doBy (version 4.6.20)

is-estimable: 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)

Value

A logical vector.

Arguments

K

A matrix.

null.basis

A basis for a null space (can be found with null_basis()).

Author

Søren Højsgaard,

Details

Consider the setting $E(Y)=Xb$. A linear function of $b$, say $l^{\prime }b$ is estimable if and only if there exists an $r$ such that $r^{\prime }X=l^{\prime }$ or equivalently $l=X^{\prime }r$. Hence $l$ must be in the column space of $X^{\prime }$, 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 $B$.

References

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

See Also

null_basis

Examples

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