biVar is a generic function that accepts a formula and usual
data, subset, and na.action parameters plus a
list statinfo that specifies a function of two variables to
compute along with information about labeling results for printing and
plotting. The function is called separately with each right hand side
variable and the same left hand variable. The result is a matrix of
bivariate statistics and the statinfo list that drives printing
and plotting. The plot method draws a dot plot with x-axis values by
default sorted in order of one of the statistics computed by the function.
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.
biVar is used to do the looping and bookkeeping. By default the
plot shows the adjusted rho^2, using the same formula used for
the ordinary adjusted R^2. The F test uses the unadjusted
R2.
spearman computes Spearman's rho on non-missing values of two
variables. spearman.test is a simple version of
spearman2.default.
chiSquare is set up like spearman2 except it is intended
for a categorical response variable. Separate Pearson chi-square tests
are done for each predictor, with optional collapsing of infrequent
categories. Numeric predictors having more than g levels are
categorized into g quantile groups. chiSquare uses
biVar.
biVar(formula, statinfo, data=NULL, subset=NULL,
na.action=na.retain, exclude.imputed=TRUE, ...)# S3 method for biVar
print(x, ...)
# S3 method for biVar
plot(x, what=info$defaultwhat,
sort.=TRUE, main, xlab,
vnames=c('names','labels'), ...)
spearman2(x, ...)
# S3 method for default
spearman2(x, y, p=1, minlev=0, na.rm=TRUE, exclude.imputed=na.rm, ...)
# S3 method for formula
spearman2(formula, data=NULL,
subset, na.action=na.retain, exclude.imputed=TRUE, ...)
spearman(x, y)
spearman.test(x, y, p=1)
chiSquare(formula, data=NULL, subset=NULL, na.action=na.retain,
exclude.imputed=TRUE, ...)
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.
biVar, spearman2.formula, and chiSquare return a
matrix with rows corresponding to predictors.
a formula with a single left side variable
see spearman2.formula or chiSquare code
the usual options for models. Default for na.action is to retain
all values, NA or not, so that NAs can be deleted in only a pairwise
fashion.
set to FALSE to include imputed values (created by
impute) in the calculations.
other arguments that are passed to the function used to
compute the bivariate statistics or to dotchart3 for
plot.
logical; delete NA values?
a numeric matrix with at least 5 rows and at least 2 columns (if
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 or plot, x
is an object produced by biVar. For spearman and
spearman.test x is a numeric vector, as is y. For
chiSquare, x is a formula.
a numeric vector
for numeric variables, specifies the order of the Spearman 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.
minimum relative frequency that a level of a categorical predictor
should have before it is pooled with other categories (see
combine.levels) in spearman2 and chiSquare (in
which case it also applies to the response). The default,
minlev=0 causes no pooling.
specifies which statistic to plot. Possibilities include the column names that appear with the print method is used.
set sort.=FALSE to suppress sorting variables by the
statistic being plotted
main title for plot. Default title shows the name of the response variable.
x-axis label. Default constructed from what.
set to "labels" to use variable labels in place of names for
plotting. If a variable does not have a label the name is always
used.
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
Uses midranks in case of ties, as described by Hollander and Wolfe.
P-values for Spearman, Wilcoxon, or Kruskal-Wallis tests are
approximated by using the t or F distributions.
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.
combine.levels,
varclus, dotchart3, impute,
chisq.test, cut2.
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)
spearman2(x, y)
plot(spearman2(z ~ x + y + v, p=2))
f <- chiSquare(z ~ x + y + v)
f
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