Tetrachoric correlation: Special case of the polychoric correlation applicable when both observed variables are dichotomous.
Partial correlations are estimated as the correlation between two
variables after adjusting for the (linear) effect of one or more other
variable. The correlation test is then run after having partialized the
dataset, independently from it. In other words, it considers partialization
as an independent step generating a different dataset, rather than belonging
to the same model. This is why some discrepancies are to be expected for the
t and pvalues, CIs, BFs etc (but not the correlation coefficient)
compared to other implementations (e.g., ppcor
). (The size of these
discrepancies depends on the number of covariates partialledout and the
strength of the linear association between all variables.) Such partial
correlations can 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).
Multilevel correlations are a special case of partial correlations where
the variable to be adjusted for is a factor and is included as a random
effect in a mixed model (note that the remaining continuous variables of the
dataset will still be included as fixed effects, similarly to regular partial
correlations). The model is a random intercept model, i.e. the multilevel
correlation is adjusted for (1  groupfactor)
.That said, there is an
important difference between using cor_test()
and correlation()
: If you
set multilevel=TRUE
in correlation()
but partial
is set to FALSE
(as
per default), then a backtransformation from partial to nonpartial
correlation will be attempted (through pcor_to_cor()
).
However, this is not possible when using cor_test()
so that if you set
multilevel=TRUE
in it, the resulting correlations are partial one. Note
that for Bayesian multilevel correlations, if partial = FALSE
, the back
transformation will also recompute pvalues based on the new r scores,
and will drop the Bayes factors (as they are not relevant anymore). To keep
Bayesian scores, set partial = TRUE
.
Kendall and Spearman correlations when bayesian=TRUE
: These are technically
Pearson Bayesian correlations of rank transformed data, rather than pure
Bayesian rank correlations (which have different priors).
A correlation object that can be displayed using the print
, summary
or
table
methods.
The p_adjust
argument can be used to adjust pvalues for multiple
comparisons. All adjustment methods available in p.adjust
function
stats
package are supported.
Boudt, K., Cornelissen, J., & Croux, C. (2012). The Gaussian rank correlation estimator: robustness properties. Statistics and Computing, 22(2), 471483.
Bhushan, N., Mohnert, F., Sloot, D., Jans, L., Albers, C., & Steg, L. (2019). Using a Gaussian graphical model to explore relationships between items and variables in environmental psychology research. Frontiers in psychology, 10, 1050.
Bishara, A. J., & Hittner, J. B. (2017). Confidence intervals for correlations when data are not normal. Behavior research methods, 49(1), 294309.
Fieller, E. C., Hartley, H. O., & Pearson, E. S. (1957). Tests for rank correlation coefficients. I. Biometrika, 44(3/4), 470481.
Langfelder, P., & Horvath, S. (2012). Fast R functions for robust correlations and hierarchical clustering. Journal of statistical software, 46(11).
Blomqvist, N. (1950). On a measure of dependence between two random variables,Annals of Mathematical Statistics,21, 593–600
Somers, R. H. (1962). A new asymmetric measure of association for ordinal variables. American Sociological Review. 27 (6).
library(correlation) library(poorman) results < correlation(iris) results summary(results) summary(results, redundant = TRUE) # pipefriendly usage with grouped dataframes from {dplyr} package iris %>% correlation(select = "Petal.Width", select2 = "Sepal.Length") # Grouped dataframe # grouped correlations iris %>% group_by(Species) %>% correlation() # selecting specific variables for correlation mtcars %>% group_by(am) %>% correlation( select = c("cyl", "wt"), select2 = c("hp") ) # supplying custom variable names correlation(anscombe, select = c("x1", "x2"), rename = c("var1", "var2")) # automatic selection of correlation method correlation(mtcars[2], method = "auto")
library(correlation) library(poorman) results < correlation(iris) results summary(results) summary(results, redundant = TRUE) # pipefriendly usage with grouped dataframes from {dplyr} package iris %>% correlation(select = "Petal.Width", select2 = "Sepal.Length") # Grouped dataframe # grouped correlations iris %>% group_by(Species) %>% correlation() # selecting specific variables for correlation mtcars %>% group_by(am) %>% correlation( select = c("cyl", "wt"), select2 = c("hp") ) # supplying custom variable names correlation(anscombe, select = c("x1", "x2"), rename = c("var1", "var2")) # automatic selection of correlation method correlation(mtcars[2], method = "auto")
Deprecated functions
distance_mahalanobis(...)
distance_mahalanobis(...)
... 
Args. 
Export tables (i.e. data frame) into different output formats.
print_md()
is a alias for display(format = "markdown")
.
## S3 method for class 'easycormatrix' display( object, format = "markdown", digits = 2, p_digits = 3, stars = TRUE, include_significance = NULL, ... ) ## S3 method for class 'easycorrelation' print_md(x, digits = NULL, p_digits = NULL, stars = NULL, ...) ## S3 method for class 'easycorrelation' print_html(x, digits = NULL, p_digits = NULL, stars = NULL, ...) ## S3 method for class 'easycormatrix' print_md( x, digits = NULL, p_digits = NULL, stars = NULL, include_significance = NULL, ... ) ## S3 method for class 'easycormatrix' print_html( x, digits = NULL, p_digits = NULL, stars = NULL, include_significance = NULL, ... )
## S3 method for class 'easycormatrix' display( object, format = "markdown", digits = 2, p_digits = 3, stars = TRUE, include_significance = NULL, ... ) ## S3 method for class 'easycorrelation' print_md(x, digits = NULL, p_digits = NULL, stars = NULL, ...) ## S3 method for class 'easycorrelation' print_html(x, digits = NULL, p_digits = NULL, stars = NULL, ...) ## S3 method for class 'easycormatrix' print_md( x, digits = NULL, p_digits = NULL, stars = NULL, include_significance = NULL, ... ) ## S3 method for class 'easycormatrix' print_html( x, digits = NULL, p_digits = NULL, stars = NULL, include_significance = NULL, ... )
object , x

