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D statistics for all possible
pairs of columns of a matrix. D
is a measure of the distance
between F(x,y) and G(x)H(y), where F(x,y) is the joint CDF of X and Y,
and G and H are marginal CDFs. Missing values are deleted in pairs rather than deleting all rows
of x having any missing variables.
The D statistic is robust against a wide
variety of alternatives to independence, such as non-monotonic relationships.
The larger the value of D, the more dependent are X and Y (for many types
of dependencies). D used here is 30 times Hoeffding's original D, and
ranges from -0.5 to 1.0 if there are no ties in the data.
print.HoeffD prints the information derived by HoeffD. The higher
the value of D, the more dependent are x and y.HoeffD(x, y)
## S3 method for class 'HoeffD':
print(x, \dots)y is absent), or an object created by HoeffDxD, the
matrix of D statistics, n the
matrix of number of observations used in analyzing each pair of variables,
and P, the asymptotic P-values.
Pairs with fewer than 5 non-missing values have the D statistic set to NA.
The diagonals of n are the number of non-NAs for the single variable
corresponding to that row and column.P<.0001< code=""> or >0.5, P values are
computed using a well-fitting linear regression function in log P vs.
the test statistic.
Ranks (but not bivariate ranks) are computed using efficient
algorithms (see reference 3).rcorr, varclusx <- c(-2, -1, 0, 1, 2)
y <- c(4, 1, 0, 1, 4)
z <- c(1, 2, 3, 4, NA)
q <- c(1, 2, 3, 4, 5)
HoeffD(cbind(x, y, z, q))
# Hoeffding's test can detect even one-to-many dependency
set.seed(1)
x <- seq(-10, 10, length=200)
y <- x * sign(runif(200, -1, 1))
plot(x, y)
HoeffD(x, y)Run the code above in your browser using DataLab