`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.

- formula
a formula with a single left side variable

- statinfo
see

`spearman2.formula`

or`chiSquare`

code- data, subset, na.action
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.- exclude.imputed
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`

.- na.rm
logical; delete NA values?

- x
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.

- y
a numeric vector

- p
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.- minlev
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.- what
specifies which statistic to plot. Possibilities include the column names that appear with the print method is used.

- sort.
set

`sort.=FALSE`

to suppress sorting variables by the statistic being plotted- main
main title for plot. Default title shows the name of the response variable.

- xlab
x-axis label. Default constructed from

`what`

.- vnames
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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