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Compute Multiple Robust Correlations Between Numeric Variables

Source: R/ob_correlation.R
obcorr.Rd

This function computes various correlation coefficients between all pairs of numeric variables in a data frame. It implements several classical and robust correlation measures, including Pearson, Spearman, Kendall, Hoeffding's D, Distance Correlation, Biweight Midcorrelation, and Percentage Bend correlation.

Usage

obcorr(df, method = "all", threads = 0L)

Arguments

df

A data frame containing numeric variables. Non-numeric columns will be automatically excluded. At least two numeric variables are required.

method

A character string specifying which correlation method(s) to compute. Possible values are:

  • "all": Compute all available correlation methods (default).

  • "pearson": Compute only Pearson correlation.

  • "spearman": Compute only Spearman correlation.

  • "kendall": Compute only Kendall correlation.

  • "hoeffding": Compute only Hoeffding's D.

  • "distance": Compute only distance correlation.

  • "biweight": Compute only biweight midcorrelation.

  • "pbend": Compute only percentage bend correlation.

  • "robust": Compute robust correlations (biweight and pbend).

  • "alternative": Compute alternative correlations (hoeffding and distance).

threads

An integer specifying the number of threads to use for parallel computation. If 0 (default), uses all available cores. Ignored if OpenMP is not available.

Value

A data frame with the following columns:

x, y

Names of the variable pairs being correlated.

pearson

Pearson correlation coefficient.

spearman

Spearman rank correlation coefficient.

kendall

Kendall's tau-b correlation coefficient.

hoeffding

Hoeffding's D statistic (scaled).

distance

Distance correlation coefficient.

biweight

Biweight midcorrelation coefficient.

pbend

Percentage bend correlation coefficient.

The exact columns returned depend on the method parameter.

Details

The function supports multiple correlation methods simultaneously and utilizes OpenMP for parallel computation when available.

Available correlation methods:

  • Pearson: Standard linear correlation coefficient.

  • Spearman: Rank-based correlation coefficient.

  • Kendall: Kendall's tau-b correlation coefficient.

  • Hoeffding: Hoeffding's D statistic (scaled by 30).

  • Distance: Distance correlation (Székely et al., 2007).

  • Biweight: Biweight midcorrelation (robust alternative).

  • Pbend: Percentage bend correlation (robust alternative).

Note

  • Missing values (NA) are handled appropriately for each correlation method.

  • For robust methods (biweight, pbend), fallback to Pearson correlation occurs when there are insufficient data points or numerical instability.

  • Hoeffding's D requires at least 5 complete pairs.

  • Distance correlation is computed without forming NxN distance matrices for memory efficiency.

  • When OpenMP is available, computations are automatically parallelized across variable pairs.

References

Székely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007). Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6), 2769-2794.

Wilcox, R.R. (1994). The percentage bend correlation coefficient. Psychometrika, 59(4), 601-616.

Examples

# Create sample data
set.seed(123)
n <- 100
df <- data.frame(
  x1 = rnorm(n),
  x2 = rnorm(n),
  x3 = rt(n, df = 3), # Heavy-tailed distribution
  x4 = sample(c(0, 1), n, replace = TRUE), # Binary variable
  category = sample(letters[1:3], n, replace = TRUE) # Non-numeric column
)

# Add some relationships
df$x2 <- df$x1 + rnorm(n, 0, 0.5)
df$x3 <- df$x1^2 + rnorm(n, 0, 0.5)

# Compute all correlations
result_all <- obcorr(df)
head(result_all)
#>    x  y     pearson    spearman      kendall    hoeffding  distance    biweight
#> 1 x1 x3  0.09556132  0.06517852  0.048080808  0.047496185 0.7460724  0.11266947
#> 2 x2 x3  0.10385820  0.07159916  0.050505051  0.016285581 0.5003787  0.15306172
#> 3 x1 x4  0.11946052  0.11432107  0.093808315 -0.005827769 0.2600756  0.11946052
#> 4 x2 x4 -0.02020361 -0.01039282 -0.008528029 -0.008435515 0.1420518 -0.02020361
#> 5 x1 x2  0.86981390  0.87913591  0.700202020  0.397341844 1.4207684  0.87255023
#> 6 x3 x4 -0.09009510 -0.06720693 -0.055147919 -0.006921340 0.1976969 -0.09009510
#>         pbend
#> 1  0.06725434
#> 2  0.08868743
#> 3  0.09814141
#> 4 -0.01342052
#> 5  0.88270163
#> 6 -0.04556955

# Compute only robust correlations
result_robust <- obcorr(df, method = "robust")

# Compute only Pearson correlation with 2 threads
result_pearson <- obcorr(df, method = "pearson", threads = 2)