An object returned by

format 
String, indicating the output format. Currently, only

digits , p_digits

To do... 
stars 
To do... 
include_significance 
To do... 
... 
Currently not used. 
display()
is useful when the tableoutput from functions,
which is usually printed as formatted texttable to console, should
be formatted for pretty tablerendering in markdown documents, or if
knitted from rmarkdown to PDF or Word files.
A character vector. If format = "markdown"
, the return value
will be a character vector in markdowntable format.
data(iris) corr < correlation(iris) display(corr) s < summary(corr) display(s)
data(iris) corr < correlation(iris) display(corr) s < summary(corr) display(s)
Check if matrix ressembles a correlation matrix
is.cor(x)
is.cor(x)
x 
A matrix. 
TRUE
of the matrix is a correlation matrix or FALSE
otherwise.
Check if Square Matrix
isSquare(m)
isSquare(m)
m 
A matrix. 
TRUE
of the matrix is square or FALSE
otherwise.
Performs a MoorePenrose generalized inverse (also called the Pseudoinverse).
matrix_inverse(m, tol = .Machine$double.eps^(2/3))
matrix_inverse(m, tol = .Machine$double.eps^(2/3))
m 
Matrix for which the inverse is required. 
tol 
Relative tolerance to detect zero singular values. 
An inversed matrix.
pinv from the pracma package
m < cor(iris[1:4]) matrix_inverse(m)
m < cor(iris[1:4]) matrix_inverse(m)
Objects from the correlation
package can be easily visualized. You can
simply run plot()
on them, which will internally call the visualisation_recipe()
method to produce a basic ggplot
. You can customize this plot adhoc or via
the arguments described below.
See examples here.
## S3 method for class 'easycor_test' visualisation_recipe( x, show_data = "point", show_text = "subtitle", smooth = NULL, point = NULL, text = NULL, labs = NULL, ... ) ## S3 method for class 'easycormatrix' visualisation_recipe( x, show_data = "tile", show_text = "text", show_legend = TRUE, tile = NULL, point = NULL, text = NULL, scale = NULL, scale_fill = NULL, labs = NULL, type = show_data, ... ) ## S3 method for class 'easycorrelation' visualisation_recipe(x, ...)
## S3 method for class 'easycor_test' visualisation_recipe( x, show_data = "point", show_text = "subtitle", smooth = NULL, point = NULL, text = NULL, labs = NULL, ... ) ## S3 method for class 'easycormatrix' visualisation_recipe( x, show_data = "tile", show_text = "text", show_legend = TRUE, tile = NULL, point = NULL, text = NULL, scale = NULL, scale_fill = NULL, labs = NULL, type = show_data, ... ) ## S3 method for class 'easycorrelation' visualisation_recipe(x, ...)
x 
A correlation object. 
show_data 
Show data. For correlation matrices, can be 
show_text 
Show labels with matrix values. 
... 
Other arguments passed to other functions. 
show_legend 
Show legend. Can be set to 
tile , point , text , scale , scale_fill , smooth , labs

