rcorr Computes a matrix of Pearson's
r or Spearman's
rho
rank correlation coefficients for all possible pairs of
columns of a matrix. Missing values are deleted in pairs rather than
deleting all rows of
x having any missing variables. Ranks are
computed using efficient algorithms (see reference 2), using midranks
for ties.
spearman2 computes the square of Spearman's rho rank correlation
and a generalization of it in which
x can relate
non-monotonically to
y. This is done by computing the Spearman
multiple rho-squared between
(rank(x), rank(x)^2) and
y.
When
x is categorical, a different kind of Spearman correlation
used in the Kruskal-Wallis test is computed (and
spearman2 can do
the Kruskal-Wallis test). This is done by computing the ordinary
multiple
R^2 between
k-1 dummy variables and
rank(y)
, where
x has
k categories.
x can
also be a formula, in which case each predictor is correlated separately
with
y, using non-missing observations for that predictor.
print
and
plot methods allow one to easily print or plot
the results of
spearman2(formula). The adjusted
rho^2 is
also computed, using the same formula used for the ordinary adjusted
R^2
. The
F test uses the unadjusted R2. For
plot,
a dot chart is drawn which by default shows, in sorted order, the
adjusted
rho^2.
spearman computes Spearman's rho on non-missing values of two
variables.
spearman.test is a simple version of
spearman2.default.
rcorr(x, y, type=c("pearson","spearman"))
## S3 method for class 'rcorr':
print(x, ...)
spearman2(x, ...)
## Default S3 method:
spearman2(x, y, p=1, minlev=0, exclude.imputed=TRUE, ...)
## S3 method for class 'formula':
spearman2(x, p=1,
data, subset, na.action, minlev=0, exclude.imputed=TRUE, ...)
## S3 method for class 'spearman2.formula':
print(x, ...)
## S3 method for class 'spearman2.formula':
plot(x, what=c('Adjusted rho2','rho2','P'),
sort.=TRUE, main, xlab, ...)
spearman(x, y)
spearman.test(x, y, p=1)
y is absent). For
spearman2, the first argument may be a vector
of any type, including character or factor. The first argument may also be a
formula, in which case all predictors are correlated individually with
the response variable.
x may be a formula for
spearman2
in which case
spearman2.formula is invoked. Each
predictor in the right hand side of the formula is separately correlated
with the response variable. For
print,
x is an object
produced by
rcorr or
spearman2. For
plot,
x
is a result returned by
spearman2. For
spearman and
spearman.test
x is a numeric vector, as is
y.
x. If
y is omitted for
rcorr,
x must be a matrix.
rho^2 to
use. The default is
p=1 to compute the ordinary
rho^2. Use
p=2
to compute the quadratic rank generalization to allow
non-monotonicity.
p is ignored for categorical predictors.
na.action is to retain
all values, NA or not, so that NAs can be deleted in only a pairwise
fashion.
combine.levels) in
spearman2. The default,
minlev=0 causes no pooling.
FALSE to include imputed values (created by
impute) in the calculations.
sort.=FALSE to suppress sorting variables by the statistic being plotted
what.
dotchart2
Uses midranks in case of ties, as described by Hollander and Wolfe.
P-values are approximated by using the
t distribution.
rcorr returns a list with elements
r, the
matrix of correlations,
n the
matrix of number of observations used in analyzing each pair of variables,
and
P, the asymptotic P-values.
Pairs with fewer than 2 non-missing values have the r values set to NA.
The diagonals of
n are the number of non-NAs for the single variable
corresponding to that row and column.
spearman2.default (the
function that is called for a single
x, i.e., when there is no
formula) returns a vector of statistics for the variable.
spearman2.formula
returns a matrix with rows corresponding to
predictors.
Frank Harrell
Department of Biostatistics
Vanderbilt University
mailto:f.harrell@vanderbilt.edu
Hollander M. and Wolfe D.A. (1973). Nonparametric Statistical Methods. New York: Wiley.
Press WH, Flannery BP, Teukolsky SA, Vetterling, WT (1988): Numerical Recipes in C. Cambridge: Cambridge University Press.
x <- c(-2, -1, 0, 1, 2) y <- c(4, 1, 0, 1, 4) z <- c(1, 2, 3, 4, NA) v <- c(1, 2, 3, 4, 5) rcorr(cbind(x,y,z,v)) spearman2(x, y) plot(spearman2(z ~ x + y + v, p=2))