GiniMd
Gini's Mean Difference
GiniMD
computes Gini's mean difference on a
numeric vector. This index is defined as the mean absolute difference
between any two distinct elements of a vector. For a Bernoulli
(binary) variable with proportion of ones equal to \(p\) and sample
size \(n\), Gini's mean difference is
\(2\frac{n}{n-1}p(1-p)\). For a
trinomial variable (e.g., predicted values for a 3-level categorical
predictor using two dummy variables) having (predicted)
values \(A, B, C\) with corresponding proportions \(a, b, c\),
Gini's mean difference is
\(2\frac{n}{n-1}[ab|A-B|+ac|A-C|+bc|B-C|]\)
Usage
GiniMd(x, na.rm=FALSE)
Arguments
- x
a numeric vector (for
GiniMd
)- na.rm
set to
TRUE
if you suspect there may beNA
s inx
; these will then be removed. Otherwise an error will result.
Value
a scalar numeric
References
David HA (1968): Gini's mean difference rediscovered. Biometrika 55:573--575.
Examples
# NOT RUN {
set.seed(1)
x <- rnorm(40)
# Test GiniMd against a brute-force solution
gmd <- function(x) {
n <- length(x)
sum(outer(x, x, function(a, b) abs(a - b))) / n / (n - 1)
}
GiniMd(x)
gmd(x)
z <- c(rep(0,17), rep(1,6))
n <- length(z)
GiniMd(z)
2*mean(z)*(1-mean(z))*n/(n-1)
a <- 12; b <- 13; c <- 7; n <- a + b + c
A <- -.123; B <- -.707; C <- 0.523
xx <- c(rep(A, a), rep(B, b), rep(C, c))
GiniMd(xx)
2*(a*b*abs(A-B) + a*c*abs(A-C) + b*c*abs(B-C))/n/(n-1)
# }