https://github.com/cran/coin
Tip revision: 4f813a5f635d62178763b975c32f68fce30097c5 authored by Torsten Hothorn on 27 September 2023, 16:10:02 UTC
version 1.4-3
version 1.4-3
Tip revision: 4f813a5
expectation-methods.Rd
\name{expectation-methods}
\docType{methods}
\alias{expectation}
\alias{expectation-methods}
\alias{expectation,IndependenceLinearStatistic-method}
\alias{expectation,IndependenceTest-method}
\alias{variance}
\alias{variance-methods}
\alias{variance,Variance-method}
\alias{variance,CovarianceMatrix-method}
\alias{variance,IndependenceLinearStatistic-method}
\alias{variance,IndependenceTest-method}
\alias{covariance}
\alias{covariance-methods}
\alias{covariance,CovarianceMatrix-method}
\alias{covariance,IndependenceLinearStatistic-method}
\alias{covariance,QuadTypeIndependenceTestStatistic-method}
\alias{covariance,IndependenceTest-method}
\title{Extraction of the Expectation, Variance and Covariance of the Linear
Statistic}
\description{
Methods for extraction of the expectation, variance and covariance of the
linear statistic.
}
\usage{
\S4method{expectation}{IndependenceLinearStatistic}(object, partial = FALSE, ...)
\S4method{expectation}{IndependenceTest}(object, partial = FALSE, ...)
\S4method{variance}{Variance}(object, ...)
\S4method{variance}{CovarianceMatrix}(object, ...)
\S4method{variance}{IndependenceLinearStatistic}(object, partial = FALSE, ...)
\S4method{variance}{IndependenceTest}(object, partial = FALSE, ...)
\S4method{covariance}{CovarianceMatrix}(object, ...)
\S4method{covariance}{IndependenceLinearStatistic}(object, invert = FALSE, partial = FALSE, ...)
\S4method{covariance}{QuadTypeIndependenceTestStatistic}(object, invert = FALSE, partial = FALSE, ...)
\S4method{covariance}{IndependenceTest}(object, invert = FALSE, partial = FALSE, ...)
}
\arguments{
\item{object}{
an object from which the expectation, variance or covariance of the linear
statistic can be extracted.
}
\item{partial}{
a logical indicating that the partial result for each block should be
extracted. Defaults to \code{FALSE}.
}
\item{invert}{
a logical indicating that the Moore-Penrose inverse of the covariance should
be extracted. Defaults to \code{FALSE}.
}
\item{...}{
further arguments (currently ignored).
}
}
\details{
The methods \code{expectation}, \code{variance} and \code{covariance} extract
the expectation, variance and covariance, respectively, of the linear
statistic.
For tests of conditional independence within blocks, the partial result for
each block is obtained by setting \code{partial = TRUE}.
}
\value{
The expectation, variance or covariance of the linear statistic extracted from
\code{object}. A matrix or array.
}
\examples{
## Example data
dta <- data.frame(
y = gl(3, 2),
x = sample(gl(3, 2))
)
## Asymptotic Cochran-Mantel-Haenszel Test
ct <- cmh_test(y ~ x, data = dta)
## The linear statistic, i.e., the contingency table...
(T <- statistic(ct, type = "linear"))
## ...and its expectation...
(mu <- expectation(ct))
## ...and variance...
(sigma <- variance(ct))
## ...and covariance...
(Sigma <- covariance(ct))
## ...and its inverse
(SigmaPlus <- covariance(ct, invert = TRUE))
## The standardized contingency table...
(T - mu) / sqrt(sigma)
## ...is identical to the standardized linear statistic
statistic(ct, type = "standardized")
## The quadratic form...
U <- as.vector(T - mu)
U \%*\% SigmaPlus \%*\% U
## ...is identical to the test statistic
statistic(ct, type = "test")
}
\keyword{methods}