Lambda {DescTools}  R Documentation 
Goodman Kruskal Lambda
Description
Calculate symmetric and asymmetric Goodman Kruskal lambda and their confidence intervals. Lamdba is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be treated nominally), it indicates the extent to which the modal categories and frequencies for each value of the independent variable differ from the overall modal category and frequency, i.e. for all values of the independent variable together
Usage
Lambda(x, y = NULL, direction = c("symmetric", "row", "column"), conf.level = NA, ...)
Arguments
x 
a numeric vector, a matrix or a table. 
y 

direction 
type of lambda. Can be one out of 
conf.level 
confidence level for the returned confidence interval, restricted to lie between 0 and 1. 
... 
further arguments are passed to the function 
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(CR) and Lambda(RC).
Lambda (asymmetric and symmetric) has a scale ranging from 0 to 1.
Data can be passed to the function either as matrix or data.frame in x
, or as two numeric vectors x
and y
. In the latter case table(x, y, ...)
is calculated. Thus NA
s are handled the same way as table
does. Note that tables are by default calculated without NAs (which breaks the package's law to in general not omit NAs silently). The specific argument useNA
can be passed via the ... argument.
PairApply
can be used to calculate pairwise lambdas.
Value
if no confidence intervals are requested:
the estimate as numeric value
else a named numeric vector with 3 elements
lambda 
estimate 
lwr.ci 
lower confidence interval 
upr.ci 
upper confidence interval 
Author(s)
Andri Signorell <andri@signorell.net> based on code from Antti Arppe <antti.arppe@helsinki.fi>,
Nanina Anderegg (confidence interval symmetric lambda)
References
Agresti, A. (2002) Categorical Data Analysis. John Wiley & Sons
Goodman, L. A., Kruskal W. H. (1979) Measures of Association for Cross Classifications. New
York: SpringerVerlag (contains articles appearing in J. Amer. Statist. Assoc. in 1954,
1959, 1963, 1972).
http://www.nssl.noaa.gov/users/brooks/public_html/feda/papers/goodmankruskal1.pdf (might be outdated)
Liebetrau, A. M. (1983) Measures of Association, Sage University Papers Series on Quantitative Applications in the Social Sciences, 07004. Newbury Park, CA: Sage, pp. 17–24
See Also
GoodmanKruskalTau
, GoodmanKruskalGamma
, KendallTauA
, KendallTauB
, StuartTauC
, SomersDelta
, cor
Examples
# 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")