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Uncertainty Coefficient

Source: R/uncertCoef.R
uncertCoef.Rd

Computes directional or symmetric uncertainty coefficients. The directional 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 single vectors.

Usage

uncertCoef(
  x,
  y = NULL,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  direction = c("symmetric", "row", "column"),
  pZeroCorrection = 1/sum(x)^2,
  ...
)

Arguments

x

a numeric vector, factor, matrix, or data frame

y

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

conf.level

confidence level of the interval. If set to NA (the default), only the point estimate is returned.

sides

character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().

direction

direction of calculation, one of "symmetric" (default), "row", or "column". The row direction calculates U(R|C), and the column direction calculates U(C|R).

pZeroCorrection

small positive value used to replace zero cells before taking logarithms

...

further arguments are passed to the function table(), allowing, for example, useNA to be set. This refers only to the vector interface.

Value

if conf.level = NA, a numeric scalar. Otherwise a named numeric vector with elements:

est

uncertainty coefficient estimate

lci

lower confidence interval bound

uci

upper confidence interval bound

Details

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

Note

Based on code from Antti Arppe

Confidence interval

The interval is based on the asymptotic standard error (Goodman & Kruskal) and is truncated to the parameter range \([0, 1]\). For a one-sided interval (sides = "left" or "right") the open side is reported at the corresponding range limit, not at \(\pm\infty\).

References

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

See also

Association()

Other assoc.nominal: contCoef(), cramerV(), gkTau(), lambda(), mutInf(), phi(), tschuprowT(), yule

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] 0.07991026
uncertCoef(m, conf.level=0.95)
#>        est        lci        uci 
#> 0.07991026 0.07131377 0.08850675 

uncertCoef(m, direction="row")
#> [1] 0.08506956
uncertCoef(m, direction="column")
#> [1] 0.07534098