Uncertainty Coefficient

The uncertainty coefficient U(C|R) measures the proportion of uncertainty (entropy) in the column variable Y that is explained by the row variable X. The function has interfaces for a table, a matrix, a data.frame and for single vectors.

UncertCoef(x, y = NULL, direction = c("symmetric", "row", "column"), 
           conf.level = NA, p.zero.correction = 1/sum(x)^2, ...)

Arguments

x

a numeric vector, a factor, matrix or data frame.

y

NULL (default) or a vector, an ordered factor, matrix or data frame with compatible dimensions to x.

direction

direction of the calculation. Can be "row" (default) or "column", where "row" calculates UncertCoef (R|C) ("column dependent").

conf.level

confidence level of the interval. If set to NA (which is the default) no confidence interval will be calculated.

p.zero.correction

slightly nudge zero values so that their logarithm can be calculated

...

further arguments are passed to the function table, allowing i.e. to set useNA. This refers only to the vector interface.

Details

The uncertainty coefficient is computed as $$U(C|R) = \frac{H(X) + H(Y) - H(XY)}{H(Y)} $$ and ranges from [0, 1].

Value

Either a single numeric value, if no confidence interval is required,
or a vector with 3 elements for estimate, lower and upper confidence intervall.

References

Theil, H. (1972), Statistical Decomposition Analysis, Amsterdam: North-Holland Publishing Company.

Author

Andri Signorell <andri@signorell.net> strongly based on code from Antti Arppe <antti.arppe@helsinki.fi>

See also

Entropy, Lambda, Assocs

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
#>      B 1  B 2  B 3  B 4
#> A 1 1768  807  189   47
#> A 2  946 1387  746   53
#> A 3  115  438  288   16

# direction default is "symmetric"
UncertCoef(m)
#> [1] 0.0799
UncertCoef(m, conf.level=0.95)
#>     uc lwr.ci upr.ci 
#> 0.0799 0.0713 0.0885 

UncertCoef(m, direction="row")
#> [1] 0.0851
UncertCoef(m, direction="column")
#> [1] 0.0753