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))