Extraction of the Expectation, Variance and Covariance of the Linear Statistic
Methods for extraction of the expectation, variance and covariance of the linear statistic.
## S4 method for signature 'IndependenceLinearStatistic' expectation(object, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' expectation(object, partial = FALSE, ...) ## S4 method for signature 'Variance' variance(object, ...) ## S4 method for signature 'CovarianceMatrix' variance(object, ...) ## S4 method for signature 'IndependenceLinearStatistic' variance(object, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' variance(object, partial = FALSE, ...) ## S4 method for signature 'CovarianceMatrix' covariance(object, ...) ## S4 method for signature 'IndependenceLinearStatistic' covariance(object, invert = FALSE, partial = FALSE, ...) ## S4 method for signature 'QuadTypeIndependenceTestStatistic' covariance(object, invert = FALSE, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' covariance(object, invert = FALSE, partial = FALSE, ...)
object |
an object from which the expectation, variance or covariance of the linear statistic can be extracted. |
partial |
a logical indicating that the partial result for each block should be
extracted. Defaults to |
invert |
a logical indicating that the Moore-Penrose inverse of the covariance should
be extracted. Defaults to |
... |
further arguments (currently ignored). |
The methods expectation, variance and 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 partial = TRUE.
The expectation, variance or covariance of the linear statistic extracted from
object. A matrix or array.
## 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")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.