R: General Independence Tests

IndependenceTest {coin}

R Documentation

General Independence Tests

Description

The independence between two sets of variables of arbitrary measurement scales, possibly stratified in blocks, is tested conditional on the data.

Usage

## S3 method for class 'formula'
independence_test(formula, data, subset = NULL, 
    weights = NULL, ...)
## S3 method for class 'IndependenceProblem'
independence_test(object, 
    teststat = c("max", "quad", "scalar"),
    distribution = c("asymptotic", "approximate", "exact"),
    alternative = c("two.sided", "less", "greater"),
    xtrafo = trafo, ytrafo = trafo, scores = NULL, 
    check = NULL, ...)
## S3 method for class 'table'
independence_test(object, 
    distribution = c("asymptotic", "approximate"), ...)

Arguments

`formula`	a formula of the form `y1 + ... + yp ~ x1 + ... + xq \| block` where the variables on the left and right hand side may be measured on arbitrary scales (including censored ones on the left hand side) and `block` is an optional factor for stratification.
`data`	an optional data frame containing the variables in the model formula. Alternatively, an object of class `class.ExpressionSet` may be specified. In this case, all variables in `formula`, except `.`, are first evaluated in the `pData` data frame. The dot (`.`) refers to the matrix of expression levels (`exprs` slot).
`subset`	an optional vector specifying a subset of observations to be used.
`weights`	an optional formula of the form `~ w` defining integer valued weights for the observations.
`object`	an object inheriting from class `IndependenceProblem` or an object of class `table`.
`teststat`	a character, the type of test statistic to be applied: either a standardized scalar test statistic (`scalar`), or a maximum type statistic (`max`) or a quadratic form (`quad`).
`alternative`	a character, the alternative hypothesis must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`distribution`	a character, the null distribution of the test statistic can be computed `exact`ly or can be approximated by its asymptotic distribution (`asymptotic`) or via Monte-Carlo resampling (`approximate`). Alternatively, the functions `exact`, `approximate` or `asymptotic` can be used to specify how the exact conditional distribution of the test statistic should be calculated or approximated. It is also possible to specify a function with one argument (taking objects inheriting from `IndependenceTestStatistic`) which return an object of class `NullDistribution`.
`xtrafo`	a function of transformations (see `trafo`) to be applied to the variables on the right hand side of `formula`, see below.
`ytrafo`	a function of transformations (see `trafo`) to be applied to the variables on the left hand side of `formula`, see below.
`scores`	a named list of scores to be attached to ordered factors. In case a variable is an unordered factor, it is coerced to `ordered` first.
`check`	a function to be applied to objects of class `IndendenceTest` in order to check for specific properties of the data.
`...`	further arguments to be passed to or from methods. Currently, none of the additional arguments is passed to any function.

Details

The null hypothesis of the independence between the variables on the left hand side and the variables on the right hand side of formula, possibly stratified by block, is tested. The vector supplied via the weights argument is interpreted as observation counts.

This function is the basic workhorse called by all other convenience functions, mainly by supplying transformations via the xtrafo argument and influence functions via the ytrafo argument.

The scores argument leads to linear-by-linear association tests against ordered alternatives. If the formula y ~ x was supplied and both y and x are factors, scores = list(y = 1:k, x = c(1, 4, 6)) first triggers a coercion to class ordered of both variables and attaches the list elements as scores. The length of a score vector needs to be equal the number of levels of the factor of interest.

The basis of this function is the framework for conditional inference procedures by Strasser & Weber (1999). The theory and this implementation are explained and illustrated in Hothorn, Hornik, van de Wiel and Zeileis (2006).

Value

An object inheriting from class IndependenceTest-class with methods show, statistic, expectation, covariance and pvalue. The null distribution can be inspected by pperm, dperm, qperm and support methods.

References

Helmut Strasser \& Christian Weber (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics 8, 220–250.

Torsten Hothorn, Kurt Hornik, Mark A. van de Wiel \& Achim Zeileis (2006). A Lego System for Conditional Inference. The American Statistician, 60(3), 257–263.

Torsten Hothorn, Kurt Hornik, Mark A. van de Wiel \& Achim Zeileis (2008). Implementing a class of permutation tests: The coin package, Journal of Statistical Software, 28(8), 1–23. http://www.jstatsoft.org/v28/i08/

Examples


  ### independence of asat and group via normal scores test
  independence_test(asat ~ group, data = asat,

    ### exact null distribution
    distribution = "exact", 

    ### one-sided test
    alternative = "greater",

    ### apply normal scores to asat$asat
    ytrafo = function(data) trafo(data, numeric_trafo = normal_trafo),

    ### indicator matrix of 1st level of group
    xtrafo = function(data) trafo(data, factor_trafo = function(x)
        matrix(x == levels(x)[1], ncol = 1))
  )

  ### same as
  normal_test(asat ~ group, data = asat, distribution = "exact", 
              alternative = "greater")


  ### if you are interested in the internals:
  ## Not run: 
      browseURL(system.file("documentation", "html", "index.html", 
                            package = "coin"))
  
## End(Not run)

[Package coin version 1.0-20 Index]