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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
)

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 single number strictly between 0 and 1 giving the confidence level (default 0.95). Only used when detail = TRUE. Set to NULL to omit the confidence interval. Any other value – including percentages such as 95 – raises a classed error (spicy_invalid_input).

digits

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

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).

The default direction = "symmetric" follows the SPSS and DescTools convention: symmetric lambda is a standard, well-defined variant with its own asymptotic standard error. somers_d() deliberately differs (its default is "row") because its symmetric form is a derived quantity without an analytic SE; see its documentation.

Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

References

Goodman, L. A., & Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49(268), 732-764. doi:10.2307/2281536

See also

goodman_kruskal_tau(), uncertainty_coef(), assoc_measures()

Other association measures: assoc_measures(), contingency_coef(), cramer_v(), gamma_gk(), goodman_kruskal_tau(), kendall_tau_b(), kendall_tau_c(), phi(), somers_d(), uncertainty_coef(), yule_q()

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     SE  CI lower  CI upper   p
#>    0.000  0.000     0.000     0.000  --