Perform Correlation Tests with Frequentist and Bayesian Methods

This function computes pairwise correlations for all variables in a given dataset, supporting both frequentist and Bayesian approaches. It provides multiple correlation estimates, confidence intervals, Bayesian credible intervals, probability of direction (pd), and Bayes factors.

Usage

cor_test_all(
  dat,
  cor = TRUE,
  cor_EAP = FALSE,
  cor_MAP = FALSE,
  cor_MED = FALSE,
  pd = FALSE,
  bf = FALSE,
  ci = c("freq", "bayes_central", "bayes_hdi"),
  triangle = c("upper", "lower", "full"),
  alternative = c("two.sided", "less", "greater"),
  method = c("pearson", "kendall", "spearman"),
  exact = NULL,
  conf.level = 0.95,
  alpha = 0.05,
  continuity = FALSE,
  rscale_est = "ultrawide",
  rscale_bf = "ultrawide",
  iterations = 10000,
  map_density_n = 512,
  detailed = FALSE,
  fullbayes = FALSE
)

Arguments

dat

A data frame or matrix containing numeric variables for correlation analysis.

cor

Logical. If TRUE, computes frequentist correlation coefficients (default: TRUE).

cor_EAP

Logical. If TRUE, computes the expected a posteriori (EAP) estimate of the correlation coefficient (default: FALSE).

cor_MAP

Logical. If TRUE, computes the maximum a posteriori (MAP) estimate of the correlation coefficient (default: FALSE).

cor_MED

Logical. If TRUE, computes the median of the posterior distribution (MED) for the correlation coefficient (default: FALSE).

pd

Logical. If TRUE, computes the probability of direction (pd) based on posterior distributions (default: FALSE).

bf

Logical. If TRUE, computes Bayes factors for the presence of correlation versus the null hypothesis (default: FALSE).

ci

Character. Specifies the type of confidence or credible interval: "freq" (frequentist confidence interval), "bayes_central" (Bayesian central credible interval), or "bayes_hdi" (highest density interval based on the posterior distribution) (default: "freq").

triangle

Character. Specifies which part of the correlation matrix to return: "upper", "lower", or "full" (default: "upper").

alternative

Character. Specifies the alternative hypothesis for the frequentist test: "two.sided", "less", or "greater" (default: "two.sided").

method

Character. Specifies the correlation method for the frequentist test: "pearson", "kendall", or "spearman" (default: "pearson").

exact

Logical or NULL. If TRUE, computes exact p-values for small sample sizes when using Spearman or Kendall correlations.

conf.level

Numeric. The confidence level for frequentist intervals or credibility level for Bayesian intervals (default: 0.95).

alpha

Numeric. Significance level. Defaults to 0.05.

continuity

Logical. If TRUE, applies a continuity correction for Kendall correlations (default: FALSE).

rscale_est

Numeric or character. Specifies the Cauchy prior scale for Bayesian estimation of the posterior distribution. Options: "ultrawide", "wide", "medium", or a positive real number (default: "ultrawide"). Passed to BayesFactor::correlationBF().

rscale_bf

Numeric or character. Specifies the Cauchy prior scale for Bayes factor calculation. Options: "ultrawide", "wide", "medium", or a positive real number (default: "ultrawide"). Passed to BayesFactor::correlationBF().

iterations

Integer. Number of MCMC samples for Bayesian estimation (default: 10000).

map_density_n

Integer. Number of bins for MAP density estimation (default: 512).

detailed

Logical. Whether to return detailed results (TRUE) or minimal output (FALSE, default).

fullbayes

Logical. Whether to show only Bayesian results (TRUE) or both frequentist and Bayesian results (FALSE, default).

Value

A list containing:

all

A data frame with all computed correlation statistics.

table_XX

A data frame corresponding to a table named "table_XX", where "XX" is derived from the output variables (e.g., "table_cor", "table_p", "table_BF10"). The content of the table depends on the provided inputs.