Additional aesthetics and parameters for the geoms (see customization example). 
type 
Alias for 
rez < cor_test(mtcars, "mpg", "wt") layers < visualisation_recipe(rez, labs = list(x = "Miles per Gallon (mpg)")) layers plot(layers) plot(rez, show_text = "label", point = list(color = "#f44336"), text = list(fontface = "bold"), show_statistic = FALSE, show_ci = FALSE, stars = TRUE ) rez < correlation(mtcars) x < cor_sort(as.matrix(rez)) layers < visualisation_recipe(x) layers plot(layers) #' Get more details using `summary()` x < summary(rez, redundant = TRUE, digits = 3) plot(visualisation_recipe(x)) # Customize x < summary(rez) layers < visualisation_recipe(x, show_data = "points", scale = list(range = c(10, 20)), scale_fill = list( high = "#FF5722", low = "#673AB7", name = "r" ), text = list(color = "white"), labs = list(title = "My Plot") ) plot(layers) + theme_modern() rez < correlation(iris) layers < visualisation_recipe(rez) layers plot(layers)
rez < cor_test(mtcars, "mpg", "wt") layers < visualisation_recipe(rez, labs = list(x = "Miles per Gallon (mpg)")) layers plot(layers) plot(rez, show_text = "label", point = list(color = "#f44336"), text = list(fontface = "bold"), show_statistic = FALSE, show_ci = FALSE, stars = TRUE ) rez < correlation(mtcars) x < cor_sort(as.matrix(rez)) layers < visualisation_recipe(x) layers plot(layers) #' Get more details using `summary()` x < summary(rez, redundant = TRUE, digits = 3) plot(visualisation_recipe(x)) # Customize x < summary(rez) layers < visualisation_recipe(x, show_data = "points", scale = list(range = c(10, 20)), scale_fill = list( high = "#FF5722", low = "#673AB7", name = "r" ), text = list(color = "white"), labs = list(title = "My Plot") ) plot(layers) + theme_modern() rez < correlation(iris) layers < visualisation_recipe(rez) layers plot(layers)
The Fisher ztransformation converts the standard Pearson's r to a normally distributed variable z'. It is used to compute confidence intervals to correlations. The z' variable is different from the zstatistic.
z_fisher(r = NULL, z = NULL)
z_fisher(r = NULL, z = NULL)
r , z

The r or the z' value to be converted. 
The transformed value.
Zar, J.H., (2014). Spearman Rank Correlation: Overview. Wiley StatsRef: Statistics Reference Online. doi:10.1002/9781118445112.stat05964
z_fisher(r = 0.7) z_fisher(z = 0.867)
z_fisher(r = 0.7) z_fisher(z = 0.867)