Lambda: Goodman Kruskal Lambda

Description

Calculate symmetric and asymmetric Goodman Kruskal lambda and their confidence intervals.

Usage

Lambda(x, y = NULL, direction = c("symmetric", "row", "column"), conf.level = NA, ...)

Arguments

a numeric vector, a matrix or a table.

NULL (default) or a vector with compatible dimensions to x. If y is provided, table(x, y, ...) is calculated.

direction

direction of the calculation. Can be one out of "symmetric" (default), "row", "column" (abbreviations are allowed). If direction is set to "row" then Lambda(R|C) (column dependent) will be reported.

conf.level

confidence level for the returned confidence interval, restricted to lie between 0 and 1.

...

further arguments are passed to the function table, allowing i.e. to set useNA.

Value

a single numeric value if no confidence intervals are requested, and otherwise a numeric vector with 3 elements for the estimate, the lower and the upper confidence interval

Details

Asymmetric lambda is interpreted as the probable improvement in predicting the column variable Y given knowledge of the row variable X. The nondirectional lambda is the average of the two asymmetric lambdas, Lambda(C|R) and Lambda(R|C). Lambda (asymmetric and symmetric) has a scale ranging from 0 to 1. For x either a matrix or data.frame, or two vectors x and y are expected. In latter case table(x, y) is calculated. The function handles NAs the same way the table function does, so tables are by default calculated with omitted NAs. Use PairApply to calculate pairwise lambdas. Use complete.cases, if only the complete cases of a data.frame are to be used.

References

Agresti, A. (2002) Categorical Data Analysis. John Wiley & Sons Goodman, L. A., and W. H. Kruskal. 1979. Measures of Association for Cross Classifications. New York: Springer-Verlag (contains articles appearing in J. Amer. Statist. Assoc. in 1954, 1959, 1963, 1972).

Examples

Run this code

# example from Goodman Kruskal (1954)
m <- as.table(cbind(c(1768,946,115), c(807,1387,438), c(189,746,288), c(47,53,16)))
dimnames(m) <- list(paste("A", 1:3), paste("B", 1:4))
m

# direction default is "symmetric"
Lambda(m)
Lambda(m, conf.level=0.95)

Lambda(m, direction="row")
Lambda(m, direction="column")

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