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coin (version 1.0-24)

IndependenceTest: 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, \dots)
## 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
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
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 exactly or can be approximated by its asymptotic distribution (asymptotic) or via Monte-Carlo resampling (approximate). Alternativ
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.

Value

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).

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

Run this code
### 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:
  browseURL(system.file("documentation", "html", "index.html", 
                            package = "coin"))

Run the code above in your browser using DataLab