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Quantify association between categorical variables

Source: R/cor_cramer.R
cor_cramer.Rd

Cramer's V extends the chi-squared test to quantify how strongly the categories of two variables co-occur. The value ranges from 0 to 1, where 0 indicates no association and 1 indicates perfect association.

This function implements a bias-corrected version of Cramer's V, which adjusts for sample size and is more accurate for small samples. However, this bias correction means that even for binary variables, Cramer's V will no equal the Pearson correlation (the standard, uncorrected Cramer's V does match Pearson for binary data).

As the number of categories increases, Cramer's V and Pearson correlation measure increasingly different aspects of association and should not be directly compared.

If you intend to combine these measures in a multicollinearity analysis, interpret them with care. It is often preferable to convert non-numeric variables to numeric form (for example, via target encoding) before assessing multicollinearity.

Usage

cor_cramer(x = NULL, y = NULL, check_input = TRUE, ...)

Arguments

x

(required; vector) Values of a categorical variable (character or vector). Converted to character if numeric or logical. Default: NULL

y

(required; vector) Values of a categorical variable (character or vector). Converted to character if numeric or logical. Default: NULL

check_input

(required; logical) If FALSE, disables data checking for a slightly faster execution. Default: TRUE

...

(optional) Internal args (e.g. function_name for validate_arg_function_name, a precomputed correlation matrix m, or cross-validation args for preference_order).

Value

numeric: Cramer's V

References

  • Cramér, H. (1946). Mathematical Methods of Statistics. Princeton: Princeton University Press, page 282 (Chapter 21. The two-dimensional case). ISBN 0-691-08004-6

See also

Other multicollinearity_assessment: collinear_stats(), cor_clusters(), cor_df(), cor_matrix(), cor_stats(), vif(), vif_df(), vif_stats()

Author

Blas M. Benito, PhD

Examples


# perfect one-to-one association
cor_cramer(
  x = c("a", "a", "b", "c"),
  y = c("a", "a", "b", "c")
)
#> [1] 1

# still perfect: labels differ but mapping is unique
cor_cramer(
  x = c("a", "a", "b", "c"),
  y = c("a", "a", "b", "d")
)
#> [1] 1

# high but < 1: mostly aligned, one category of y repeats
cor_cramer(
  x = c("a", "a", "b", "c"),
  y = c("a", "a", "b", "b")
)
#> [1] 0.7071068

# appears similar by position, but no association by distribution
# (x = "a" mixes with y = "a" and "b")
cor_cramer(
  x = c("a", "a", "a", "c"),
  y = c("a", "a", "b", "b")
)
#> [1] 0

# numeric inputs are coerced to character internally
cor_cramer(
  x = c(1, 1, 2, 3),
  y = c(1, 1, 2, 2)
)
#> [1] 0.7071068

# logical inputs are also coerced to character
cor_cramer(
  x = c(TRUE, TRUE, FALSE, FALSE),
  y = c(TRUE, TRUE, FALSE, FALSE)
)
#> [1] 1