R: Determines if contrasts are estimable.

is-estimable {doBy} | R Documentation

## Determines if contrasts are estimable.

### Description

Determines if contrasts are estimable, that is, if the contrasts can be written as a linear function of the data.

### Usage

    is_estimable(K, null.basis)

### Arguments

`K` | A matrix.
`null.basis` | A basis for a null space (can be found with `null_basis()`).

### Details

Consider the setting E(Y)=Xb. A linear function of b, say l'b is estimable if and only if there exists an r such that r'X=l' or equivalently l=X'r. Hence l must be in the column space of X', i.e. in the orthogonal complement of the null space of X. Hence, with a basis B for the null space, `is_estimable()` checks if each row l of the matrix K is perpendicular to each column basis vector in B.

### Value

A logical vector.

### Author(s)

Søren Højsgaard, sorenh@math.aau.dk

### References

http://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf

### See Also

`null_basis`

### Examples

    ## TO BE WRITTEN

[Package doBy version 4.6.5 Index]