is_estimable function

Determines if contrasts are estimable.

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

is_estimable(K, null.basis)

Arguments

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

Returns

A logical vector.

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 $B$.

References

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

Author(s)

Søren Højsgaard, sorenh@math.aau.dk