expectation-methods {coin} R Documentation

## 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

```## 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, ...)
```

### Arguments

 `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 `FALSE`. `invert` a logical indicating that the Moore-Penrose inverse of the covariance should be extracted. Defaults to `FALSE`. `...` further arguments (currently ignored).

### Details

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`.

### Value

The expectation, variance or covariance of the linear statistic extracted from `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")