Examples

# Frequentist analysis
results <- cor_test_all(mtcars[, 1:5])
results$all  # View detailed results in a tidy format
#>    var_row var_col row col    cor  lower  upper     t df    p sig n_pair
#> 1      mpg     cyl   1   2 -0.852 -0.926 -0.716 -8.92 30 0.00   *     32
#> 2      mpg    disp   1   3 -0.848 -0.923 -0.708 -8.75 30 0.00   *     32
#> 3      mpg      hp   1   4 -0.776 -0.885 -0.586 -6.74 30 0.00   *     32
#> 4      mpg    drat   1   5  0.681  0.436  0.832  5.10 30 0.00   *     32
#> 5      cyl    disp   2   3  0.902  0.807  0.951 11.45 30 0.00   *     32
#> 6      cyl      hp   2   4  0.832  0.682  0.915  8.23 30 0.00   *     32
#> 7      cyl    drat   2   5 -0.700 -0.843 -0.465 -5.37 30 0.00   *     32
#> 8     disp      hp   3   4  0.791  0.611  0.893  7.08 30 0.00   *     32
#> 9     disp    drat   3   5 -0.710 -0.849 -0.481 -5.53 30 0.00   *     32
#> 10      hp    drat   4   5 -0.449 -0.690 -0.119 -2.75 30 0.01   *     32
results$table_cor  # View correlation matrix
#>      mpg    cyl   disp     hp   drat
#> mpg   NA -0.852 -0.848 -0.776  0.681
#> cyl   NA     NA  0.902  0.832 -0.700
#> disp  NA     NA     NA  0.791 -0.710
#> hp    NA     NA     NA     NA -0.449
#> drat  NA     NA     NA     NA     NA

# Calculation of Bayesian statistics
results <- cor_test_all(mtcars[, 1:5], cor_MAP = TRUE, ci = "bayes_hdi",
                        bf = TRUE, pd = TRUE, rscale_est = "ultrawide",
                        rscale_bf = "ultrawide")
results$all  # View detailed results in a tidy format
#>    var_row var_col row col    cor cor_MAP  lower  upper     t df    p sig    pd
#> 1      mpg     cyl   1   2 -0.852  -0.855 -0.930 -0.710 -8.92 30 0.00   * 1.000
#> 2      mpg    disp   1   3 -0.848  -0.847 -0.918 -0.699 -8.75 30 0.00   * 1.000
#> 3      mpg      hp   1   4 -0.776  -0.776 -0.894 -0.576 -6.74 30 0.00   * 1.000
#> 4      mpg    drat   1   5  0.681   0.660  0.415  0.824  5.10 30 0.00   * 1.000
#> 5      cyl    disp   2   3  0.902   0.901  0.797  0.955 11.45 30 0.00   * 1.000
#> 6      cyl      hp   2   4  0.832   0.826  0.662  0.907  8.23 30 0.00   * 1.000
#> 7      cyl    drat   2   5 -0.700  -0.700 -0.836 -0.453 -5.37 30 0.00   * 1.000
#> 8     disp      hp   3   4  0.791   0.779  0.604  0.898  7.08 30 0.00   * 1.000
#> 9     disp    drat   3   5 -0.710  -0.697 -0.845 -0.471 -5.53 30 0.00   * 1.000
#> 10      hp    drat   4   5 -0.449  -0.422 -0.675 -0.123 -2.75 30 0.01   * 0.994
#>            BF10 log10_BF10 favor evidence n_pair
#> 1  1.832837e+07  7.2631237  alt.  extreme     32
#> 2  1.233151e+07  7.0910164  alt.  extreme     32
#> 3  9.718143e+04  4.9875833  alt.  extreme     32
#> 4  1.451650e+03  3.1618619  alt.  extreme     32
#> 5  4.069716e+09  9.6095641  alt.  extreme     32
#> 6  3.671160e+06  6.5648033  alt.  extreme     32
#> 7  2.916590e+03  3.4648754  alt.  extreme     32
#> 8  2.259954e+05  5.3540997  alt.  extreme     32
#> 9  4.375586e+03  3.6410363  alt.  extreme     32
#> 10 5.263000e+00  0.7212022  alt. moderate     32
results$table_BF10  # View Bayes factor matrix
#>      mpg      cyl       disp         hp     drat
#> mpg   NA 18328365   12331514   97181.43 1451.650
#> cyl   NA       NA 4069716342 3671159.87 2916.590
#> disp  NA       NA         NA  225995.44 4375.586
#> hp    NA       NA         NA         NA    5.263
#> drat  NA       NA         NA         NA       NA