biVar {Hmisc} | R Documentation

## Bivariate Summaries Computed Separately by a Series of Predictors

### Description

`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`.

### Usage

    biVar(formula, statinfo, data=NULL, subset=NULL,
          na.action=na.retain, exclude.imputed=TRUE, ...)

    ## S3 method for class 'biVar'
    print(x, ...)

    ## S3 method for class 'biVar'
    plot(x, what=info$defaultwhat,
                           sort.=TRUE, main, xlab,
                           vnames=c('names','labels'), ...)

    spearman2(x, ...)

    ## Default S3 method:
    spearman2(x, y, p=1, minlev=0, na.rm=TRUE, exclude.imputed=na.rm, ...)

    ## S3 method for class '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, ...)

### Arguments

`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.

### Details

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.

### Value

`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.

### Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University
f.harrell@vanderbilt.edu

### References

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.

### See Also

`combine.levels`, `varclus`, `dotchart3`, `impute`, `chisq.test`, `cut2`.

### Examples

    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

[Package Hmisc version 4.0-3 Index]