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Goodman-Kruskal's Lambda

Source: R/assoc.R
lambda_gk.Rd

lambda_gk() computes Goodman-Kruskal's Lambda, a proportional reduction in error (PRE) measure for nominal variables.

Usage

lambda_gk(
  x,
  direction = c("symmetric", "row", "column"),
  detail = FALSE,
  conf_level = 0.95,
  digits = 3L,
  .include_se = FALSE
)

Arguments

x

A contingency table (of class table).

direction

Direction of prediction: "symmetric" (default), "row" (column predicts row), or "column" (row predicts column).

detail

Logical. If FALSE (default), return the estimate as a numeric scalar. If TRUE, return a named numeric vector including confidence interval and p-value.

conf_level

A number between 0 and 1 giving the confidence level (default 0.95). Only used when detail = TRUE. Set to NULL to omit the confidence interval.

digits

Number of decimal places used when printing the result (default 3). Only affects the detail = TRUE output.

.include_se

Internal parameter; do not use.

Value

Same structure as cramer_v(): a scalar when detail = FALSE, a named vector when detail = TRUE. The p-value tests H0: lambda = 0 (Wald z-test).

Details

Lambda measures how much prediction error is reduced when the independent variable is used to predict the dependent variable. It ranges from 0 (no reduction) to 1 (perfect prediction). Lambda can equal zero even when variables are associated if the modal category dominates in every column (or row). Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

goodman_kruskal_tau(), uncertainty_coef(), assoc_measures()

Examples

tab <- table(sochealth$smoking, sochealth$education)
lambda_gk(tab)
#> [1] 0
lambda_gk(tab, direction = "row")
#> [1] 0
lambda_gk(tab, direction = "column", detail = TRUE)
#> Estimate  CI lower  CI upper   p
#>    0.000     0.000     0.000  --